K_means_clustering_Examples(test).ipynb

{
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div align=\"center\" style=\" font-size: 80%; text-align: center; margin: 0 auto\">\n",
    "<img src=\"https://raw.githubusercontent.com/Explore-AI/Pictures/master/Python-Notebook-Banners/Examples.png\"  style=\"display: block; margin-left: auto; margin-right: auto;\";/>\n",
    "</div>"
   ]
  },
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   "cell_type": "markdown",
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    "id": "k52b0R_HjaKt"
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   "source": [
    "# Examples: K-means clustering\n",
    "© ExploreAI Academy\n",
    "\n",
    "In the train, we will explore the application of K-means clustering, an unsupervised learning technique, to group data points based on similarities in their features. We'll cover theory, implementation using sklearn, and methods for determining the optimal number of clusters, providing insights into underlying patterns within datasets."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Learning Objectives\n",
    "By the end of this train, you should be able to:\n",
    "- Implement the K-means clustering algorithm\n",
    "- Implement a K-means clustering model in sklearn\n",
    "- Choose the optimal number of clusters."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction \n",
    "\n",
    "**Unsupervised learning** is an area of statistical learning that we use to infer trends to group cases based on similar attributes, naturally occurring trends, patterns, or relationships from unlabeled data. These models are often referred to as self-organising maps. A variety of methods are used as a strategy for dividing data into groups to carry out unsupervised learning, one of which is known as **clustering**. Clustering methods use data features to group observations into either distinct or overlapping sets.\n",
    "\n",
    "Let's learn more about how clustering works!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "sm6oc90_x5y-"
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   "source": [
    "## Clustering\n",
    "Clustering is the process of grouping similar data points together, such that data points in the same groups are more similar to other data points in that group than those in other groups. \n",
    "\n",
    "The aim is to divide groups with similar characteristics and assign them to clusters. This will give us insights into the underlying patterns of the different groups/clusters. In this course, we will explore three types of clustering:\n",
    "\n",
    "* **Hard Clustering**\n",
    "* **Hierarchical Clustering**\n",
    "* **Soft/Fuzzy Clustering**\n",
    "\n",
    "Explanations are given in the image below."
   ]
  },
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   "cell_type": "markdown",
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    "id": "209V9V0ox5y_"
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   "source": [
    "<img src=\"https://raw.githubusercontent.com/Explore-AI/Pictures/master/sketch-clustering-types.png?raw=true\" alt=\"Types of Clustering\" style=\"width: 80%;\"/>"
   ]
  },
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    "id": "aVk7tJ9YjaK1"
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   "source": [
    "\n",
    "## The K-means clustering algorithm\n",
    "K-means is an example of what is known as a **hard clustering** method, which means that the clusters, or groups that result, are distinct and non-overlapping. In other words, each observation will ultimately belong to only one cluster, although it may be passed around between clusters during the iterative training of the clustering model.\n",
    "\n",
    "<img src=\"https://raw.githubusercontent.com/Explore-AI/Pictures/master/sketch-kmeans-clusters.png?raw=true\" alt=\"Types of Clustering\" style=\"width: 70%\">\n",
    "\n",
    "The main objective in K-means is to partition a dataset into K clusters. This is achieved by randomly initialising K cluster centroids (points to be used as the cluster centres), assigning each data point to the nearest centroid (according to some **distance measure**), and then updating the cluster centroids as well as data point membership at each iteration until the centroids stop changing.\n",
    "\n",
    "One drawback of the K-means algorithm (and many other clustering algorithms) is that the analyst needs to specify the number of clusters, K. This is a difficult task because this number is seldom obvious for most real-world datasets. However, we do have methods available which we can use to determine the optimal number of clusters. We will cover some of these later on, but for now, let's take a look at the K-means algorithm, which, although it comes in many flavours, generally works as follows:\n",
    "\n",
    "1. Pick the number of clusters K and randomly assign each observation a cluster number from 1 to K.\n",
    "2. Repeat the following until cluster assignments stop changing:  \n",
    "    a. For each of the K clusters, compute the cluster centroid. The $k^{th}$ cluster centroid is the mean of the observations in the $k^{th}$ cluster.  \n",
    "    b. Assign each observation to the cluster whose centroid is closest (where closest is defined using a chosen distance metric such as **Euclidean distance**).\n",
    "    \n",
    "The sequence of images below illustrates the K-means algorithm as it iterates over a data set (these correspond to the algorithm above).\n",
    "\n",
    "<img src=\"https://raw.githubusercontent.com/Explore-AI/Pictures/master/clustering_algorithm.png?raw=true\" alt=\"Types of Clustering\" style=\"width: 70%\">\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## K-means in sklearn\n",
    "\n",
    "Let's cement this theory by implementing, or fitting, a K-means model to some data.  \n",
    "\n",
    "### Setting up the data\n",
    "Before we dive in, let's load in our libraries and go ahead and create some toy data to work with. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {},
    "colab_type": "code",
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   "outputs": [],
   "source": [
    "# data processing\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import datetime\n",
    "from sklearn import preprocessing\n",
    "from sklearn.datasets import make_blobs\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "# plotting\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Feature 2')"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 768x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# make 8 blobs in 2D space\n",
    "n_features = 2\n",
    "centers = 8\n",
    "\n",
    "X, y = make_blobs(n_samples=1000, centers=centers, n_features=n_features, random_state=68) #rand = 8, 42\n",
    "\n",
    "data = np.concatenate([X, y.reshape(-1, 1)], axis=1)\n",
    "df = pd.DataFrame(data, columns=[*[f'feature_{i}' for i in range(n_features)], 'y'])\n",
    "df['y'] = df['y'].astype(int)\n",
    "\n",
    "# plot data\n",
    "plt.figure(dpi=120)\n",
    "for center in range(centers):\n",
    "    x1 = df[df['y'] == center]['feature_0']\n",
    "    x2 = df[df['y'] == center]['feature_1']\n",
    "    plt.scatter(x1, x2, label=str(center))\n",
    "\n",
    "plt.legend()\n",
    "plt.title(\"Figure 1\")\n",
    "plt.xlabel('Feature 1')\n",
    "plt.ylabel('Feature 2')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Great! We've successfully created a dataset consisting of two features and a few distinct clusters (indicated by different colours in the plot shown above). These colours act as a sort of label, i.e., for any pair of features $X$, we know what the corresponding label $y$ (the colour or cluster number) is. As such, this means that we have a labelled dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>feature_0</th>\n",
       "      <th>feature_1</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-5.295432</td>\n",
       "      <td>-9.053238</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2.058577</td>\n",
       "      <td>-5.251177</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3.687847</td>\n",
       "      <td>9.551016</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-3.914157</td>\n",
       "      <td>-8.430547</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2.510445</td>\n",
       "      <td>9.198077</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   feature_0  feature_1  y\n",
       "0  -5.295432  -9.053238  0\n",
       "1   2.058577  -5.251177  2\n",
       "2   3.687847   9.551016  4\n",
       "3  -3.914157  -8.430547  0\n",
       "4   2.510445   9.198077  4"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# what does the data look like?\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, in unsupervised learning, we do not have access to these labels. As such, let's pretend we don't know the number of clusters (or their locations) and pretend that we just came across the following dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# same data with the y column dropped\n",
    "df_no_labels = df.drop('y',axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Feature 2')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 768x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(dpi=120)\n",
    "x1 = df_no_labels['feature_0']\n",
    "x2 = df_no_labels['feature_1']\n",
    "plt.scatter(x1, x2)\n",
    "plt.title(\"Figure 2\")\n",
    "plt.xlabel('Feature 1')\n",
    "plt.ylabel('Feature 2')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This leaves us with two problems to solve:\n",
    "\n",
    "1. We don't know which pair of features, $X$, belong to which cluster.\n",
    "\n",
    "2. We don't know how many clusters, $K$, there are in the dataset. \n",
    "\n",
    "\n",
    "We usually address the first problem by building a clustering machine learning model, and we address the second problem by making an educated guess of how many clusters there are. As you will notice with the K-means algorithm, many clustering algorithms require that we first select the number of clusters 𝐾 before training the machine learning model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Preprocessing the data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "fy0vRz5ZjaL1"
   },
   "source": [
    "Since clustering algorithms rely on computing some form of distance metric, it is good practice to scale the data. If we don't do this, then we risk having features that contribute way more than others when deciding which cluster a given data point belongs to. For example, let's suppose we had a dataset with two features: `age` (ranging from `18` to `60`) and `income` (ranging from `10000` to `45000`). If we attempt to cluster without rescaling or normalising, then the `income` feature will always dominate the distance calculation to the extent that our results would be the same as if we didn't have the `age` feature in our dataset. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Let's test out knowledge so far!!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div id=\"scrRJzohVShm\" data-shufflequestions=\"False\"\n",
       "               data-shuffleanswers=\"True\"\n",
       "               data-preserveresponses=\"false\"\n",
       "               data-numquestions=\"1000000\"\n",
       "               data-maxwidth=\"600\"\n",
       "               style=\"border-radius: 10px; text-align: left\"> <style>\n",
       "#scrRJzohVShm {\n",
       "   --jq-multiple-choice-bg: #6f78ffff;\n",
       "   --jq-mc-button-bg: #fafafa;\n",
       "   --jq-mc-button-border: #e0e0e0e0;\n",
       "   --jq-mc-button-inset-shadow: #555555;\n",
       "   --jq-many-choice-bg: #f75c03ff;\n",
       "   --jq-numeric-bg: #392061ff;\n",
       "   --jq-numeric-input-bg: #c0c0c0;\n",
       "   --jq-numeric-input-label: #101010;\n",
       "   --jq-numeric-input-shadow: #999999;\n",
       "   --jq-incorrect-color: #c80202;\n",
       "   --jq-correct-color: #009113;\n",
       "   --jq-text-color: #fafafa;\n",
       "}\n",
       "\n",
       ".Quiz {\n",
       "    max-width: 600px;\n",
       "    margin-top: 15px;\n",
       "    margin-left: auto;\n",
       "    margin-right: auto;\n",
       "    margin-bottom: 15px;\n",
       "    padding-bottom: 4px;\n",
       "    padding-top: 4px;\n",
       "    line-height: 1.1;\n",
       "    font-size: 16pt;\n",
       "    border-radius: inherit;\n",
       "}\n",
       "\n",
       ".QuizCode {\n",
       "    font-size: 14pt;\n",
       "    margin-top: 10px;\n",
       "    margin-left: 20px;\n",
       "    margin-right: 20px;\n",
       "}\n",
       "\n",
       ".QuizCode>pre {\n",
       "    padding: 4px;\n",
       "}\n",
       "\n",
       ".Answer {\n",
       "    margin: 10px 0;\n",
       "    display: grid;\n",
       "    grid-template-columns: 1fr 1fr;\n",
       "    grid-gap: 10px;\n",
       "    border-radius: inherit;\n",
       "}\n",
       "\n",
       ".Feedback {\n",
       "    font-size: 16pt;\n",
       "    text-align: center;\n",
       "    min-height: 2em;\n",
       "}\n",
       "\n",
       ".Input {\n",
       "    align: left;\n",
       "    font-size: 20pt;\n",
       "}\n",
       "\n",
       ".Input-text {\n",
       "    display: block;\n",
       "    margin: 10px;\n",
       "    color: inherit;\n",
       "    width: 140px;\n",
       "    background-color: var(--jq-numeric-input-bg);\n",
       "    color: var(--jq-text-color);\n",
       "    padding: 5px;\n",
       "    padding-left: 10px;\n",
       "    font-family: inherit;\n",
       "    font-size: 20px;\n",
       "    font-weight: inherit;\n",
       "    line-height: 20pt;\n",
       "    border: none;\n",
       "    border-radius: 0.2rem;\n",
       "    transition: box-shadow 0.1s);\n",
       "}\n",
       "\n",
       ".Input-text:focus {\n",
       "    outline: none;\n",
       "    background-color: var(--jq-numeric-input-bg);\n",
       "    box-shadow: 0.6rem 0.8rem 1.4rem -0.5rem var(--jq-numeric-input-shadow);\n",
       "}\n",
       "\n",
       ".MCButton {\n",
       "    background: var(--jq-mc-button-bg);\n",
       "    border: 1px solid var(--jq-mc-button-border);\n",
       "    border-radius: inherit;\n",
       "    padding: 10px;\n",
       "    font-size: 16px;\n",
       "    cursor: pointer;\n",
       "    text-align: center;\n",
       "    display: flex;\n",
       "    align-items: center;\n",
       "    justify-content: center;\n",
       "}\n",
       "\n",
       ".MCButton p {\n",
       "    color: inherit;\n",
       "}\n",
       "\n",
       ".MultipleChoiceQn {\n",
       "    padding: 10px;\n",
       "    background: var(--jq-multiple-choice-bg);\n",
       "    color: var(--jq-text-color);\n",
       "    border-radius: inherit;\n",
       "}\n",
       "\n",
       ".ManyChoiceQn {\n",
       "    padding: 10px;\n",
       "    background: var(--jq-many-choice-bg);\n",
       "    color: var(--jq-text-color);\n",
       "    border-radius: inherit;\n",
       "}\n",
       "\n",
       ".NumericQn {\n",
       "    padding: 10px;\n",
       "    background: var(--jq-numeric-bg);\n",
       "    color: var(--jq-text-color);\n",
       "    border-radius: inherit;\n",
       "}\n",
       "\n",
       ".NumericQn p {\n",
       "    color: inherit;\n",
       "}\n",
       "\n",
       ".InpLabel {\n",
       "    line-height: 34px;\n",
       "    float: left;\n",
       "    margin-right: 10px;\n",
       "    color: var(--jq-numeric-input-label);\n",
       "    font-size: 15pt;\n",
       "}\n",
       "\n",
       ".incorrect {\n",
       "    color: var(--jq-incorrect-color);\n",
       "}\n",
       "\n",
       ".correct {\n",
       "    color: var(--jq-correct-color);\n",
       "}\n",
       "\n",
       ".correctButton {\n",
       "    /*\n",
       "    background: var(--jq-correct-color);\n",
       "   */\n",
       "    animation: correct-anim 0.6s ease;\n",
       "    animation-fill-mode: forwards;\n",
       "    color: var(--jq-text-color);\n",
       "    box-shadow: inset 0px 0px 5px var(--jq-mc-button-inset-shadow);\n",
       "    outline: none;\n",
       "}\n",
       "\n",
       ".incorrectButton {\n",
       "    animation: incorrect-anim 0.8s ease;\n",
       "    animation-fill-mode: forwards;\n",
       "    color: var(--jq-text-color);\n",
       "    box-shadow: inset 0px 0px 5px var(--jq-mc-button-inset-shadow);\n",
       "    outline: none;\n",
       "}\n",
       "\n",
       "@keyframes incorrect-anim {\n",
       "    100% {\n",
       "        background-color: var(--jq-incorrect-color);\n",
       "    }\n",
       "}\n",
       "\n",
       "@keyframes correct-anim {\n",
       "    100% {\n",
       "        background-color: var(--jq-correct-color);\n",
       "    }\n",
       "}\n",
       "</style>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "var questionsscrRJzohVShm=[\n",
       "    {\n",
       "        \"question\": \"What does the inertia_ attribute of a fitted K-means model represent?\",\n",
       "        \"type\": \"multiple_choice\",\n",
       "        \"answers\": [\n",
       "            {\n",
       "                \"answer\": \"The sum of squared distances of samples to their closest cluster centre\",\n",
       "                \"correct\": true,\n",
       "                \"feedback\": \"This option is correct because inertia_ is defined as the sum of squared distances from each point to its assigned cluster centre, measuring how tightly the clusters are packed.\"\n",
       "            },\n",
       "            {\n",
       "                \"answer\": \"The number of iterations the algorithm ran before converging\",\n",
       "                \"correct\": false,\n",
       "                \"feedback\": \"Incorrect.\"\n",
       "            },\n",
       "            {\n",
       "                \"answer\": \"To maximize the number of clusters\",\n",
       "                \"correct\": false,\n",
       "                \"feedback\": \"This option is incorrect because the number of iterations is not related to inertia.\"\n",
       "            },\n",
       "            {\n",
       "                \"answer\": \"The average distance between cluster centres\",\n",
       "                \"correct\": false,\n",
       "                \"feedback\": \"This option is incorrect because the average distance between cluster centres is not the definition of inertia.\"\n",
       "            },\n",
       "            {\n",
       "                \"answer\": \"The number of clusters used in the model\",\n",
       "                \"correct\": false,\n",
       "                \"feedback\": \"This option is incorrect because the number of clusters is specified by the user, not represented by inertia.\"\n",
       "            }\n",
       "        ]\n",
       "    },\n",
       "    {\n",
       "        \"question\": \"Which of the following metrics would you use to evaluate the compactness of clusters in K-means?\",\n",
       "        \"type\": \"multiple_choice\",\n",
       "        \"answers\": [\n",
       "            {\n",
       "                \"answer\": \"Silhouette Score\",\n",
       "                \"correct\": true,\n",
       "                \"feedback\": \"This option is correct because the silhouette score measures how similar each point is to its own cluster compared to other clusters, which directly evaluates the compactness and separation of clusters.\"\n",
       "            },\n",
       "            {\n",
       "                \"answer\": \"Mean Squared Error\",\n",
       "                \"correct\": false,\n",
       "                \"feedback\": \"Mean Squared Error is typically used in regression, not clustering.\"\n",
       "            },\n",
       "            {\n",
       "                \"answer\": \"R-squared\",\n",
       "                \"correct\": false,\n",
       "                \"feedback\": \"R-squared is used in regression to measure the goodness of fit.\"\n",
       "            },\n",
       "            {\n",
       "                \"answer\": \"Precision and Recall\",\n",
       "                \"correct\": false,\n",
       "                \"feedback\": \"Precision and Recall are metrics used for classification tasks.\"\n",
       "            }\n",
       "        ]\n",
       "    }\n",
       "    \n",
       "];\n",
       "    // Make a random ID\n",
       "function makeid(length) {\n",
       "    var result = [];\n",
       "    var characters = 'ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz';\n",
       "    var charactersLength = characters.length;\n",
       "    for (var i = 0; i < length; i++) {\n",
       "        result.push(characters.charAt(Math.floor(Math.random() * charactersLength)));\n",
       "    }\n",
       "    return result.join('');\n",
       "}\n",
       "\n",
       "// Choose a random subset of an array. Can also be used to shuffle the array\n",
       "function getRandomSubarray(arr, size) {\n",
       "    var shuffled = arr.slice(0), i = arr.length, temp, index;\n",
       "    while (i--) {\n",
       "        index = Math.floor((i + 1) * Math.random());\n",
       "        temp = shuffled[index];\n",
       "        shuffled[index] = shuffled[i];\n",
       "        shuffled[i] = temp;\n",
       "    }\n",
       "    return shuffled.slice(0, size);\n",
       "}\n",
       "\n",
       "function printResponses(responsesContainer) {\n",
       "    var responses=JSON.parse(responsesContainer.dataset.responses);\n",
       "    var stringResponses='<B>IMPORTANT!</B>To preserve this answer sequence for submission, when you have finalized your answers: <ol> <li> Copy the text in this cell below \"Answer String\"</li> <li> Double click on the cell directly below the Answer String, labeled \"Replace Me\"</li> <li> Select the whole \"Replace Me\" text</li> <li> Paste in your answer string and press shift-Enter.</li><li>Save the notebook using the save icon or File->Save Notebook menu item</li></ul><br><br><br><b>Answer String:</b><br> ';\n",
       "    console.log(responses);\n",
       "    responses.forEach((response, index) => {\n",
       "        if (response) {\n",
       "            console.log(index + ': ' + response);\n",
       "            stringResponses+= index + ': ' + response +\"<BR>\";\n",
       "        }\n",
       "    });\n",
       "    responsesContainer.innerHTML=stringResponses;\n",
       "}\n",
       "function check_mc() {\n",
       "    var id = this.id.split('-')[0];\n",
       "    //var response = this.id.split('-')[1];\n",
       "    //console.log(response);\n",
       "    //console.log(\"In check_mc(), id=\"+id);\n",
       "    //console.log(event.srcElement.id)           \n",
       "    //console.log(event.srcElement.dataset.correct)   \n",
       "    //console.log(event.srcElement.dataset.feedback)\n",
       "\n",
       "    var label = event.srcElement;\n",
       "    //console.log(label, label.nodeName);\n",
       "    var depth = 0;\n",
       "    while ((label.nodeName != \"LABEL\") && (depth < 20)) {\n",
       "        label = label.parentElement;\n",
       "        console.log(depth, label);\n",
       "        depth++;\n",
       "    }\n",
       "\n",
       "\n",
       "\n",
       "    var answers = label.parentElement.children;\n",
       "\n",
       "    //console.log(answers);\n",
       "\n",
       "\n",
       "    // Split behavior based on multiple choice vs many choice:\n",
       "    var fb = document.getElementById(\"fb\" + id);\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "    if (fb.dataset.numcorrect == 1) {\n",
       "        // What follows is for the saved responses stuff\n",
       "        var outerContainer = fb.parentElement.parentElement;\n",
       "        var responsesContainer = document.getElementById(\"responses\" + outerContainer.id);\n",
       "        if (responsesContainer) {\n",
       "            //console.log(responsesContainer);\n",
       "            var response = label.firstChild.innerText;\n",
       "            if (label.querySelector(\".QuizCode\")){\n",
       "                response+= label.querySelector(\".QuizCode\").firstChild.innerText;\n",
       "            }\n",
       "            console.log(response);\n",
       "            //console.log(document.getElementById(\"quizWrap\"+id));\n",
       "            var qnum = document.getElementById(\"quizWrap\"+id).dataset.qnum;\n",
       "            console.log(\"Question \" + qnum);\n",
       "            //console.log(id, \", got numcorrect=\",fb.dataset.numcorrect);\n",
       "            var responses=JSON.parse(responsesContainer.dataset.responses);\n",
       "            console.log(responses);\n",
       "            responses[qnum]= response;\n",
       "            responsesContainer.setAttribute('data-responses', JSON.stringify(responses));\n",
       "            printResponses(responsesContainer);\n",
       "        }\n",
       "        // End code to preserve responses\n",
       "        \n",
       "        for (var i = 0; i < answers.length; i++) {\n",
       "            var child = answers[i];\n",
       "            //console.log(child);\n",
       "            child.className = \"MCButton\";\n",
       "        }\n",
       "\n",
       "\n",
       "\n",
       "        if (label.dataset.correct == \"true\") {\n",
       "            // console.log(\"Correct action\");\n",
       "            if (\"feedback\" in label.dataset) {\n",
       "                fb.textContent = jaxify(label.dataset.feedback);\n",
       "            } else {\n",
       "                fb.textContent = \"Correct!\";\n",
       "            }\n",
       "            label.classList.add(\"correctButton\");\n",
       "\n",
       "            fb.className = \"Feedback\";\n",
       "            fb.classList.add(\"correct\");\n",
       "\n",
       "        } else {\n",
       "            if (\"feedback\" in label.dataset) {\n",
       "                fb.textContent = jaxify(label.dataset.feedback);\n",
       "            } else {\n",
       "                fb.textContent = \"Incorrect -- try again.\";\n",
       "            }\n",
       "            //console.log(\"Error action\");\n",
       "            label.classList.add(\"incorrectButton\");\n",
       "            fb.className = \"Feedback\";\n",
       "            fb.classList.add(\"incorrect\");\n",
       "        }\n",
       "    }\n",
       "    else {\n",
       "        var reset = false;\n",
       "        var feedback;\n",
       "         if (label.dataset.correct == \"true\") {\n",
       "            if (\"feedback\" in label.dataset) {\n",
       "                feedback = jaxify(label.dataset.feedback);\n",
       "            } else {\n",
       "                feedback = \"Correct!\";\n",
       "            }\n",
       "            if (label.dataset.answered <= 0) {\n",
       "                if (fb.dataset.answeredcorrect < 0) {\n",
       "                    fb.dataset.answeredcorrect = 1;\n",
       "                    reset = true;\n",
       "                } else {\n",
       "                    fb.dataset.answeredcorrect++;\n",
       "                }\n",
       "                if (reset) {\n",
       "                    for (var i = 0; i < answers.length; i++) {\n",
       "                        var child = answers[i];\n",
       "                        child.className = \"MCButton\";\n",
       "                        child.dataset.answered = 0;\n",
       "                    }\n",
       "                }\n",
       "                label.classList.add(\"correctButton\");\n",
       "                label.dataset.answered = 1;\n",
       "                fb.className = \"Feedback\";\n",
       "                fb.classList.add(\"correct\");\n",
       "\n",
       "            }\n",
       "        } else {\n",
       "            if (\"feedback\" in label.dataset) {\n",
       "                feedback = jaxify(label.dataset.feedback);\n",
       "            } else {\n",
       "                feedback = \"Incorrect -- try again.\";\n",
       "            }\n",
       "            if (fb.dataset.answeredcorrect > 0) {\n",
       "                fb.dataset.answeredcorrect = -1;\n",
       "                reset = true;\n",
       "            } else {\n",
       "                fb.dataset.answeredcorrect--;\n",
       "            }\n",
       "\n",
       "            if (reset) {\n",
       "                for (var i = 0; i < answers.length; i++) {\n",
       "                    var child = answers[i];\n",
       "                    child.className = \"MCButton\";\n",
       "                    child.dataset.answered = 0;\n",
       "                }\n",
       "            }\n",
       "            label.classList.add(\"incorrectButton\");\n",
       "            fb.className = \"Feedback\";\n",
       "            fb.classList.add(\"incorrect\");\n",
       "        }\n",
       "        // What follows is for the saved responses stuff\n",
       "        var outerContainer = fb.parentElement.parentElement;\n",
       "        var responsesContainer = document.getElementById(\"responses\" + outerContainer.id);\n",
       "        if (responsesContainer) {\n",
       "            //console.log(responsesContainer);\n",
       "            var response = label.firstChild.innerText;\n",
       "            if (label.querySelector(\".QuizCode\")){\n",
       "                response+= label.querySelector(\".QuizCode\").firstChild.innerText;\n",
       "            }\n",
       "            console.log(response);\n",
       "            //console.log(document.getElementById(\"quizWrap\"+id));\n",
       "            var qnum = document.getElementById(\"quizWrap\"+id).dataset.qnum;\n",
       "            console.log(\"Question \" + qnum);\n",
       "            //console.log(id, \", got numcorrect=\",fb.dataset.numcorrect);\n",
       "            var responses=JSON.parse(responsesContainer.dataset.responses);\n",
       "            if (label.dataset.correct == \"true\") {\n",
       "                if (typeof(responses[qnum]) == \"object\"){\n",
       "                    if (!responses[qnum].includes(response))\n",
       "                        responses[qnum].push(response);\n",
       "                } else{\n",
       "                    responses[qnum]= [ response ];\n",
       "                }\n",
       "            } else {\n",
       "                responses[qnum]= response;\n",
       "            }\n",
       "            console.log(responses);\n",
       "            responsesContainer.setAttribute('data-responses', JSON.stringify(responses));\n",
       "            printResponses(responsesContainer);\n",
       "        }\n",
       "        // End save responses stuff\n",
       "\n",
       "\n",
       "\n",
       "        var numcorrect = fb.dataset.numcorrect;\n",
       "        var answeredcorrect = fb.dataset.answeredcorrect;\n",
       "        if (answeredcorrect >= 0) {\n",
       "            fb.textContent = feedback + \" [\" + answeredcorrect + \"/\" + numcorrect + \"]\";\n",
       "        } else {\n",
       "            fb.textContent = feedback + \" [\" + 0 + \"/\" + numcorrect + \"]\";\n",
       "        }\n",
       "\n",
       "\n",
       "    }\n",
       "\n",
       "    if (typeof MathJax != 'undefined') {\n",
       "        var version = MathJax.version;\n",
       "        console.log('MathJax version', version);\n",
       "        if (version[0] == \"2\") {\n",
       "            MathJax.Hub.Queue([\"Typeset\", MathJax.Hub]);\n",
       "        } else if (version[0] == \"3\") {\n",
       "            MathJax.typeset([fb]);\n",
       "        }\n",
       "    } else {\n",
       "        console.log('MathJax not detected');\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "function make_mc(qa, shuffle_answers, outerqDiv, qDiv, aDiv, id) {\n",
       "    var shuffled;\n",
       "    if (shuffle_answers == \"True\") {\n",
       "        //console.log(shuffle_answers+\" read as true\");\n",
       "        shuffled = getRandomSubarray(qa.answers, qa.answers.length);\n",
       "    } else {\n",
       "        //console.log(shuffle_answers+\" read as false\");\n",
       "        shuffled = qa.answers;\n",
       "    }\n",
       "\n",
       "\n",
       "    var num_correct = 0;\n",
       "\n",
       "\n",
       "\n",
       "    shuffled.forEach((item, index, ans_array) => {\n",
       "        //console.log(answer);\n",
       "\n",
       "        // Make input element\n",
       "        var inp = document.createElement(\"input\");\n",
       "        inp.type = \"radio\";\n",
       "        inp.id = \"quizo\" + id + index;\n",
       "        inp.style = \"display:none;\";\n",
       "        aDiv.append(inp);\n",
       "\n",
       "        //Make label for input element\n",
       "        var lab = document.createElement(\"label\");\n",
       "        lab.className = \"MCButton\";\n",
       "        lab.id = id + '-' + index;\n",
       "        lab.onclick = check_mc;\n",
       "        var aSpan = document.createElement('span');\n",
       "        aSpan.classsName = \"\";\n",
       "        //qDiv.id=\"quizQn\"+id+index;\n",
       "        if (\"answer\" in item) {\n",
       "            aSpan.innerHTML = jaxify(item.answer);\n",
       "            //aSpan.innerHTML=item.answer;\n",
       "        }\n",
       "        lab.append(aSpan);\n",
       "\n",
       "        // Create div for code inside question\n",
       "        var codeSpan;\n",
       "        if (\"code\" in item) {\n",
       "            codeSpan = document.createElement('span');\n",
       "            codeSpan.id = \"code\" + id + index;\n",
       "            codeSpan.className = \"QuizCode\";\n",
       "            var codePre = document.createElement('pre');\n",
       "            codeSpan.append(codePre);\n",
       "            var codeCode = document.createElement('code');\n",
       "            codePre.append(codeCode);\n",
       "            codeCode.innerHTML = item.code;\n",
       "            lab.append(codeSpan);\n",
       "            //console.log(codeSpan);\n",
       "        }\n",
       "\n",
       "        //lab.textContent=item.answer;\n",
       "\n",
       "        // Set the data attributes for the answer\n",
       "        lab.setAttribute('data-correct', item.correct);\n",
       "        if (item.correct) {\n",
       "            num_correct++;\n",
       "        }\n",
       "        if (\"feedback\" in item) {\n",
       "            lab.setAttribute('data-feedback', item.feedback);\n",
       "        }\n",
       "        lab.setAttribute('data-answered', 0);\n",
       "\n",
       "        aDiv.append(lab);\n",
       "\n",
       "    });\n",
       "\n",
       "    if (num_correct > 1) {\n",
       "        outerqDiv.className = \"ManyChoiceQn\";\n",
       "    } else {\n",
       "        outerqDiv.className = \"MultipleChoiceQn\";\n",
       "    }\n",
       "\n",
       "    return num_correct;\n",
       "\n",
       "}\n",
       "function check_numeric(ths, event) {\n",
       "\n",
       "    if (event.keyCode === 13) {\n",
       "        ths.blur();\n",
       "\n",
       "        var id = ths.id.split('-')[0];\n",
       "\n",
       "        var submission = ths.value;\n",
       "        if (submission.indexOf('/') != -1) {\n",
       "            var sub_parts = submission.split('/');\n",
       "            //console.log(sub_parts);\n",
       "            submission = sub_parts[0] / sub_parts[1];\n",
       "        }\n",
       "        //console.log(\"Reader entered\", submission);\n",
       "\n",
       "        if (\"precision\" in ths.dataset) {\n",
       "            var precision = ths.dataset.precision;\n",
       "            // console.log(\"1:\", submission)\n",
       "            submission = Math.round((1 * submission + Number.EPSILON) * 10 ** precision) / 10 ** precision;\n",
       "            // console.log(\"Rounded to \", submission, \" precision=\", precision  );\n",
       "        }\n",
       "\n",
       "\n",
       "        //console.log(\"In check_numeric(), id=\"+id);\n",
       "        //console.log(event.srcElement.id)           \n",
       "        //console.log(event.srcElement.dataset.feedback)\n",
       "\n",
       "        var fb = document.getElementById(\"fb\" + id);\n",
       "        fb.style.display = \"none\";\n",
       "        fb.textContent = \"Incorrect -- try again.\";\n",
       "\n",
       "        var answers = JSON.parse(ths.dataset.answers);\n",
       "        //console.log(answers);\n",
       "\n",
       "        var defaultFB = \"\";\n",
       "        var correct;\n",
       "        var done = false;\n",
       "        answers.every(answer => {\n",
       "            //console.log(answer.type);\n",
       "\n",
       "            correct = false;\n",
       "            // if (answer.type==\"value\"){\n",
       "            if ('value' in answer) {\n",
       "                if (submission == answer.value) {\n",
       "                    if (\"feedback\" in answer) {\n",
       "                        fb.textContent = jaxify(answer.feedback);\n",
       "                    } else {\n",
       "                        fb.textContent = jaxify(\"Correct\");\n",
       "                    }\n",
       "                    correct = answer.correct;\n",
       "                    //console.log(answer.correct);\n",
       "                    done = true;\n",
       "                }\n",
       "                // } else if (answer.type==\"range\") {\n",
       "            } else if ('range' in answer) {\n",
       "                //console.log(answer.range);\n",
       "                if ((submission >= answer.range[0]) && (submission < answer.range[1])) {\n",
       "                    fb.textContent = jaxify(answer.feedback);\n",
       "                    correct = answer.correct;\n",
       "                    //console.log(answer.correct);\n",
       "                    done = true;\n",
       "                }\n",
       "            } else if (answer.type == \"default\") {\n",
       "                defaultFB = answer.feedback;\n",
       "            }\n",
       "            if (done) {\n",
       "                return false; // Break out of loop if this has been marked correct\n",
       "            } else {\n",
       "                return true; // Keep looking for case that includes this as a correct answer\n",
       "            }\n",
       "        });\n",
       "\n",
       "        if ((!done) && (defaultFB != \"\")) {\n",
       "            fb.innerHTML = jaxify(defaultFB);\n",
       "            //console.log(\"Default feedback\", defaultFB);\n",
       "        }\n",
       "\n",
       "        fb.style.display = \"block\";\n",
       "        if (correct) {\n",
       "            ths.className = \"Input-text\";\n",
       "            ths.classList.add(\"correctButton\");\n",
       "            fb.className = \"Feedback\";\n",
       "            fb.classList.add(\"correct\");\n",
       "        } else {\n",
       "            ths.className = \"Input-text\";\n",
       "            ths.classList.add(\"incorrectButton\");\n",
       "            fb.className = \"Feedback\";\n",
       "            fb.classList.add(\"incorrect\");\n",
       "        }\n",
       "\n",
       "        // What follows is for the saved responses stuff\n",
       "        var outerContainer = fb.parentElement.parentElement;\n",
       "        var responsesContainer = document.getElementById(\"responses\" + outerContainer.id);\n",
       "        if (responsesContainer) {\n",
       "            console.log(submission);\n",
       "            var qnum = document.getElementById(\"quizWrap\"+id).dataset.qnum;\n",
       "            //console.log(\"Question \" + qnum);\n",
       "            //console.log(id, \", got numcorrect=\",fb.dataset.numcorrect);\n",
       "            var responses=JSON.parse(responsesContainer.dataset.responses);\n",
       "            console.log(responses);\n",
       "            if (submission == ths.value){\n",
       "                responses[qnum]= submission;\n",
       "            } else {\n",
       "                responses[qnum]= ths.value + \"(\" + submission +\")\";\n",
       "            }\n",
       "            responsesContainer.setAttribute('data-responses', JSON.stringify(responses));\n",
       "            printResponses(responsesContainer);\n",
       "        }\n",
       "        // End code to preserve responses\n",
       "\n",
       "        if (typeof MathJax != 'undefined') {\n",
       "            var version = MathJax.version;\n",
       "            console.log('MathJax version', version);\n",
       "            if (version[0] == \"2\") {\n",
       "                MathJax.Hub.Queue([\"Typeset\", MathJax.Hub]);\n",
       "            } else if (version[0] == \"3\") {\n",
       "                MathJax.typeset([fb]);\n",
       "            }\n",
       "        } else {\n",
       "            console.log('MathJax not detected');\n",
       "        }\n",
       "        return false;\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "function isValid(el, charC) {\n",
       "    //console.log(\"Input char: \", charC);\n",
       "    if (charC == 46) {\n",
       "        if (el.value.indexOf('.') === -1) {\n",
       "            return true;\n",
       "        } else if (el.value.indexOf('/') != -1) {\n",
       "            var parts = el.value.split('/');\n",
       "            if (parts[1].indexOf('.') === -1) {\n",
       "                return true;\n",
       "            }\n",
       "        }\n",
       "        else {\n",
       "            return false;\n",
       "        }\n",
       "    } else if (charC == 47) {\n",
       "        if (el.value.indexOf('/') === -1) {\n",
       "            if ((el.value != \"\") && (el.value != \".\")) {\n",
       "                return true;\n",
       "            } else {\n",
       "                return false;\n",
       "            }\n",
       "        } else {\n",
       "            return false;\n",
       "        }\n",
       "    } else if (charC == 45) {\n",
       "        var edex = el.value.indexOf('e');\n",
       "        if (edex == -1) {\n",
       "            edex = el.value.indexOf('E');\n",
       "        }\n",
       "\n",
       "        if (el.value == \"\") {\n",
       "            return true;\n",
       "        } else if (edex == (el.value.length - 1)) { // If just after e or E\n",
       "            return true;\n",
       "        } else {\n",
       "            return false;\n",
       "        }\n",
       "    } else if (charC == 101) { // \"e\"\n",
       "        if ((el.value.indexOf('e') === -1) && (el.value.indexOf('E') === -1) && (el.value.indexOf('/') == -1)) {\n",
       "            // Prev symbol must be digit or decimal point:\n",
       "            if (el.value.slice(-1).search(/\\d/) >= 0) {\n",
       "                return true;\n",
       "            } else if (el.value.slice(-1).search(/\\./) >= 0) {\n",
       "                return true;\n",
       "            } else {\n",
       "                return false;\n",
       "            }\n",
       "        } else {\n",
       "            return false;\n",
       "        }\n",
       "    } else {\n",
       "        if (charC > 31 && (charC < 48 || charC > 57))\n",
       "            return false;\n",
       "    }\n",
       "    return true;\n",
       "}\n",
       "\n",
       "function numeric_keypress(evnt) {\n",
       "    var charC = (evnt.which) ? evnt.which : evnt.keyCode;\n",
       "\n",
       "    if (charC == 13) {\n",
       "        check_numeric(this, evnt);\n",
       "    } else {\n",
       "        return isValid(this, charC);\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "function make_numeric(qa, outerqDiv, qDiv, aDiv, id) {\n",
       "\n",
       "\n",
       "\n",
       "    //console.log(answer);\n",
       "\n",
       "\n",
       "    outerqDiv.className = \"NumericQn\";\n",
       "    aDiv.style.display = 'block';\n",
       "\n",
       "    var lab = document.createElement(\"label\");\n",
       "    lab.className = \"InpLabel\";\n",
       "    lab.textContent = \"Type numeric answer here:\";\n",
       "    aDiv.append(lab);\n",
       "\n",
       "    var inp = document.createElement(\"input\");\n",
       "    inp.type = \"text\";\n",
       "    //inp.id=\"input-\"+id;\n",
       "    inp.id = id + \"-0\";\n",
       "    inp.className = \"Input-text\";\n",
       "    inp.setAttribute('data-answers', JSON.stringify(qa.answers));\n",
       "    if (\"precision\" in qa) {\n",
       "        inp.setAttribute('data-precision', qa.precision);\n",
       "    }\n",
       "    aDiv.append(inp);\n",
       "    //console.log(inp);\n",
       "\n",
       "    //inp.addEventListener(\"keypress\", check_numeric);\n",
       "    //inp.addEventListener(\"keypress\", numeric_keypress);\n",
       "    /*\n",
       "    inp.addEventListener(\"keypress\", function(event) {\n",
       "        return numeric_keypress(this, event);\n",
       "    }\n",
       "                        );\n",
       "                        */\n",
       "    //inp.onkeypress=\"return numeric_keypress(this, event)\";\n",
       "    inp.onkeypress = numeric_keypress;\n",
       "    inp.onpaste = event => false;\n",
       "\n",
       "    inp.addEventListener(\"focus\", function (event) {\n",
       "        this.value = \"\";\n",
       "        return false;\n",
       "    }\n",
       "    );\n",
       "\n",
       "\n",
       "}\n",
       "function jaxify(string) {\n",
       "    var mystring = string;\n",
       "\n",
       "    var count = 0;\n",
       "    var loc = mystring.search(/([^\\\\]|^)(\\$)/);\n",
       "\n",
       "    var count2 = 0;\n",
       "    var loc2 = mystring.search(/([^\\\\]|^)(\\$\\$)/);\n",
       "\n",
       "    //console.log(loc);\n",
       "\n",
       "    while ((loc >= 0) || (loc2 >= 0)) {\n",
       "\n",
       "        /* Have to replace all the double $$ first with current implementation */\n",
       "        if (loc2 >= 0) {\n",
       "            if (count2 % 2 == 0) {\n",
       "                mystring = mystring.replace(/([^\\\\]|^)(\\$\\$)/, \"$1\\\\[\");\n",
       "            } else {\n",
       "                mystring = mystring.replace(/([^\\\\]|^)(\\$\\$)/, \"$1\\\\]\");\n",
       "            }\n",
       "            count2++;\n",
       "        } else {\n",
       "            if (count % 2 == 0) {\n",
       "                mystring = mystring.replace(/([^\\\\]|^)(\\$)/, \"$1\\\\(\");\n",
       "            } else {\n",
       "                mystring = mystring.replace(/([^\\\\]|^)(\\$)/, \"$1\\\\)\");\n",
       "            }\n",
       "            count++;\n",
       "        }\n",
       "        loc = mystring.search(/([^\\\\]|^)(\\$)/);\n",
       "        loc2 = mystring.search(/([^\\\\]|^)(\\$\\$)/);\n",
       "        //console.log(mystring,\", loc:\",loc,\", loc2:\",loc2);\n",
       "    }\n",
       "\n",
       "    //console.log(mystring);\n",
       "    return mystring;\n",
       "}\n",
       "\n",
       "\n",
       "function show_questions(json, mydiv) {\n",
       "    console.log('show_questions');\n",
       "    //var mydiv=document.getElementById(myid);\n",
       "    var shuffle_questions = mydiv.dataset.shufflequestions;\n",
       "    var num_questions = mydiv.dataset.numquestions;\n",
       "    var shuffle_answers = mydiv.dataset.shuffleanswers;\n",
       "    var max_width = mydiv.dataset.maxwidth;\n",
       "\n",
       "    if (num_questions > json.length) {\n",
       "        num_questions = json.length;\n",
       "    }\n",
       "\n",
       "    var questions;\n",
       "    if ((num_questions < json.length) || (shuffle_questions == \"True\")) {\n",
       "        //console.log(num_questions+\",\"+json.length);\n",
       "        questions = getRandomSubarray(json, num_questions);\n",
       "    } else {\n",
       "        questions = json;\n",
       "    }\n",
       "\n",
       "    //console.log(\"SQ: \"+shuffle_questions+\", NQ: \" + num_questions + \", SA: \", shuffle_answers);\n",
       "\n",
       "    // Iterate over questions\n",
       "    questions.forEach((qa, index, array) => {\n",
       "        //console.log(qa.question); \n",
       "\n",
       "        var id = makeid(8);\n",
       "        //console.log(id);\n",
       "\n",
       "\n",
       "        // Create Div to contain question and answers\n",
       "        var iDiv = document.createElement('div');\n",
       "        //iDiv.id = 'quizWrap' + id + index;\n",
       "        iDiv.id = 'quizWrap' + id;\n",
       "        iDiv.className = 'Quiz';\n",
       "        iDiv.setAttribute('data-qnum', index);\n",
       "        iDiv.style.maxWidth  =max_width+\"px\";\n",
       "        mydiv.appendChild(iDiv);\n",
       "        // iDiv.innerHTML=qa.question;\n",
       "        \n",
       "        var outerqDiv = document.createElement('div');\n",
       "        outerqDiv.id = \"OuterquizQn\" + id + index;\n",
       "        // Create div to contain question part\n",
       "        var qDiv = document.createElement('div');\n",
       "        qDiv.id = \"quizQn\" + id + index;\n",
       "        \n",
       "        if (qa.question) {\n",
       "            iDiv.append(outerqDiv);\n",
       "\n",
       "            //qDiv.textContent=qa.question;\n",
       "            qDiv.innerHTML = jaxify(qa.question);\n",
       "            outerqDiv.append(qDiv);\n",
       "        }\n",
       "\n",
       "        // Create div for code inside question\n",
       "        var codeDiv;\n",
       "        if (\"code\" in qa) {\n",
       "            codeDiv = document.createElement('div');\n",
       "            codeDiv.id = \"code\" + id + index;\n",
       "            codeDiv.className = \"QuizCode\";\n",
       "            var codePre = document.createElement('pre');\n",
       "            codeDiv.append(codePre);\n",
       "            var codeCode = document.createElement('code');\n",
       "            codePre.append(codeCode);\n",
       "            codeCode.innerHTML = qa.code;\n",
       "            outerqDiv.append(codeDiv);\n",
       "            //console.log(codeDiv);\n",
       "        }\n",
       "\n",
       "\n",
       "        // Create div to contain answer part\n",
       "        var aDiv = document.createElement('div');\n",
       "        aDiv.id = \"quizAns\" + id + index;\n",
       "        aDiv.className = 'Answer';\n",
       "        iDiv.append(aDiv);\n",
       "\n",
       "        //console.log(qa.type);\n",
       "\n",
       "        var num_correct;\n",
       "        if ((qa.type == \"multiple_choice\") || (qa.type == \"many_choice\") ) {\n",
       "            num_correct = make_mc(qa, shuffle_answers, outerqDiv, qDiv, aDiv, id);\n",
       "            if (\"answer_cols\" in qa) {\n",
       "                //aDiv.style.gridTemplateColumns = 'auto '.repeat(qa.answer_cols);\n",
       "                aDiv.style.gridTemplateColumns = 'repeat(' + qa.answer_cols + ', 1fr)';\n",
       "            }\n",
       "        } else if (qa.type == \"numeric\") {\n",
       "            //console.log(\"numeric\");\n",
       "            make_numeric(qa, outerqDiv, qDiv, aDiv, id);\n",
       "        }\n",
       "\n",
       "\n",
       "        //Make div for feedback\n",
       "        var fb = document.createElement(\"div\");\n",
       "        fb.id = \"fb\" + id;\n",
       "        //fb.style=\"font-size: 20px;text-align:center;\";\n",
       "        fb.className = \"Feedback\";\n",
       "        fb.setAttribute(\"data-answeredcorrect\", 0);\n",
       "        fb.setAttribute(\"data-numcorrect\", num_correct);\n",
       "        iDiv.append(fb);\n",
       "\n",
       "\n",
       "    });\n",
       "    var preserveResponses = mydiv.dataset.preserveresponses;\n",
       "    console.log(preserveResponses);\n",
       "    console.log(preserveResponses == \"true\");\n",
       "    if (preserveResponses == \"true\") {\n",
       "        console.log(preserveResponses);\n",
       "        // Create Div to contain record of answers\n",
       "        var iDiv = document.createElement('div');\n",
       "        iDiv.id = 'responses' + mydiv.id;\n",
       "        iDiv.className = 'JCResponses';\n",
       "        // Create a place to store responses as an empty array\n",
       "        iDiv.setAttribute('data-responses', '[]');\n",
       "\n",
       "        // Dummy Text\n",
       "        iDiv.innerHTML=\"<b>Select your answers and then follow the directions that will appear here.</b>\"\n",
       "        //iDiv.className = 'Quiz';\n",
       "        mydiv.appendChild(iDiv);\n",
       "    }\n",
       "//console.log(\"At end of show_questions\");\n",
       "    if (typeof MathJax != 'undefined') {\n",
       "        console.log(\"MathJax version\", MathJax.version);\n",
       "        var version = MathJax.version;\n",
       "        setTimeout(function(){\n",
       "            var version = MathJax.version;\n",
       "            console.log('After sleep, MathJax version', version);\n",
       "            if (version[0] == \"2\") {\n",
       "                MathJax.Hub.Queue([\"Typeset\", MathJax.Hub]);\n",
       "            } else if (version[0] == \"3\") {\n",
       "                MathJax.typeset([mydiv]);\n",
       "            }\n",
       "        }, 500);\n",
       "if (typeof version == 'undefined') {\n",
       "        } else\n",
       "        {\n",
       "            if (version[0] == \"2\") {\n",
       "                MathJax.Hub.Queue([\"Typeset\", MathJax.Hub]);\n",
       "            } else if (version[0] == \"3\") {\n",
       "                MathJax.typeset([mydiv]);\n",
       "            } else {\n",
       "                console.log(\"MathJax not found\");\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "    return false;\n",
       "}\n",
       "/* This is to handle asynchrony issues in loading Jupyter notebooks\n",
       "           where the quiz has been previously run. The Javascript was generally\n",
       "           being run before the div was added to the DOM. I tried to do this\n",
       "           more elegantly using Mutation Observer, but I didn't get it to work.\n",
       "\n",
       "           Someone more knowledgeable could make this better ;-) */\n",
       "\n",
       "        function try_show() {\n",
       "          if(document.getElementById(\"scrRJzohVShm\")) {\n",
       "            show_questions(questionsscrRJzohVShm,  scrRJzohVShm); \n",
       "          } else {\n",
       "             setTimeout(try_show, 200);\n",
       "          }\n",
       "        };\n",
       "    \n",
       "        {\n",
       "        // console.log(element);\n",
       "\n",
       "        //console.log(\"scrRJzohVShm\");\n",
       "        // console.log(document.getElementById(\"scrRJzohVShm\"));\n",
       "\n",
       "        try_show();\n",
       "        }\n",
       "        "
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from jupyterquiz import display_quiz\n",
    "display_quiz(\"examples.json\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Deciding on K\n",
    "\n",
    "With clustering, we can't be too sure how many clusters we will get, and what information they will be clustered on! Looking at Figure 2 above, it seems that we have 4 or 5 distinct clusters. Let's pick $K=4$ for now."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "K = 4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "akzczS8QjaLB"
   },
   "source": [
    "### Fitting the K-means model\n",
    "\n",
    "Finally, apply Sklearn's `KMeans` model to our data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import KMeans model\n",
    "from sklearn.cluster import KMeans\n",
    "# Import time to measure algorithm runtime \n",
    "from time import time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "km = KMeans(n_clusters=K, random_state=42)\n",
    "km.fit(X_scaled)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that we have only picked two hyperparameters in this case: `n_clusters` (K) and `random_state` (the algorithm has random elements, and this helps ensure that we can reproduce our results). However, there are other useful hyperparameters such as `max_iter`, `tol`, etc. You can find out what each of these is for by using the `help()` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# help(KMeans)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Evaluating k-means\n",
    "\n",
    "Notice the useful method `.cluster_centers_` on the `KMeans` model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# obtain cluster memberships for each item in the data\n",
    "y_preds = km.predict(X_scaled)\n",
    "df_no_labels['cluster_label'] = y_preds\n",
    "centers = scaler.inverse_transform(km.cluster_centers_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's visualise how well we did with $K=4$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# plot data\n",
    "plt.figure(dpi=120)\n",
    "for k in range(K):\n",
    "    x1 = df_no_labels[df_no_labels['cluster_label'] == k]['feature_0']\n",
    "    x2 = df_no_labels[df_no_labels['cluster_label'] == k]['feature_1']\n",
    "    plt.scatter(x1, x2, label=\"k = \"+str(k+1))\n",
    "    \n",
    "# show cluster centroid locations\n",
    "plt.scatter(centers[:,0],centers[:,1],label=\"centroid\")\n",
    "\n",
    "\n",
    "plt.legend()\n",
    "plt.title(\"K = 4\")\n",
    "plt.xlabel('Feature 1')\n",
    "plt.ylabel('Feature 2')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Although K-means tried, this configuration is a far cry from the initial clusters we generated in Figure 1. A useful observation here is that cluster centroids can also occur in places where there is no data. \n",
    "\n",
    "Anyway, let's see if we can pick a better K.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Knowledge check!!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div id=\"MDliucXfjwCR\" data-shufflequestions=\"False\"\n",
       "               data-shuffleanswers=\"True\"\n",
       "               data-preserveresponses=\"false\"\n",
       "               data-numquestions=\"1000000\"\n",
       "               data-maxwidth=\"600\"\n",
       "               style=\"border-radius: 10px; text-align: left\"> <style>\n",
       "#MDliucXfjwCR {\n",
       "   --jq-multiple-choice-bg: #6f78ffff;\n",
       "   --jq-mc-button-bg: #fafafa;\n",
       "   --jq-mc-button-border: #e0e0e0e0;\n",
       "   --jq-mc-button-inset-shadow: #555555;\n",
       "   --jq-many-choice-bg: #f75c03ff;\n",
       "   --jq-numeric-bg: #392061ff;\n",
       "   --jq-numeric-input-bg: #c0c0c0;\n",
       "   --jq-numeric-input-label: #101010;\n",
       "   --jq-numeric-input-shadow: #999999;\n",
       "   --jq-incorrect-color: #c80202;\n",
       "   --jq-correct-color: #009113;\n",
       "   --jq-text-color: #fafafa;\n",
       "}\n",
       "\n",
       ".Quiz {\n",
       "    max-width: 600px;\n",
       "    margin-top: 15px;\n",
       "    margin-left: auto;\n",
       "    margin-right: auto;\n",
       "    margin-bottom: 15px;\n",
       "    padding-bottom: 4px;\n",
       "    padding-top: 4px;\n",
       "    line-height: 1.1;\n",
       "    font-size: 16pt;\n",
       "    border-radius: inherit;\n",
       "}\n",
       "\n",
       ".QuizCode {\n",
       "    font-size: 14pt;\n",
       "    margin-top: 10px;\n",
       "    margin-left: 20px;\n",
       "    margin-right: 20px;\n",
       "}\n",
       "\n",
       ".QuizCode>pre {\n",
       "    padding: 4px;\n",
       "}\n",
       "\n",
       ".Answer {\n",
       "    margin: 10px 0;\n",
       "    display: grid;\n",
       "    grid-template-columns: 1fr 1fr;\n",
       "    grid-gap: 10px;\n",
       "    border-radius: inherit;\n",
       "}\n",
       "\n",
       ".Feedback {\n",
       "    font-size: 16pt;\n",
       "    text-align: center;\n",
       "    min-height: 2em;\n",
       "}\n",
       "\n",
       ".Input {\n",
       "    align: left;\n",
       "    font-size: 20pt;\n",
       "}\n",
       "\n",
       ".Input-text {\n",
       "    display: block;\n",
       "    margin: 10px;\n",
       "    color: inherit;\n",
       "    width: 140px;\n",
       "    background-color: var(--jq-numeric-input-bg);\n",
       "    color: var(--jq-text-color);\n",
       "    padding: 5px;\n",
       "    padding-left: 10px;\n",
       "    font-family: inherit;\n",
       "    font-size: 20px;\n",
       "    font-weight: inherit;\n",
       "    line-height: 20pt;\n",
       "    border: none;\n",
       "    border-radius: 0.2rem;\n",
       "    transition: box-shadow 0.1s);\n",
       "}\n",
       "\n",
       ".Input-text:focus {\n",
       "    outline: none;\n",
       "    background-color: var(--jq-numeric-input-bg);\n",
       "    box-shadow: 0.6rem 0.8rem 1.4rem -0.5rem var(--jq-numeric-input-shadow);\n",
       "}\n",
       "\n",
       ".MCButton {\n",
       "    background: var(--jq-mc-button-bg);\n",
       "    border: 1px solid var(--jq-mc-button-border);\n",
       "    border-radius: inherit;\n",
       "    padding: 10px;\n",
       "    font-size: 16px;\n",
       "    cursor: pointer;\n",
       "    text-align: center;\n",
       "    display: flex;\n",
       "    align-items: center;\n",
       "    justify-content: center;\n",
       "}\n",
       "\n",
       ".MCButton p {\n",
       "    color: inherit;\n",
       "}\n",
       "\n",
       ".MultipleChoiceQn {\n",
       "    padding: 10px;\n",
       "    background: var(--jq-multiple-choice-bg);\n",
       "    color: var(--jq-text-color);\n",
       "    border-radius: inherit;\n",
       "}\n",
       "\n",
       ".ManyChoiceQn {\n",
       "    padding: 10px;\n",
       "    background: var(--jq-many-choice-bg);\n",
       "    color: var(--jq-text-color);\n",
       "    border-radius: inherit;\n",
       "}\n",
       "\n",
       ".NumericQn {\n",
       "    padding: 10px;\n",
       "    background: var(--jq-numeric-bg);\n",
       "    color: var(--jq-text-color);\n",
       "    border-radius: inherit;\n",
       "}\n",
       "\n",
       ".NumericQn p {\n",
       "    color: inherit;\n",
       "}\n",
       "\n",
       ".InpLabel {\n",
       "    line-height: 34px;\n",
       "    float: left;\n",
       "    margin-right: 10px;\n",
       "    color: var(--jq-numeric-input-label);\n",
       "    font-size: 15pt;\n",
       "}\n",
       "\n",
       ".incorrect {\n",
       "    color: var(--jq-incorrect-color);\n",
       "}\n",
       "\n",
       ".correct {\n",
       "    color: var(--jq-correct-color);\n",
       "}\n",
       "\n",
       ".correctButton {\n",
       "    /*\n",
       "    background: var(--jq-correct-color);\n",
       "   */\n",
       "    animation: correct-anim 0.6s ease;\n",
       "    animation-fill-mode: forwards;\n",
       "    color: var(--jq-text-color);\n",
       "    box-shadow: inset 0px 0px 5px var(--jq-mc-button-inset-shadow);\n",
       "    outline: none;\n",
       "}\n",
       "\n",
       ".incorrectButton {\n",
       "    animation: incorrect-anim 0.8s ease;\n",
       "    animation-fill-mode: forwards;\n",
       "    color: var(--jq-text-color);\n",
       "    box-shadow: inset 0px 0px 5px var(--jq-mc-button-inset-shadow);\n",
       "    outline: none;\n",
       "}\n",
       "\n",
       "@keyframes incorrect-anim {\n",
       "    100% {\n",
       "        background-color: var(--jq-incorrect-color);\n",
       "    }\n",
       "}\n",
       "\n",
       "@keyframes correct-anim {\n",
       "    100% {\n",
       "        background-color: var(--jq-correct-color);\n",
       "    }\n",
       "}\n",
       "</style>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "var questionsMDliucXfjwCR=[\n",
       "    \n",
       "    {\n",
       "        \"question\": \"Enter the value of $\\\\pi$ to 2 decimal places.\",\n",
       "        \"type\": \"numeric\",\n",
       "        \"answers\": [\n",
       "            {\n",
       "                \"type\": \"value\",\n",
       "                \"value\": 3.14,\n",
       "                \"correct\": true,\n",
       "                \"feedback\": \"Correct.\"\n",
       "            },\n",
       "            {\n",
       "                \"type\": \"range\",\n",
       "                \"range\": [\n",
       "                    3.142857,\n",
       "                    3.142858\n",
       "                ],\n",
       "                \"correct\": true,\n",
       "                \"feedback\": \"True to 2 decimal places, but you know $\\\\pi$ is not really 22/7, right?\"\n",
       "            },\n",
       "            {\n",
       "                \"type\": \"range\",\n",
       "                \"range\": [\n",
       "                    -100000000,\n",
       "                    0\n",
       "                ],\n",
       "                \"correct\": false,\n",
       "                \"feedback\": \"$\\\\pi$ is the AREA of a circle of radius 1. Try again.\"\n",
       "            },\n",
       "            {\n",
       "                \"type\": \"default\",\n",
       "                \"feedback\": \"$\\\\pi$ is the area of a circle of radius 1. Try again.\"\n",
       "            }\n",
       "        ]\n",
       "    },\n",
       "    \n",
       "    {\n",
       "        \"question\": \"Determine the output of the following Python code:\",\n",
       "        \"code\": \"a=\\\"1\\\"\\nb=\\\"2\\\"\\nprint(a+b)\",\n",
       "        \"type\": \"multiple_choice\",\n",
       "        \"answers\": [\n",
       "            {\n",
       "                \"answer\": \"1\",\n",
       "                \"correct\": false,\n",
       "                \"feedback\": \"No. When strings are operated on by +, they are concatenated.\"\n",
       "            },\n",
       "            {\n",
       "                \"answer\": \"2\",\n",
       "                \"correct\": false,\n",
       "                \"feedback\": \"No. When strings are operated on by +, they are concatenated.\"\n",
       "            },\n",
       "            {\n",
       "                \"answer\": \"3\",\n",
       "                \"correct\": false,\n",
       "                \"feedback\": \"No. When strings are operated on by +, they are concatenated.\"\n",
       "            },\n",
       "            {\n",
       "                \"answer\": \"12\",\n",
       "                \"correct\": true,\n",
       "                \"feedback\": \"Yes. The + operator will concatenate the strings \\\"1\\\" and \\\"2\\\".\"\n",
       "            },\n",
       "            {\n",
       "                \"answer\": \"error\",\n",
       "                \"correct\": false,\n",
       "                \"feedback\": \"No. The + operator for strings performs string concatenation.\"\n",
       "            }\n",
       "        ]\n",
       "    }\n",
       "    \n",
       "];\n",
       "    // Make a random ID\n",
       "function makeid(length) {\n",
       "    var result = [];\n",
       "    var characters = 'ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz';\n",
       "    var charactersLength = characters.length;\n",
       "    for (var i = 0; i < length; i++) {\n",
       "        result.push(characters.charAt(Math.floor(Math.random() * charactersLength)));\n",
       "    }\n",
       "    return result.join('');\n",
       "}\n",
       "\n",
       "// Choose a random subset of an array. Can also be used to shuffle the array\n",
       "function getRandomSubarray(arr, size) {\n",
       "    var shuffled = arr.slice(0), i = arr.length, temp, index;\n",
       "    while (i--) {\n",
       "        index = Math.floor((i + 1) * Math.random());\n",
       "        temp = shuffled[index];\n",
       "        shuffled[index] = shuffled[i];\n",
       "        shuffled[i] = temp;\n",
       "    }\n",
       "    return shuffled.slice(0, size);\n",
       "}\n",
       "\n",
       "function printResponses(responsesContainer) {\n",
       "    var responses=JSON.parse(responsesContainer.dataset.responses);\n",
       "    var stringResponses='<B>IMPORTANT!</B>To preserve this answer sequence for submission, when you have finalized your answers: <ol> <li> Copy the text in this cell below \"Answer String\"</li> <li> Double click on the cell directly below the Answer String, labeled \"Replace Me\"</li> <li> Select the whole \"Replace Me\" text</li> <li> Paste in your answer string and press shift-Enter.</li><li>Save the notebook using the save icon or File->Save Notebook menu item</li></ul><br><br><br><b>Answer String:</b><br> ';\n",
       "    console.log(responses);\n",
       "    responses.forEach((response, index) => {\n",
       "        if (response) {\n",
       "            console.log(index + ': ' + response);\n",
       "            stringResponses+= index + ': ' + response +\"<BR>\";\n",
       "        }\n",
       "    });\n",
       "    responsesContainer.innerHTML=stringResponses;\n",
       "}\n",
       "function check_mc() {\n",
       "    var id = this.id.split('-')[0];\n",
       "    //var response = this.id.split('-')[1];\n",
       "    //console.log(response);\n",
       "    //console.log(\"In check_mc(), id=\"+id);\n",
       "    //console.log(event.srcElement.id)           \n",
       "    //console.log(event.srcElement.dataset.correct)   \n",
       "    //console.log(event.srcElement.dataset.feedback)\n",
       "\n",
       "    var label = event.srcElement;\n",
       "    //console.log(label, label.nodeName);\n",
       "    var depth = 0;\n",
       "    while ((label.nodeName != \"LABEL\") && (depth < 20)) {\n",
       "        label = label.parentElement;\n",
       "        console.log(depth, label);\n",
       "        depth++;\n",
       "    }\n",
       "\n",
       "\n",
       "\n",
       "    var answers = label.parentElement.children;\n",
       "\n",
       "    //console.log(answers);\n",
       "\n",
       "\n",
       "    // Split behavior based on multiple choice vs many choice:\n",
       "    var fb = document.getElementById(\"fb\" + id);\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "    if (fb.dataset.numcorrect == 1) {\n",
       "        // What follows is for the saved responses stuff\n",
       "        var outerContainer = fb.parentElement.parentElement;\n",
       "        var responsesContainer = document.getElementById(\"responses\" + outerContainer.id);\n",
       "        if (responsesContainer) {\n",
       "            //console.log(responsesContainer);\n",
       "            var response = label.firstChild.innerText;\n",
       "            if (label.querySelector(\".QuizCode\")){\n",
       "                response+= label.querySelector(\".QuizCode\").firstChild.innerText;\n",
       "            }\n",
       "            console.log(response);\n",
       "            //console.log(document.getElementById(\"quizWrap\"+id));\n",
       "            var qnum = document.getElementById(\"quizWrap\"+id).dataset.qnum;\n",
       "            console.log(\"Question \" + qnum);\n",
       "            //console.log(id, \", got numcorrect=\",fb.dataset.numcorrect);\n",
       "            var responses=JSON.parse(responsesContainer.dataset.responses);\n",
       "            console.log(responses);\n",
       "            responses[qnum]= response;\n",
       "            responsesContainer.setAttribute('data-responses', JSON.stringify(responses));\n",
       "            printResponses(responsesContainer);\n",
       "        }\n",
       "        // End code to preserve responses\n",
       "        \n",
       "        for (var i = 0; i < answers.length; i++) {\n",
       "            var child = answers[i];\n",
       "            //console.log(child);\n",
       "            child.className = \"MCButton\";\n",
       "        }\n",
       "\n",
       "\n",
       "\n",
       "        if (label.dataset.correct == \"true\") {\n",
       "            // console.log(\"Correct action\");\n",
       "            if (\"feedback\" in label.dataset) {\n",
       "                fb.textContent = jaxify(label.dataset.feedback);\n",
       "            } else {\n",
       "                fb.textContent = \"Correct!\";\n",
       "            }\n",
       "            label.classList.add(\"correctButton\");\n",
       "\n",
       "            fb.className = \"Feedback\";\n",
       "            fb.classList.add(\"correct\");\n",
       "\n",
       "        } else {\n",
       "            if (\"feedback\" in label.dataset) {\n",
       "                fb.textContent = jaxify(label.dataset.feedback);\n",
       "            } else {\n",
       "                fb.textContent = \"Incorrect -- try again.\";\n",
       "            }\n",
       "            //console.log(\"Error action\");\n",
       "            label.classList.add(\"incorrectButton\");\n",
       "            fb.className = \"Feedback\";\n",
       "            fb.classList.add(\"incorrect\");\n",
       "        }\n",
       "    }\n",
       "    else {\n",
       "        var reset = false;\n",
       "        var feedback;\n",
       "         if (label.dataset.correct == \"true\") {\n",
       "            if (\"feedback\" in label.dataset) {\n",
       "                feedback = jaxify(label.dataset.feedback);\n",
       "            } else {\n",
       "                feedback = \"Correct!\";\n",
       "            }\n",
       "            if (label.dataset.answered <= 0) {\n",
       "                if (fb.dataset.answeredcorrect < 0) {\n",
       "                    fb.dataset.answeredcorrect = 1;\n",
       "                    reset = true;\n",
       "                } else {\n",
       "                    fb.dataset.answeredcorrect++;\n",
       "                }\n",
       "                if (reset) {\n",
       "                    for (var i = 0; i < answers.length; i++) {\n",
       "                        var child = answers[i];\n",
       "                        child.className = \"MCButton\";\n",
       "                        child.dataset.answered = 0;\n",
       "                    }\n",
       "                }\n",
       "                label.classList.add(\"correctButton\");\n",
       "                label.dataset.answered = 1;\n",
       "                fb.className = \"Feedback\";\n",
       "                fb.classList.add(\"correct\");\n",
       "\n",
       "            }\n",
       "        } else {\n",
       "            if (\"feedback\" in label.dataset) {\n",
       "                feedback = jaxify(label.dataset.feedback);\n",
       "            } else {\n",
       "                feedback = \"Incorrect -- try again.\";\n",
       "            }\n",
       "            if (fb.dataset.answeredcorrect > 0) {\n",
       "                fb.dataset.answeredcorrect = -1;\n",
       "                reset = true;\n",
       "            } else {\n",
       "                fb.dataset.answeredcorrect--;\n",
       "            }\n",
       "\n",
       "            if (reset) {\n",
       "                for (var i = 0; i < answers.length; i++) {\n",
       "                    var child = answers[i];\n",
       "                    child.className = \"MCButton\";\n",
       "                    child.dataset.answered = 0;\n",
       "                }\n",
       "            }\n",
       "            label.classList.add(\"incorrectButton\");\n",
       "            fb.className = \"Feedback\";\n",
       "            fb.classList.add(\"incorrect\");\n",
       "        }\n",
       "        // What follows is for the saved responses stuff\n",
       "        var outerContainer = fb.parentElement.parentElement;\n",
       "        var responsesContainer = document.getElementById(\"responses\" + outerContainer.id);\n",
       "        if (responsesContainer) {\n",
       "            //console.log(responsesContainer);\n",
       "            var response = label.firstChild.innerText;\n",
       "            if (label.querySelector(\".QuizCode\")){\n",
       "                response+= label.querySelector(\".QuizCode\").firstChild.innerText;\n",
       "            }\n",
       "            console.log(response);\n",
       "            //console.log(document.getElementById(\"quizWrap\"+id));\n",
       "            var qnum = document.getElementById(\"quizWrap\"+id).dataset.qnum;\n",
       "            console.log(\"Question \" + qnum);\n",
       "            //console.log(id, \", got numcorrect=\",fb.dataset.numcorrect);\n",
       "            var responses=JSON.parse(responsesContainer.dataset.responses);\n",
       "            if (label.dataset.correct == \"true\") {\n",
       "                if (typeof(responses[qnum]) == \"object\"){\n",
       "                    if (!responses[qnum].includes(response))\n",
       "                        responses[qnum].push(response);\n",
       "                } else{\n",
       "                    responses[qnum]= [ response ];\n",
       "                }\n",
       "            } else {\n",
       "                responses[qnum]= response;\n",
       "            }\n",
       "            console.log(responses);\n",
       "            responsesContainer.setAttribute('data-responses', JSON.stringify(responses));\n",
       "            printResponses(responsesContainer);\n",
       "        }\n",
       "        // End save responses stuff\n",
       "\n",
       "\n",
       "\n",
       "        var numcorrect = fb.dataset.numcorrect;\n",
       "        var answeredcorrect = fb.dataset.answeredcorrect;\n",
       "        if (answeredcorrect >= 0) {\n",
       "            fb.textContent = feedback + \" [\" + answeredcorrect + \"/\" + numcorrect + \"]\";\n",
       "        } else {\n",
       "            fb.textContent = feedback + \" [\" + 0 + \"/\" + numcorrect + \"]\";\n",
       "        }\n",
       "\n",
       "\n",
       "    }\n",
       "\n",
       "    if (typeof MathJax != 'undefined') {\n",
       "        var version = MathJax.version;\n",
       "        console.log('MathJax version', version);\n",
       "        if (version[0] == \"2\") {\n",
       "            MathJax.Hub.Queue([\"Typeset\", MathJax.Hub]);\n",
       "        } else if (version[0] == \"3\") {\n",
       "            MathJax.typeset([fb]);\n",
       "        }\n",
       "    } else {\n",
       "        console.log('MathJax not detected');\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "function make_mc(qa, shuffle_answers, outerqDiv, qDiv, aDiv, id) {\n",
       "    var shuffled;\n",
       "    if (shuffle_answers == \"True\") {\n",
       "        //console.log(shuffle_answers+\" read as true\");\n",
       "        shuffled = getRandomSubarray(qa.answers, qa.answers.length);\n",
       "    } else {\n",
       "        //console.log(shuffle_answers+\" read as false\");\n",
       "        shuffled = qa.answers;\n",
       "    }\n",
       "\n",
       "\n",
       "    var num_correct = 0;\n",
       "\n",
       "\n",
       "\n",
       "    shuffled.forEach((item, index, ans_array) => {\n",
       "        //console.log(answer);\n",
       "\n",
       "        // Make input element\n",
       "        var inp = document.createElement(\"input\");\n",
       "        inp.type = \"radio\";\n",
       "        inp.id = \"quizo\" + id + index;\n",
       "        inp.style = \"display:none;\";\n",
       "        aDiv.append(inp);\n",
       "\n",
       "        //Make label for input element\n",
       "        var lab = document.createElement(\"label\");\n",
       "        lab.className = \"MCButton\";\n",
       "        lab.id = id + '-' + index;\n",
       "        lab.onclick = check_mc;\n",
       "        var aSpan = document.createElement('span');\n",
       "        aSpan.classsName = \"\";\n",
       "        //qDiv.id=\"quizQn\"+id+index;\n",
       "        if (\"answer\" in item) {\n",
       "            aSpan.innerHTML = jaxify(item.answer);\n",
       "            //aSpan.innerHTML=item.answer;\n",
       "        }\n",
       "        lab.append(aSpan);\n",
       "\n",
       "        // Create div for code inside question\n",
       "        var codeSpan;\n",
       "        if (\"code\" in item) {\n",
       "            codeSpan = document.createElement('span');\n",
       "            codeSpan.id = \"code\" + id + index;\n",
       "            codeSpan.className = \"QuizCode\";\n",
       "            var codePre = document.createElement('pre');\n",
       "            codeSpan.append(codePre);\n",
       "            var codeCode = document.createElement('code');\n",
       "            codePre.append(codeCode);\n",
       "            codeCode.innerHTML = item.code;\n",
       "            lab.append(codeSpan);\n",
       "            //console.log(codeSpan);\n",
       "        }\n",
       "\n",
       "        //lab.textContent=item.answer;\n",
       "\n",
       "        // Set the data attributes for the answer\n",
       "        lab.setAttribute('data-correct', item.correct);\n",
       "        if (item.correct) {\n",
       "            num_correct++;\n",
       "        }\n",
       "        if (\"feedback\" in item) {\n",
       "            lab.setAttribute('data-feedback', item.feedback);\n",
       "        }\n",
       "        lab.setAttribute('data-answered', 0);\n",
       "\n",
       "        aDiv.append(lab);\n",
       "\n",
       "    });\n",
       "\n",
       "    if (num_correct > 1) {\n",
       "        outerqDiv.className = \"ManyChoiceQn\";\n",
       "    } else {\n",
       "        outerqDiv.className = \"MultipleChoiceQn\";\n",
       "    }\n",
       "\n",
       "    return num_correct;\n",
       "\n",
       "}\n",
       "function check_numeric(ths, event) {\n",
       "\n",
       "    if (event.keyCode === 13) {\n",
       "        ths.blur();\n",
       "\n",
       "        var id = ths.id.split('-')[0];\n",
       "\n",
       "        var submission = ths.value;\n",
       "        if (submission.indexOf('/') != -1) {\n",
       "            var sub_parts = submission.split('/');\n",
       "            //console.log(sub_parts);\n",
       "            submission = sub_parts[0] / sub_parts[1];\n",
       "        }\n",
       "        //console.log(\"Reader entered\", submission);\n",
       "\n",
       "        if (\"precision\" in ths.dataset) {\n",
       "            var precision = ths.dataset.precision;\n",
       "            // console.log(\"1:\", submission)\n",
       "            submission = Math.round((1 * submission + Number.EPSILON) * 10 ** precision) / 10 ** precision;\n",
       "            // console.log(\"Rounded to \", submission, \" precision=\", precision  );\n",
       "        }\n",
       "\n",
       "\n",
       "        //console.log(\"In check_numeric(), id=\"+id);\n",
       "        //console.log(event.srcElement.id)           \n",
       "        //console.log(event.srcElement.dataset.feedback)\n",
       "\n",
       "        var fb = document.getElementById(\"fb\" + id);\n",
       "        fb.style.display = \"none\";\n",
       "        fb.textContent = \"Incorrect -- try again.\";\n",
       "\n",
       "        var answers = JSON.parse(ths.dataset.answers);\n",
       "        //console.log(answers);\n",
       "\n",
       "        var defaultFB = \"\";\n",
       "        var correct;\n",
       "        var done = false;\n",
       "        answers.every(answer => {\n",
       "            //console.log(answer.type);\n",
       "\n",
       "            correct = false;\n",
       "            // if (answer.type==\"value\"){\n",
       "            if ('value' in answer) {\n",
       "                if (submission == answer.value) {\n",
       "                    if (\"feedback\" in answer) {\n",
       "                        fb.textContent = jaxify(answer.feedback);\n",
       "                    } else {\n",
       "                        fb.textContent = jaxify(\"Correct\");\n",
       "                    }\n",
       "                    correct = answer.correct;\n",
       "                    //console.log(answer.correct);\n",
       "                    done = true;\n",
       "                }\n",
       "                // } else if (answer.type==\"range\") {\n",
       "            } else if ('range' in answer) {\n",
       "                //console.log(answer.range);\n",
       "                if ((submission >= answer.range[0]) && (submission < answer.range[1])) {\n",
       "                    fb.textContent = jaxify(answer.feedback);\n",
       "                    correct = answer.correct;\n",
       "                    //console.log(answer.correct);\n",
       "                    done = true;\n",
       "                }\n",
       "            } else if (answer.type == \"default\") {\n",
       "                defaultFB = answer.feedback;\n",
       "            }\n",
       "            if (done) {\n",
       "                return false; // Break out of loop if this has been marked correct\n",
       "            } else {\n",
       "                return true; // Keep looking for case that includes this as a correct answer\n",
       "            }\n",
       "        });\n",
       "\n",
       "        if ((!done) && (defaultFB != \"\")) {\n",
       "            fb.innerHTML = jaxify(defaultFB);\n",
       "            //console.log(\"Default feedback\", defaultFB);\n",
       "        }\n",
       "\n",
       "        fb.style.display = \"block\";\n",
       "        if (correct) {\n",
       "            ths.className = \"Input-text\";\n",
       "            ths.classList.add(\"correctButton\");\n",
       "            fb.className = \"Feedback\";\n",
       "            fb.classList.add(\"correct\");\n",
       "        } else {\n",
       "            ths.className = \"Input-text\";\n",
       "            ths.classList.add(\"incorrectButton\");\n",
       "            fb.className = \"Feedback\";\n",
       "            fb.classList.add(\"incorrect\");\n",
       "        }\n",
       "\n",
       "        // What follows is for the saved responses stuff\n",
       "        var outerContainer = fb.parentElement.parentElement;\n",
       "        var responsesContainer = document.getElementById(\"responses\" + outerContainer.id);\n",
       "        if (responsesContainer) {\n",
       "            console.log(submission);\n",
       "            var qnum = document.getElementById(\"quizWrap\"+id).dataset.qnum;\n",
       "            //console.log(\"Question \" + qnum);\n",
       "            //console.log(id, \", got numcorrect=\",fb.dataset.numcorrect);\n",
       "            var responses=JSON.parse(responsesContainer.dataset.responses);\n",
       "            console.log(responses);\n",
       "            if (submission == ths.value){\n",
       "                responses[qnum]= submission;\n",
       "            } else {\n",
       "                responses[qnum]= ths.value + \"(\" + submission +\")\";\n",
       "            }\n",
       "            responsesContainer.setAttribute('data-responses', JSON.stringify(responses));\n",
       "            printResponses(responsesContainer);\n",
       "        }\n",
       "        // End code to preserve responses\n",
       "\n",
       "        if (typeof MathJax != 'undefined') {\n",
       "            var version = MathJax.version;\n",
       "            console.log('MathJax version', version);\n",
       "            if (version[0] == \"2\") {\n",
       "                MathJax.Hub.Queue([\"Typeset\", MathJax.Hub]);\n",
       "            } else if (version[0] == \"3\") {\n",
       "                MathJax.typeset([fb]);\n",
       "            }\n",
       "        } else {\n",
       "            console.log('MathJax not detected');\n",
       "        }\n",
       "        return false;\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "function isValid(el, charC) {\n",
       "    //console.log(\"Input char: \", charC);\n",
       "    if (charC == 46) {\n",
       "        if (el.value.indexOf('.') === -1) {\n",
       "            return true;\n",
       "        } else if (el.value.indexOf('/') != -1) {\n",
       "            var parts = el.value.split('/');\n",
       "            if (parts[1].indexOf('.') === -1) {\n",
       "                return true;\n",
       "            }\n",
       "        }\n",
       "        else {\n",
       "            return false;\n",
       "        }\n",
       "    } else if (charC == 47) {\n",
       "        if (el.value.indexOf('/') === -1) {\n",
       "            if ((el.value != \"\") && (el.value != \".\")) {\n",
       "                return true;\n",
       "            } else {\n",
       "                return false;\n",
       "            }\n",
       "        } else {\n",
       "            return false;\n",
       "        }\n",
       "    } else if (charC == 45) {\n",
       "        var edex = el.value.indexOf('e');\n",
       "        if (edex == -1) {\n",
       "            edex = el.value.indexOf('E');\n",
       "        }\n",
       "\n",
       "        if (el.value == \"\") {\n",
       "            return true;\n",
       "        } else if (edex == (el.value.length - 1)) { // If just after e or E\n",
       "            return true;\n",
       "        } else {\n",
       "            return false;\n",
       "        }\n",
       "    } else if (charC == 101) { // \"e\"\n",
       "        if ((el.value.indexOf('e') === -1) && (el.value.indexOf('E') === -1) && (el.value.indexOf('/') == -1)) {\n",
       "            // Prev symbol must be digit or decimal point:\n",
       "            if (el.value.slice(-1).search(/\\d/) >= 0) {\n",
       "                return true;\n",
       "            } else if (el.value.slice(-1).search(/\\./) >= 0) {\n",
       "                return true;\n",
       "            } else {\n",
       "                return false;\n",
       "            }\n",
       "        } else {\n",
       "            return false;\n",
       "        }\n",
       "    } else {\n",
       "        if (charC > 31 && (charC < 48 || charC > 57))\n",
       "            return false;\n",
       "    }\n",
       "    return true;\n",
       "}\n",
       "\n",
       "function numeric_keypress(evnt) {\n",
       "    var charC = (evnt.which) ? evnt.which : evnt.keyCode;\n",
       "\n",
       "    if (charC == 13) {\n",
       "        check_numeric(this, evnt);\n",
       "    } else {\n",
       "        return isValid(this, charC);\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "function make_numeric(qa, outerqDiv, qDiv, aDiv, id) {\n",
       "\n",
       "\n",
       "\n",
       "    //console.log(answer);\n",
       "\n",
       "\n",
       "    outerqDiv.className = \"NumericQn\";\n",
       "    aDiv.style.display = 'block';\n",
       "\n",
       "    var lab = document.createElement(\"label\");\n",
       "    lab.className = \"InpLabel\";\n",
       "    lab.textContent = \"Type numeric answer here:\";\n",
       "    aDiv.append(lab);\n",
       "\n",
       "    var inp = document.createElement(\"input\");\n",
       "    inp.type = \"text\";\n",
       "    //inp.id=\"input-\"+id;\n",
       "    inp.id = id + \"-0\";\n",
       "    inp.className = \"Input-text\";\n",
       "    inp.setAttribute('data-answers', JSON.stringify(qa.answers));\n",
       "    if (\"precision\" in qa) {\n",
       "        inp.setAttribute('data-precision', qa.precision);\n",
       "    }\n",
       "    aDiv.append(inp);\n",
       "    //console.log(inp);\n",
       "\n",
       "    //inp.addEventListener(\"keypress\", check_numeric);\n",
       "    //inp.addEventListener(\"keypress\", numeric_keypress);\n",
       "    /*\n",
       "    inp.addEventListener(\"keypress\", function(event) {\n",
       "        return numeric_keypress(this, event);\n",
       "    }\n",
       "                        );\n",
       "                        */\n",
       "    //inp.onkeypress=\"return numeric_keypress(this, event)\";\n",
       "    inp.onkeypress = numeric_keypress;\n",
       "    inp.onpaste = event => false;\n",
       "\n",
       "    inp.addEventListener(\"focus\", function (event) {\n",
       "        this.value = \"\";\n",
       "        return false;\n",
       "    }\n",
       "    );\n",
       "\n",
       "\n",
       "}\n",
       "function jaxify(string) {\n",
       "    var mystring = string;\n",
       "\n",
       "    var count = 0;\n",
       "    var loc = mystring.search(/([^\\\\]|^)(\\$)/);\n",
       "\n",
       "    var count2 = 0;\n",
       "    var loc2 = mystring.search(/([^\\\\]|^)(\\$\\$)/);\n",
       "\n",
       "    //console.log(loc);\n",
       "\n",
       "    while ((loc >= 0) || (loc2 >= 0)) {\n",
       "\n",
       "        /* Have to replace all the double $$ first with current implementation */\n",
       "        if (loc2 >= 0) {\n",
       "            if (count2 % 2 == 0) {\n",
       "                mystring = mystring.replace(/([^\\\\]|^)(\\$\\$)/, \"$1\\\\[\");\n",
       "            } else {\n",
       "                mystring = mystring.replace(/([^\\\\]|^)(\\$\\$)/, \"$1\\\\]\");\n",
       "            }\n",
       "            count2++;\n",
       "        } else {\n",
       "            if (count % 2 == 0) {\n",
       "                mystring = mystring.replace(/([^\\\\]|^)(\\$)/, \"$1\\\\(\");\n",
       "            } else {\n",
       "                mystring = mystring.replace(/([^\\\\]|^)(\\$)/, \"$1\\\\)\");\n",
       "            }\n",
       "            count++;\n",
       "        }\n",
       "        loc = mystring.search(/([^\\\\]|^)(\\$)/);\n",
       "        loc2 = mystring.search(/([^\\\\]|^)(\\$\\$)/);\n",
       "        //console.log(mystring,\", loc:\",loc,\", loc2:\",loc2);\n",
       "    }\n",
       "\n",
       "    //console.log(mystring);\n",
       "    return mystring;\n",
       "}\n",
       "\n",
       "\n",
       "function show_questions(json, mydiv) {\n",
       "    console.log('show_questions');\n",
       "    //var mydiv=document.getElementById(myid);\n",
       "    var shuffle_questions = mydiv.dataset.shufflequestions;\n",
       "    var num_questions = mydiv.dataset.numquestions;\n",
       "    var shuffle_answers = mydiv.dataset.shuffleanswers;\n",
       "    var max_width = mydiv.dataset.maxwidth;\n",
       "\n",
       "    if (num_questions > json.length) {\n",
       "        num_questions = json.length;\n",
       "    }\n",
       "\n",
       "    var questions;\n",
       "    if ((num_questions < json.length) || (shuffle_questions == \"True\")) {\n",
       "        //console.log(num_questions+\",\"+json.length);\n",
       "        questions = getRandomSubarray(json, num_questions);\n",
       "    } else {\n",
       "        questions = json;\n",
       "    }\n",
       "\n",
       "    //console.log(\"SQ: \"+shuffle_questions+\", NQ: \" + num_questions + \", SA: \", shuffle_answers);\n",
       "\n",
       "    // Iterate over questions\n",
       "    questions.forEach((qa, index, array) => {\n",
       "        //console.log(qa.question); \n",
       "\n",
       "        var id = makeid(8);\n",
       "        //console.log(id);\n",
       "\n",
       "\n",
       "        // Create Div to contain question and answers\n",
       "        var iDiv = document.createElement('div');\n",
       "        //iDiv.id = 'quizWrap' + id + index;\n",
       "        iDiv.id = 'quizWrap' + id;\n",
       "        iDiv.className = 'Quiz';\n",
       "        iDiv.setAttribute('data-qnum', index);\n",
       "        iDiv.style.maxWidth  =max_width+\"px\";\n",
       "        mydiv.appendChild(iDiv);\n",
       "        // iDiv.innerHTML=qa.question;\n",
       "        \n",
       "        var outerqDiv = document.createElement('div');\n",
       "        outerqDiv.id = \"OuterquizQn\" + id + index;\n",
       "        // Create div to contain question part\n",
       "        var qDiv = document.createElement('div');\n",
       "        qDiv.id = \"quizQn\" + id + index;\n",
       "        \n",
       "        if (qa.question) {\n",
       "            iDiv.append(outerqDiv);\n",
       "\n",
       "            //qDiv.textContent=qa.question;\n",
       "            qDiv.innerHTML = jaxify(qa.question);\n",
       "            outerqDiv.append(qDiv);\n",
       "        }\n",
       "\n",
       "        // Create div for code inside question\n",
       "        var codeDiv;\n",
       "        if (\"code\" in qa) {\n",
       "            codeDiv = document.createElement('div');\n",
       "            codeDiv.id = \"code\" + id + index;\n",
       "            codeDiv.className = \"QuizCode\";\n",
       "            var codePre = document.createElement('pre');\n",
       "            codeDiv.append(codePre);\n",
       "            var codeCode = document.createElement('code');\n",
       "            codePre.append(codeCode);\n",
       "            codeCode.innerHTML = qa.code;\n",
       "            outerqDiv.append(codeDiv);\n",
       "            //console.log(codeDiv);\n",
       "        }\n",
       "\n",
       "\n",
       "        // Create div to contain answer part\n",
       "        var aDiv = document.createElement('div');\n",
       "        aDiv.id = \"quizAns\" + id + index;\n",
       "        aDiv.className = 'Answer';\n",
       "        iDiv.append(aDiv);\n",
       "\n",
       "        //console.log(qa.type);\n",
       "\n",
       "        var num_correct;\n",
       "        if ((qa.type == \"multiple_choice\") || (qa.type == \"many_choice\") ) {\n",
       "            num_correct = make_mc(qa, shuffle_answers, outerqDiv, qDiv, aDiv, id);\n",
       "            if (\"answer_cols\" in qa) {\n",
       "                //aDiv.style.gridTemplateColumns = 'auto '.repeat(qa.answer_cols);\n",
       "                aDiv.style.gridTemplateColumns = 'repeat(' + qa.answer_cols + ', 1fr)';\n",
       "            }\n",
       "        } else if (qa.type == \"numeric\") {\n",
       "            //console.log(\"numeric\");\n",
       "            make_numeric(qa, outerqDiv, qDiv, aDiv, id);\n",
       "        }\n",
       "\n",
       "\n",
       "        //Make div for feedback\n",
       "        var fb = document.createElement(\"div\");\n",
       "        fb.id = \"fb\" + id;\n",
       "        //fb.style=\"font-size: 20px;text-align:center;\";\n",
       "        fb.className = \"Feedback\";\n",
       "        fb.setAttribute(\"data-answeredcorrect\", 0);\n",
       "        fb.setAttribute(\"data-numcorrect\", num_correct);\n",
       "        iDiv.append(fb);\n",
       "\n",
       "\n",
       "    });\n",
       "    var preserveResponses = mydiv.dataset.preserveresponses;\n",
       "    console.log(preserveResponses);\n",
       "    console.log(preserveResponses == \"true\");\n",
       "    if (preserveResponses == \"true\") {\n",
       "        console.log(preserveResponses);\n",
       "        // Create Div to contain record of answers\n",
       "        var iDiv = document.createElement('div');\n",
       "        iDiv.id = 'responses' + mydiv.id;\n",
       "        iDiv.className = 'JCResponses';\n",
       "        // Create a place to store responses as an empty array\n",
       "        iDiv.setAttribute('data-responses', '[]');\n",
       "\n",
       "        // Dummy Text\n",
       "        iDiv.innerHTML=\"<b>Select your answers and then follow the directions that will appear here.</b>\"\n",
       "        //iDiv.className = 'Quiz';\n",
       "        mydiv.appendChild(iDiv);\n",
       "    }\n",
       "//console.log(\"At end of show_questions\");\n",
       "    if (typeof MathJax != 'undefined') {\n",
       "        console.log(\"MathJax version\", MathJax.version);\n",
       "        var version = MathJax.version;\n",
       "        setTimeout(function(){\n",
       "            var version = MathJax.version;\n",
       "            console.log('After sleep, MathJax version', version);\n",
       "            if (version[0] == \"2\") {\n",
       "                MathJax.Hub.Queue([\"Typeset\", MathJax.Hub]);\n",
       "            } else if (version[0] == \"3\") {\n",
       "                MathJax.typeset([mydiv]);\n",
       "            }\n",
       "        }, 500);\n",
       "if (typeof version == 'undefined') {\n",
       "        } else\n",
       "        {\n",
       "            if (version[0] == \"2\") {\n",
       "                MathJax.Hub.Queue([\"Typeset\", MathJax.Hub]);\n",
       "            } else if (version[0] == \"3\") {\n",
       "                MathJax.typeset([mydiv]);\n",
       "            } else {\n",
       "                console.log(\"MathJax not found\");\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "    return false;\n",
       "}\n",
       "/* This is to handle asynchrony issues in loading Jupyter notebooks\n",
       "           where the quiz has been previously run. The Javascript was generally\n",
       "           being run before the div was added to the DOM. I tried to do this\n",
       "           more elegantly using Mutation Observer, but I didn't get it to work.\n",
       "\n",
       "           Someone more knowledgeable could make this better ;-) */\n",
       "\n",
       "        function try_show() {\n",
       "          if(document.getElementById(\"MDliucXfjwCR\")) {\n",
       "            show_questions(questionsMDliucXfjwCR,  MDliucXfjwCR); \n",
       "          } else {\n",
       "             setTimeout(try_show, 200);\n",
       "          }\n",
       "        };\n",
       "    \n",
       "        {\n",
       "        // console.log(element);\n",
       "\n",
       "        //console.log(\"MDliucXfjwCR\");\n",
       "        // console.log(document.getElementById(\"MDliucXfjwCR\"));\n",
       "\n",
       "        try_show();\n",
       "        }\n",
       "        "
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display_quiz(\"examples2.json\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "sJzvvvz_jaK5"
   },
   "source": [
    "## Deciding on the number of Clusters (K)\n",
    "We can now revisit the topic of having to specify a number of clusters K when using the K-means method. \n",
    "\n",
    "### 1. Within cluster variation \n",
    "We will make use of a popular technique called the **'Elbow Method'** to determine how many clusters to choose. \n",
    "\n",
    "To use the elbow method, we will perform K-means clustering a number of times, changing the value of k each time. For each value of k, we will measure the **total within-cluster sum of squares**, or **WCSS**. Put simply, the WCSS is computed by calculating the sum of squared distances between cluster centroids and the data points that belong to them. These *within-cluster sum of squares* are then added together to obtain the *total within-cluster sum of squares* or *WCSS*:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " $$ \\Large\n",
    "\\text{WCSS} = \\sum \\limits_{i=1}^{K} \\sum \\limits_{j = 1}^{|P_i|} \\text{distance}(P_{ij},C_i)^{2}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "3NKqfyFTjaK-"
   },
   "source": [
    "WCSS is a measure of the similarity of the observations within our clusters. Lower WCSS means that a cluster is more tightly grouped. Naturally, as we increase k, WCSS will decrease until k is equal to the number of data points in our data set (when WCSS will be zero). But what use is it to have as many clusters as there are observations? We need to find the optimal number of clusters so that each cluster is sufficiently consistent in its attributes without having too many clusters.   \n",
    "\n",
    "<img src=\"https://raw.githubusercontent.com/Explore-AI/Pictures/master/sketch-wcss.png?raw=true\" alt=\"Types of Clustering\" style=\"width: 80%;\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "-_KyT0u7jaMD"
   },
   "source": [
    "Take a look at the loop below.\n",
    "\n",
    "We have chosen a range of values for k between 1 and 20. For each value of k, we will run the k-means clustering algorithm and record the WCSS (referred to as **`inertia_`** in sklearn. However, for reasons that will become obvious later, we will implement our own WCSS here).\n",
    "\n",
    "_Have a look at the docstring of the **`KMeans`** function (using `help()`)to find out what the **`n_init`** and **`max_iter`** arguments do._"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Manually implement the WCSS\n",
    "def within_cluster_variation(df, label_col='label'):\n",
    "    centroids = df.groupby(label_col).mean()\n",
    "    out = 0\n",
    "    for label, point in centroids.iterrows():\n",
    "        df_features = df[df[label_col] == label].drop(label_col, axis=1)\n",
    "        out += (df_features - point).pow(2).sum(axis=1).sum()\n",
    "    return out"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "u24ThsH5jaMI"
   },
   "outputs": [],
   "source": [
    "# let's try everything between 2 and 20 clusters\n",
    "n_clusters = np.arange(2, 21)\n",
    "\n",
    "# store errors for each value of k\n",
    "errors = []\n",
    "\n",
    "# for i between 2 and 20\n",
    "for k in n_clusters:\n",
    "    # perform k-means clustering\n",
    "    km = KMeans(n_clusters=k, n_init=10, max_iter=300, random_state=42)\n",
    "    km.fit(X_scaled)\n",
    "    \n",
    "    # measure BCSS\n",
    "\n",
    "    y_preds = km.predict(X_scaled)\n",
    "    df_no_labels['cluster_label'] = y_preds\n",
    "    errors.append(within_cluster_variation(df_no_labels,'cluster_label'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "SQV8cik7jaMP"
   },
   "source": [
    "Now that we have performed k-means clustering for each value of k between 2 and 20, we need to create a plot showing the WCSS for each corresponding value of k."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "7jSHzvH5jaMQ",
    "outputId": "32f35fc5-2673-4a83-e9a0-ef2e673fccd2"
   },
   "outputs": [],
   "source": [
    "plt.figure(figsize=(12,8))\n",
    "plt.xlabel('Number of Clusters (k)')\n",
    "plt.ylabel('Within-Cluster Sum of Squares (WCSS)')\n",
    "plt.title('Elbow Method for Determining Optimal Value of k')\n",
    "plt.scatter(n_clusters, errors)\n",
    "plt.plot(n_clusters, errors)\n",
    "plt.xticks(n_clusters)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "dnY2VsN1jaMV"
   },
   "source": [
    "Using the elbow method is as simple as observing the plot of the within-cluster sum of squares (WCSS) for each number of clusters and deciding where the 'elbow' is. The elbow is loosely defined as the point at which the WCSS curve has its greatest decrease in slope. In other words, it is the point after which adding another cluster does not meaningfully decrease the WCSS.\n",
    "\n",
    "Below, we have provided a copy of the code used to generate the elbow plot from above. The 2nd last line of code is incomplete - set the `x=` argument in the `plt.axvline()` function to draw a vertical line at the number of clusters you think the elbow occurs at."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "AncCLw9-jaMX",
    "outputId": "a88c53ce-4d15-478e-cc3f-a1f42265f233"
   },
   "outputs": [],
   "source": [
    "plt.figure(figsize=(12,8))\n",
    "plt.xlabel('Number of Clusters (k)')\n",
    "plt.ylabel('Within-Cluster Sum of Squares (WCSS)')\n",
    "plt.title('Elbow Method for Determining Optimal Value of k')\n",
    "plt.scatter(n_clusters, errors)\n",
    "plt.plot(n_clusters, errors)\n",
    "plt.xticks(n_clusters)\n",
    "\n",
    "# SET THE X-VALUE BELOW TO THE NUMBER OF CLUSTERS\n",
    "# AT WHICH THE ELBOW OCCURS, e.g. plt.axvline(x=18, color='r', lw=2)\n",
    "plt.axvline(x=18, color='r', lw=2)\n",
    "plt.show()\n",
    "\n",
    "# run this code block by hitting Shift+Enter"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "r40RYQTNjaMb"
   },
   "source": [
    "Elbow plots are tricky to decipher, **particularly because this graph keeps on decreasing**. However, we can see a clear kink at k=6 - this is where you should have plotted your vertical line. We will now cluster our observations using k=6."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "7BF1i-jHjaMc",
    "outputId": "bbcfe350-a7ca-4b65-bd7f-4b4361381094"
   },
   "outputs": [],
   "source": [
    "K = 6\n",
    "# remember to set the random state for reproducibility\n",
    "km = KMeans(n_clusters=K, verbose=0, random_state=42)\n",
    "print(\"Clustering sparse data with %s\" % km)\n",
    "t0 = time()\n",
    "km.fit(X_scaled)\n",
    "print(\"done in %0.3fs\" % (time() - t0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "lFbEalXHjaMm"
   },
   "outputs": [],
   "source": [
    "# obtain cluster memberships for each item in the data\n",
    "y_preds = km.predict(X_scaled)\n",
    "df_no_labels['cluster_label'] = y_preds\n",
    "centers = scaler.inverse_transform(km.cluster_centers_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# visualise the clusters\n",
    "plt.figure(dpi=120)\n",
    "for k in range(K):\n",
    "    x1 = df_no_labels[df_no_labels['cluster_label'] == k]['feature_0']\n",
    "    x2 = df_no_labels[df_no_labels['cluster_label'] == k]['feature_1']\n",
    "    plt.scatter(x1, x2, label=\"k = \"+str(k+1))\n",
    "    \n",
    "# show cluster centroid locations\n",
    "plt.scatter(centers[:,0],centers[:,1],label=\"centroid\")\n",
    "\n",
    "\n",
    "plt.legend()\n",
    "plt.title(\"K = 6\")\n",
    "plt.xlabel('Feature 1')\n",
    "plt.ylabel('Feature 2')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So it looks like $K=6$ did much better than $K=4$. Let's see if other methods for selecting $K$ can do better. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Between-cluster variation\n",
    "\n",
    "If the WCSS measures the variation **within each cluster** (i.e., how spread apart the data in a cluster is from the centroid), between cluster variation measures how spread apart the clusters are from each other:\n",
    "\n",
    " $$ \\Large\n",
    "\\text{BCSS} =  \\sum \\limits_{k = 1}^{K} n_{k}(C_k - \\bar{X})^{2}\n",
    "$$\n",
    "\n",
    "Where:\n",
    "- $n_{k}$ is the number of data points in the $k^{th}$ cluster\n",
    "- $C_k$ is the centroid of the $k^{th}$ cluster\n",
    "- $\\bar{X}$ is the mean of all data points, i.e. $\\bar{X} = \\frac{1}{n} \\sum \\limits_{i=1}^{n}X_i$\n",
    "\n",
    "Let's implement this and compare it with the WCSS method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Between cluster variation\n",
    "def between_cluster_variation(df, label_col='label'):\n",
    "    centroids = df.groupby(label_col).mean()\n",
    "    global_mean = df.drop(label_col, axis=1).mean()\n",
    "    centroid_count = df.groupby(label_col).size()\n",
    "    centroid_to_mean_dist = (centroids - global_mean).pow(2).sum(axis=1)\n",
    "    return (centroid_count*centroid_to_mean_dist).sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# let's try everything between 2 and 20 clusters\n",
    "n_clusters = np.arange(2, 21)\n",
    "\n",
    "# store errors for each value of k\n",
    "errors = []\n",
    "\n",
    "# for i between 2 and 20\n",
    "for k in n_clusters:\n",
    "    # perform k-means clustering\n",
    "    km = KMeans(n_clusters=k, n_init=10, max_iter=300, random_state=42)\n",
    "    km.fit(X_scaled)\n",
    "    \n",
    "    # measure BCSS\n",
    "\n",
    "    y_preds = km.predict(X_scaled)\n",
    "    df_no_labels['cluster_label'] = y_preds\n",
    "    errors.append(between_cluster_variation(df_no_labels,'cluster_label'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "SQV8cik7jaMP"
   },
   "source": [
    "Now that we have performed k-means clustering for each value of k between 4 and 20, we need to create a plot showing the BCSS for each corresponding value of k. Since we are measuring how spread out the clusters are, we prefer our BCSS to be higher for clusters that are further apart and lower for those that are close. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "7jSHzvH5jaMQ",
    "outputId": "32f35fc5-2673-4a83-e9a0-ef2e673fccd2"
   },
   "outputs": [],
   "source": [
    "plt.figure(figsize=(12,8))\n",
    "plt.xlabel('Number of Clusters (k)')\n",
    "plt.ylabel('Between-Cluster Sum of Squares (BCSS)')\n",
    "plt.title('Elbow Method for Determining Optimal Value of k')\n",
    "plt.scatter(n_clusters, errors)\n",
    "plt.plot(n_clusters, errors)\n",
    "plt.xticks(n_clusters)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Picking the optimal number of clusters here is still the same as with WCSS; the only difference is that our elbow is now upside-down. Like before, we see a clear kink at $K=6$.   \n",
    "\n",
    "However, this method also has an issue where the BCSS keeps increasing. What we would like is something that stops increasing/decreasing after we have found the right number of clusters. \n",
    "\n",
    "Since we have already seen what the clusters look like with $K=4$, let's jump straight into the next method."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. The CH index\n",
    "\n",
    "Again, the ideal scenario is where our clustering assignments have a small WCSS and a large BCSS simultaneously. The CH index combines these two metrics in a clever way so that it's easy to isolate areas where the WCSS is small and the BCSS is large. For a given value of $K$, the CH index can be computed as follows: \n",
    "\n",
    " $$ \\Large\n",
    "\\text{CH(K)} =  \\frac{BCSS(K)/(K-1)}{WCSS(K)/(n-1)}\n",
    "$$\n",
    "\n",
    "Notice that this involves computing both the BCSS and the WCSS. Using the functions we've defined above, the CH index can be implemented as follows:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ch_index(df, label_col='label'):\n",
    "    n = len(df)\n",
    "    K = df[label_col].nunique()\n",
    "    B = between_cluster_variation(df, label_col)\n",
    "    W = within_cluster_variation(df, label_col)\n",
    "    return (B / (K-1)) / (W / (n-K))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# let's try everything between 1 and 20 clusters\n",
    "n_clusters = np.arange(2, 21)\n",
    "\n",
    "# store errors for each value of k\n",
    "errors = []\n",
    "\n",
    "# for i between 1 and 20\n",
    "for k in n_clusters:\n",
    "    # perform k-means clustering\n",
    "    km = KMeans(n_clusters=k, n_init=10, max_iter=300, random_state=42)\n",
    "    km.fit(X_scaled)\n",
    "    \n",
    "    # measure CH\n",
    "\n",
    "    y_preds = km.predict(X_scaled)\n",
    "    df_no_labels['cluster_label'] = y_preds\n",
    "    errors.append(ch_index(df_no_labels,'cluster_label'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.figure(figsize=(12,8))\n",
    "plt.xlabel('Number of Clusters (k)')\n",
    "plt.ylabel('CH index')\n",
    "plt.title('Elbow Method for Determining Optimal Value of k')\n",
    "plt.scatter(n_clusters, errors)\n",
    "plt.plot(n_clusters, errors)\n",
    "plt.xticks(n_clusters)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, we see a very obvious peak at $K=8$ (if you still remember, this is what we used to generate the data, but the algorithm didn't know this). This metric is definitely easier to interpret. The rule of thumb here is to investigate each peak. These include $K=4$, $K=8$, $K=13$, $K=16$, and $K=19$ in cases where things aren't clear. In this case, however, it is super clear that the obvious number of clusters is $K=8$! \n",
    "\n",
    "Let's try it out and see how it does:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "7BF1i-jHjaMc",
    "outputId": "bbcfe350-a7ca-4b65-bd7f-4b4361381094"
   },
   "outputs": [],
   "source": [
    "K = 8\n",
    "# remember to set the random state for reproducibility\n",
    "km = KMeans(n_clusters=K, verbose=0, random_state=42)\n",
    "print(\"Clustering sparse data with %s\" % km)\n",
    "t0 = time()\n",
    "km.fit(X_scaled)\n",
    "print(\"done in %0.3fs\" % (time() - t0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "lFbEalXHjaMm"
   },
   "outputs": [],
   "source": [
    "# obtain cluster memberships for each item in the data\n",
    "y_preds = km.predict(X_scaled)\n",
    "df_no_labels['cluster_label'] = y_preds\n",
    "centers = scaler.inverse_transform(km.cluster_centers_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# visualise the clusters\n",
    "plt.figure(dpi=120)\n",
    "for k in range(K):\n",
    "    x1 = df_no_labels[df_no_labels['cluster_label'] == k]['feature_0']\n",
    "    x2 = df_no_labels[df_no_labels['cluster_label'] == k]['feature_1']\n",
    "    plt.scatter(x1, x2, label=\"k = \"+str(k+1))\n",
    "    \n",
    "# show cluster centroid locations\n",
    "plt.scatter(centers[:,0],centers[:,1],label=\"centroid\")\n",
    "\n",
    "\n",
    "plt.legend()\n",
    "plt.title(\"K = 8\")\n",
    "plt.xlabel('Feature 1')\n",
    "plt.ylabel('Feature 2')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This looks great! but for good measure, let's compare with the original dataset we generated:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# plot data\n",
    "plt.figure(dpi=120)\n",
    "for center in range(8):\n",
    "    x1 = df[df['y'] == center]['feature_0']\n",
    "    x2 = df[df['y'] == center]['feature_1']\n",
    "    plt.scatter(x1, x2, label=str(center))\n",
    "\n",
    "plt.legend()\n",
    "plt.title(\"Original clusters\")\n",
    "plt.xlabel('Feature 1')\n",
    "plt.ylabel('Feature 2')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We seem to have captured most of the clusters. However, K-means could not correctly assign data points in regions where the clusters overlap. This is a characteristic of all **hard clustering algorithms**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Evaluation metrics\n",
    "\n",
    "Clustering algorithms like K-means produce clusters, but how do we know if these clusters are of good quality?\n",
    "We can use evaluation metrics to **assess the quality** of our clusters. Two common metrics are the `silhouette score` and the `Davies-Bouldin index`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Silhouette Score\n",
    "The silhouette score is a measure of how similar an object is to its own cluster (cohesion) compared to other clusters (separation).\n",
    "It ranges from -1 to 1, where a high value indicates that the object is well-matched to its own cluster and poorly matched to neighbouring clusters.\n",
    "A silhouette score close to 1 suggests that the object is appropriately assigned to its cluster, while a score near -1 indicates that it is assigned to the wrong cluster.\n",
    "In clustering, we aim for a high silhouette score, as it indicates well-separated clusters and a clear distinction between them.\n",
    "The silhouette score is computed for each sample and then averaged to obtain an overall score for the clustering.\n",
    "\n",
    "Let's calculate the Silhouette score for our clusters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import silhouette_score\n",
    "silhouette_avg = silhouette_score(X_scaled, km.labels_)\n",
    "print(\"\\nSilhouette Score:\", silhouette_avg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The silhouette score of 0.576 indicates a reasonably good clustering result. It suggests that the clusters are fairly distinct and well-defined, with minimal overlap between them. Overall, it indicates a relatively successful partitioning of the data into meaningful clusters."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Davies-Bouldin Index\n",
    "The Davies-Bouldin index is another measure of cluster validity that evaluates the average similarity between each cluster and its most similar cluster.\n",
    "It is defined as the ratio of the average intra-cluster distance to the distance between cluster centroids.\n",
    "Lower values of the Davies-Bouldin index indicate better clustering, with tight and well-separated clusters.\n",
    "A high Davies-Bouldin index suggests that clusters overlap or are poorly separated.\n",
    "Like the silhouette score, the Davies-Bouldin index is used to assess the quality of clustering solutions and guide the selection of the optimal number of clusters.\n",
    "\n",
    "Let's calculate the Davies-Bouldin index for our clusters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import davies_bouldin_score\n",
    "db_index = davies_bouldin_score(X_scaled, km.labels_)\n",
    "print(\"\\nDavies-Bouldin Index:\", db_index)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Davies-Bouldin index of 0.598 indicates a relatively good clustering result. It suggests that the clusters are reasonably well-separated, with each cluster having distinct characteristics compared to the others. While not as intuitive as the silhouette score, a lower Davies-Bouldin index still signifies a good clustering outcome, indicating that the clusters are cohesive and well-defined. Therefore, in this context, a Davies-Bouldin index of 0.598 reflects a satisfactory partitioning of the data into meaningful clusters."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The silhouette score and Davies-Bouldin index corroborate our assessment of the clustering visualisation. While K-means successfully identified the majority of clusters, it struggled with accurate assignments for some data points. Overall, K-means demonstrates moderate effectiveness as a clustering method for our dataset. However, exploring alternative clustering methods might offer improvements in clustering accuracy and overall performance."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Advantages and disadvantages of k-means clustering \n",
    "\n",
    "**Advantages**\n",
    "- Computationally efficient clustering technique \n",
    "- Suitable for large datasets \n",
    "- Easy to implement and interpret \n",
    "- Easily adaptable to new datasets\n",
    "\n",
    "**Disadvantages**\n",
    "- Lacks consistency \n",
    "- Sensitive to scaling \n",
    "- Dependent on initial values "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### We've reached the conclusion of this notebook. Tell us how you feel about what you've just learned."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
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       "    padding: 10px;\n",
       "    font-size: 16px;\n",
       "    cursor: pointer;\n",
       "    text-align: center;\n",
       "    display: flex;\n",
       "    align-items: center;\n",
       "    justify-content: center;\n",
       "}\n",
       "\n",
       ".MCButton p {\n",
       "    color: inherit;\n",
       "}\n",
       "\n",
       ".MultipleChoiceQn {\n",
       "    padding: 10px;\n",
       "    background: var(--jq-multiple-choice-bg);\n",
       "    color: var(--jq-text-color);\n",
       "    border-radius: inherit;\n",
       "}\n",
       "\n",
       ".ManyChoiceQn {\n",
       "    padding: 10px;\n",
       "    background: var(--jq-many-choice-bg);\n",
       "    color: var(--jq-text-color);\n",
       "    border-radius: inherit;\n",
       "}\n",
       "\n",
       ".NumericQn {\n",
       "    padding: 10px;\n",
       "    background: var(--jq-numeric-bg);\n",
       "    color: var(--jq-text-color);\n",
       "    border-radius: inherit;\n",
       "}\n",
       "\n",
       ".NumericQn p {\n",
       "    color: inherit;\n",
       "}\n",
       "\n",
       ".InpLabel {\n",
       "    line-height: 34px;\n",
       "    float: left;\n",
       "    margin-right: 10px;\n",
       "    color: var(--jq-numeric-input-label);\n",
       "    font-size: 15pt;\n",
       "}\n",
       "\n",
       ".incorrect {\n",
       "    color: var(--jq-incorrect-color);\n",
       "}\n",
       "\n",
       ".correct {\n",
       "    color: var(--jq-correct-color);\n",
       "}\n",
       "\n",
       ".correctButton {\n",
       "    /*\n",
       "    background: var(--jq-correct-color);\n",
       "   */\n",
       "    animation: correct-anim 0.6s ease;\n",
       "    animation-fill-mode: forwards;\n",
       "    color: var(--jq-text-color);\n",
       "    box-shadow: inset 0px 0px 5px var(--jq-mc-button-inset-shadow);\n",
       "    outline: none;\n",
       "}\n",
       "\n",
       ".incorrectButton {\n",
       "    animation: incorrect-anim 0.8s ease;\n",
       "    animation-fill-mode: forwards;\n",
       "    color: var(--jq-text-color);\n",
       "    box-shadow: inset 0px 0px 5px var(--jq-mc-button-inset-shadow);\n",
       "    outline: none;\n",
       "}\n",
       "\n",
       "@keyframes incorrect-anim {\n",
       "    100% {\n",
       "        background-color: var(--jq-incorrect-color);\n",
       "    }\n",
       "}\n",
       "\n",
       "@keyframes correct-anim {\n",
       "    100% {\n",
       "        background-color: var(--jq-correct-color);\n",
       "    }\n",
       "}\n",
       "</style>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "var questionsYtRottUUXPPU=[\n",
       "    \n",
       "    {\n",
       "        \"question\": \"This notebook helped me understand the concept of K-means clustering?\",\n",
       "        \"type\": \"multiple_choice\",\n",
       "        \"answers\": [\n",
       "            {\n",
       "                \"answer\": \"Strongly agree\",\n",
       "                \"correct\": true,\n",
       "                \"feedback\": \"Happy you enjoyed the notebook! Now that you understand feature scaling, you are ready to move to....\"\n",
       "            },\n",
       "            {\n",
       "                \"answer\": \"Agree\",\n",
       "                \"correct\": true,\n",
       "                \"feedback\": \"Be sure to look through the additional resources to further understand the topic\"\n",
       "            },\n",
       "            {\n",
       "                \"answer\": \"Uncertain\",\n",
       "                \"correct\": true,\n",
       "                \"feedback\": \"This topic is explained in more detail in the ..... Be sure to look through the additional resources to further understand the topic\"\n",
       "            },\n",
       "            {\n",
       "                \"answer\": \"Disagree\",\n",
       "                \"correct\": true,\n",
       "                \"feedback\": \"Sorry to hear that, [suggestion]\"\n",
       "            },\n",
       "            {\n",
       "                \"answer\": \"Stongly disagree\",\n",
       "                \"correct\": true,\n",
       "                \"feedback\": \"Sorry to hear that, [suggestion]\"\n",
       "            }\n",
       "        ]\n",
       "    },\n",
       "    {\n",
       "        \"question\": \"I feel more confident using K-means clustering to uncover the underlying patterns within different groups or clusters of data.\",\n",
       "        \"type\": \"multiple_choice\",\n",
       "        \"answers\": [\n",
       "            {\n",
       "                \"answer\": \"Strongly agree\",\n",
       "                \"correct\": true,\n",
       "                \"feedback\": \"Happy you enjoyed the notebook! Now that you understand feature scaling, you are ready to move to....\"\n",
       "            },\n",
       "            {\n",
       "                \"answer\": \"Agree\",\n",
       "                \"correct\": true,\n",
       "                \"feedback\": \"Be sure to look through the additional resources to further understand the topic\"\n",
       "            },\n",
       "            {\n",
       "                \"answer\": \"Uncertain\",\n",
       "                \"correct\": true,\n",
       "                \"feedback\": \"This topic is explained in more detail in the ..... Be sure to look through the additional resources to further understand the topic\"\n",
       "            },\n",
       "            {\n",
       "                \"answer\": \"Disagree\",\n",
       "                \"correct\": true,\n",
       "                \"feedback\": \"Sorry to hear that, [suggestion]\"\n",
       "            },\n",
       "            {\n",
       "                \"answer\": \"Stongly disagree\",\n",
       "                \"correct\": true,\n",
       "                \"feedback\": \"Sorry to hear that, [suggestion]\"\n",
       "            }\n",
       "        ]\n",
       "    }\n",
       "    \n",
       "];\n",
       "    // Make a random ID\n",
       "function makeid(length) {\n",
       "    var result = [];\n",
       "    var characters = 'ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz';\n",
       "    var charactersLength = characters.length;\n",
       "    for (var i = 0; i < length; i++) {\n",
       "        result.push(characters.charAt(Math.floor(Math.random() * charactersLength)));\n",
       "    }\n",
       "    return result.join('');\n",
       "}\n",
       "\n",
       "// Choose a random subset of an array. Can also be used to shuffle the array\n",
       "function getRandomSubarray(arr, size) {\n",
       "    var shuffled = arr.slice(0), i = arr.length, temp, index;\n",
       "    while (i--) {\n",
       "        index = Math.floor((i + 1) * Math.random());\n",
       "        temp = shuffled[index];\n",
       "        shuffled[index] = shuffled[i];\n",
       "        shuffled[i] = temp;\n",
       "    }\n",
       "    return shuffled.slice(0, size);\n",
       "}\n",
       "\n",
       "function printResponses(responsesContainer) {\n",
       "    var responses=JSON.parse(responsesContainer.dataset.responses);\n",
       "    var stringResponses='<B>IMPORTANT!</B>To preserve this answer sequence for submission, when you have finalized your answers: <ol> <li> Copy the text in this cell below \"Answer String\"</li> <li> Double click on the cell directly below the Answer String, labeled \"Replace Me\"</li> <li> Select the whole \"Replace Me\" text</li> <li> Paste in your answer string and press shift-Enter.</li><li>Save the notebook using the save icon or File->Save Notebook menu item</li></ul><br><br><br><b>Answer String:</b><br> ';\n",
       "    console.log(responses);\n",
       "    responses.forEach((response, index) => {\n",
       "        if (response) {\n",
       "            console.log(index + ': ' + response);\n",
       "            stringResponses+= index + ': ' + response +\"<BR>\";\n",
       "        }\n",
       "    });\n",
       "    responsesContainer.innerHTML=stringResponses;\n",
       "}\n",
       "function check_mc() {\n",
       "    var id = this.id.split('-')[0];\n",
       "    //var response = this.id.split('-')[1];\n",
       "    //console.log(response);\n",
       "    //console.log(\"In check_mc(), id=\"+id);\n",
       "    //console.log(event.srcElement.id)           \n",
       "    //console.log(event.srcElement.dataset.correct)   \n",
       "    //console.log(event.srcElement.dataset.feedback)\n",
       "\n",
       "    var label = event.srcElement;\n",
       "    //console.log(label, label.nodeName);\n",
       "    var depth = 0;\n",
       "    while ((label.nodeName != \"LABEL\") && (depth < 20)) {\n",
       "        label = label.parentElement;\n",
       "        console.log(depth, label);\n",
       "        depth++;\n",
       "    }\n",
       "\n",
       "\n",
       "\n",
       "    var answers = label.parentElement.children;\n",
       "\n",
       "    //console.log(answers);\n",
       "\n",
       "\n",
       "    // Split behavior based on multiple choice vs many choice:\n",
       "    var fb = document.getElementById(\"fb\" + id);\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "    if (fb.dataset.numcorrect == 1) {\n",
       "        // What follows is for the saved responses stuff\n",
       "        var outerContainer = fb.parentElement.parentElement;\n",
       "        var responsesContainer = document.getElementById(\"responses\" + outerContainer.id);\n",
       "        if (responsesContainer) {\n",
       "            //console.log(responsesContainer);\n",
       "            var response = label.firstChild.innerText;\n",
       "            if (label.querySelector(\".QuizCode\")){\n",
       "                response+= label.querySelector(\".QuizCode\").firstChild.innerText;\n",
       "            }\n",
       "            console.log(response);\n",
       "            //console.log(document.getElementById(\"quizWrap\"+id));\n",
       "            var qnum = document.getElementById(\"quizWrap\"+id).dataset.qnum;\n",
       "            console.log(\"Question \" + qnum);\n",
       "            //console.log(id, \", got numcorrect=\",fb.dataset.numcorrect);\n",
       "            var responses=JSON.parse(responsesContainer.dataset.responses);\n",
       "            console.log(responses);\n",
       "            responses[qnum]= response;\n",
       "            responsesContainer.setAttribute('data-responses', JSON.stringify(responses));\n",
       "            printResponses(responsesContainer);\n",
       "        }\n",
       "        // End code to preserve responses\n",
       "        \n",
       "        for (var i = 0; i < answers.length; i++) {\n",
       "            var child = answers[i];\n",
       "            //console.log(child);\n",
       "            child.className = \"MCButton\";\n",
       "        }\n",
       "\n",
       "\n",
       "\n",
       "        if (label.dataset.correct == \"true\") {\n",
       "            // console.log(\"Correct action\");\n",
       "            if (\"feedback\" in label.dataset) {\n",
       "                fb.textContent = jaxify(label.dataset.feedback);\n",
       "            } else {\n",
       "                fb.textContent = \"Correct!\";\n",
       "            }\n",
       "            label.classList.add(\"correctButton\");\n",
       "\n",
       "            fb.className = \"Feedback\";\n",
       "            fb.classList.add(\"correct\");\n",
       "\n",
       "        } else {\n",
       "            if (\"feedback\" in label.dataset) {\n",
       "                fb.textContent = jaxify(label.dataset.feedback);\n",
       "            } else {\n",
       "                fb.textContent = \"Incorrect -- try again.\";\n",
       "            }\n",
       "            //console.log(\"Error action\");\n",
       "            label.classList.add(\"incorrectButton\");\n",
       "            fb.className = \"Feedback\";\n",
       "            fb.classList.add(\"incorrect\");\n",
       "        }\n",
       "    }\n",
       "    else {\n",
       "        var reset = false;\n",
       "        var feedback;\n",
       "         if (label.dataset.correct == \"true\") {\n",
       "            if (\"feedback\" in label.dataset) {\n",
       "                feedback = jaxify(label.dataset.feedback);\n",
       "            } else {\n",
       "                feedback = \"Correct!\";\n",
       "            }\n",
       "            if (label.dataset.answered <= 0) {\n",
       "                if (fb.dataset.answeredcorrect < 0) {\n",
       "                    fb.dataset.answeredcorrect = 1;\n",
       "                    reset = true;\n",
       "                } else {\n",
       "                    fb.dataset.answeredcorrect++;\n",
       "                }\n",
       "                if (reset) {\n",
       "                    for (var i = 0; i < answers.length; i++) {\n",
       "                        var child = answers[i];\n",
       "                        child.className = \"MCButton\";\n",
       "                        child.dataset.answered = 0;\n",
       "                    }\n",
       "                }\n",
       "                label.classList.add(\"correctButton\");\n",
       "                label.dataset.answered = 1;\n",
       "                fb.className = \"Feedback\";\n",
       "                fb.classList.add(\"correct\");\n",
       "\n",
       "            }\n",
       "        } else {\n",
       "            if (\"feedback\" in label.dataset) {\n",
       "                feedback = jaxify(label.dataset.feedback);\n",
       "            } else {\n",
       "                feedback = \"Incorrect -- try again.\";\n",
       "            }\n",
       "            if (fb.dataset.answeredcorrect > 0) {\n",
       "                fb.dataset.answeredcorrect = -1;\n",
       "                reset = true;\n",
       "            } else {\n",
       "                fb.dataset.answeredcorrect--;\n",
       "            }\n",
       "\n",
       "            if (reset) {\n",
       "                for (var i = 0; i < answers.length; i++) {\n",
       "                    var child = answers[i];\n",
       "                    child.className = \"MCButton\";\n",
       "                    child.dataset.answered = 0;\n",
       "                }\n",
       "            }\n",
       "            label.classList.add(\"incorrectButton\");\n",
       "            fb.className = \"Feedback\";\n",
       "            fb.classList.add(\"incorrect\");\n",
       "        }\n",
       "        // What follows is for the saved responses stuff\n",
       "        var outerContainer = fb.parentElement.parentElement;\n",
       "        var responsesContainer = document.getElementById(\"responses\" + outerContainer.id);\n",
       "        if (responsesContainer) {\n",
       "            //console.log(responsesContainer);\n",
       "            var response = label.firstChild.innerText;\n",
       "            if (label.querySelector(\".QuizCode\")){\n",
       "                response+= label.querySelector(\".QuizCode\").firstChild.innerText;\n",
       "            }\n",
       "            console.log(response);\n",
       "            //console.log(document.getElementById(\"quizWrap\"+id));\n",
       "            var qnum = document.getElementById(\"quizWrap\"+id).dataset.qnum;\n",
       "            console.log(\"Question \" + qnum);\n",
       "            //console.log(id, \", got numcorrect=\",fb.dataset.numcorrect);\n",
       "            var responses=JSON.parse(responsesContainer.dataset.responses);\n",
       "            if (label.dataset.correct == \"true\") {\n",
       "                if (typeof(responses[qnum]) == \"object\"){\n",
       "                    if (!responses[qnum].includes(response))\n",
       "                        responses[qnum].push(response);\n",
       "                } else{\n",
       "                    responses[qnum]= [ response ];\n",
       "                }\n",
       "            } else {\n",
       "                responses[qnum]= response;\n",
       "            }\n",
       "            console.log(responses);\n",
       "            responsesContainer.setAttribute('data-responses', JSON.stringify(responses));\n",
       "            printResponses(responsesContainer);\n",
       "        }\n",
       "        // End save responses stuff\n",
       "\n",
       "\n",
       "\n",
       "        var numcorrect = fb.dataset.numcorrect;\n",
       "        var answeredcorrect = fb.dataset.answeredcorrect;\n",
       "        if (answeredcorrect >= 0) {\n",
       "            fb.textContent = feedback + \" [\" + answeredcorrect + \"/\" + numcorrect + \"]\";\n",
       "        } else {\n",
       "            fb.textContent = feedback + \" [\" + 0 + \"/\" + numcorrect + \"]\";\n",
       "        }\n",
       "\n",
       "\n",
       "    }\n",
       "\n",
       "    if (typeof MathJax != 'undefined') {\n",
       "        var version = MathJax.version;\n",
       "        console.log('MathJax version', version);\n",
       "        if (version[0] == \"2\") {\n",
       "            MathJax.Hub.Queue([\"Typeset\", MathJax.Hub]);\n",
       "        } else if (version[0] == \"3\") {\n",
       "            MathJax.typeset([fb]);\n",
       "        }\n",
       "    } else {\n",
       "        console.log('MathJax not detected');\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "function make_mc(qa, shuffle_answers, outerqDiv, qDiv, aDiv, id) {\n",
       "    var shuffled;\n",
       "    if (shuffle_answers == \"True\") {\n",
       "        //console.log(shuffle_answers+\" read as true\");\n",
       "        shuffled = getRandomSubarray(qa.answers, qa.answers.length);\n",
       "    } else {\n",
       "        //console.log(shuffle_answers+\" read as false\");\n",
       "        shuffled = qa.answers;\n",
       "    }\n",
       "\n",
       "\n",
       "    var num_correct = 0;\n",
       "\n",
       "\n",
       "\n",
       "    shuffled.forEach((item, index, ans_array) => {\n",
       "        //console.log(answer);\n",
       "\n",
       "        // Make input element\n",
       "        var inp = document.createElement(\"input\");\n",
       "        inp.type = \"radio\";\n",
       "        inp.id = \"quizo\" + id + index;\n",
       "        inp.style = \"display:none;\";\n",
       "        aDiv.append(inp);\n",
       "\n",
       "        //Make label for input element\n",
       "        var lab = document.createElement(\"label\");\n",
       "        lab.className = \"MCButton\";\n",
       "        lab.id = id + '-' + index;\n",
       "        lab.onclick = check_mc;\n",
       "        var aSpan = document.createElement('span');\n",
       "        aSpan.classsName = \"\";\n",
       "        //qDiv.id=\"quizQn\"+id+index;\n",
       "        if (\"answer\" in item) {\n",
       "            aSpan.innerHTML = jaxify(item.answer);\n",
       "            //aSpan.innerHTML=item.answer;\n",
       "        }\n",
       "        lab.append(aSpan);\n",
       "\n",
       "        // Create div for code inside question\n",
       "        var codeSpan;\n",
       "        if (\"code\" in item) {\n",
       "            codeSpan = document.createElement('span');\n",
       "            codeSpan.id = \"code\" + id + index;\n",
       "            codeSpan.className = \"QuizCode\";\n",
       "            var codePre = document.createElement('pre');\n",
       "            codeSpan.append(codePre);\n",
       "            var codeCode = document.createElement('code');\n",
       "            codePre.append(codeCode);\n",
       "            codeCode.innerHTML = item.code;\n",
       "            lab.append(codeSpan);\n",
       "            //console.log(codeSpan);\n",
       "        }\n",
       "\n",
       "        //lab.textContent=item.answer;\n",
       "\n",
       "        // Set the data attributes for the answer\n",
       "        lab.setAttribute('data-correct', item.correct);\n",
       "        if (item.correct) {\n",
       "            num_correct++;\n",
       "        }\n",
       "        if (\"feedback\" in item) {\n",
       "            lab.setAttribute('data-feedback', item.feedback);\n",
       "        }\n",
       "        lab.setAttribute('data-answered', 0);\n",
       "\n",
       "        aDiv.append(lab);\n",
       "\n",
       "    });\n",
       "\n",
       "    if (num_correct > 1) {\n",
       "        outerqDiv.className = \"ManyChoiceQn\";\n",
       "    } else {\n",
       "        outerqDiv.className = \"MultipleChoiceQn\";\n",
       "    }\n",
       "\n",
       "    return num_correct;\n",
       "\n",
       "}\n",
       "function check_numeric(ths, event) {\n",
       "\n",
       "    if (event.keyCode === 13) {\n",
       "        ths.blur();\n",
       "\n",
       "        var id = ths.id.split('-')[0];\n",
       "\n",
       "        var submission = ths.value;\n",
       "        if (submission.indexOf('/') != -1) {\n",
       "            var sub_parts = submission.split('/');\n",
       "            //console.log(sub_parts);\n",
       "            submission = sub_parts[0] / sub_parts[1];\n",
       "        }\n",
       "        //console.log(\"Reader entered\", submission);\n",
       "\n",
       "        if (\"precision\" in ths.dataset) {\n",
       "            var precision = ths.dataset.precision;\n",
       "            // console.log(\"1:\", submission)\n",
       "            submission = Math.round((1 * submission + Number.EPSILON) * 10 ** precision) / 10 ** precision;\n",
       "            // console.log(\"Rounded to \", submission, \" precision=\", precision  );\n",
       "        }\n",
       "\n",
       "\n",
       "        //console.log(\"In check_numeric(), id=\"+id);\n",
       "        //console.log(event.srcElement.id)           \n",
       "        //console.log(event.srcElement.dataset.feedback)\n",
       "\n",
       "        var fb = document.getElementById(\"fb\" + id);\n",
       "        fb.style.display = \"none\";\n",
       "        fb.textContent = \"Incorrect -- try again.\";\n",
       "\n",
       "        var answers = JSON.parse(ths.dataset.answers);\n",
       "        //console.log(answers);\n",
       "\n",
       "        var defaultFB = \"\";\n",
       "        var correct;\n",
       "        var done = false;\n",
       "        answers.every(answer => {\n",
       "            //console.log(answer.type);\n",
       "\n",
       "            correct = false;\n",
       "            // if (answer.type==\"value\"){\n",
       "            if ('value' in answer) {\n",
       "                if (submission == answer.value) {\n",
       "                    if (\"feedback\" in answer) {\n",
       "                        fb.textContent = jaxify(answer.feedback);\n",
       "                    } else {\n",
       "                        fb.textContent = jaxify(\"Correct\");\n",
       "                    }\n",
       "                    correct = answer.correct;\n",
       "                    //console.log(answer.correct);\n",
       "                    done = true;\n",
       "                }\n",
       "                // } else if (answer.type==\"range\") {\n",
       "            } else if ('range' in answer) {\n",
       "                //console.log(answer.range);\n",
       "                if ((submission >= answer.range[0]) && (submission < answer.range[1])) {\n",
       "                    fb.textContent = jaxify(answer.feedback);\n",
       "                    correct = answer.correct;\n",
       "                    //console.log(answer.correct);\n",
       "                    done = true;\n",
       "                }\n",
       "            } else if (answer.type == \"default\") {\n",
       "                defaultFB = answer.feedback;\n",
       "            }\n",
       "            if (done) {\n",
       "                return false; // Break out of loop if this has been marked correct\n",
       "            } else {\n",
       "                return true; // Keep looking for case that includes this as a correct answer\n",
       "            }\n",
       "        });\n",
       "\n",
       "        if ((!done) && (defaultFB != \"\")) {\n",
       "            fb.innerHTML = jaxify(defaultFB);\n",
       "            //console.log(\"Default feedback\", defaultFB);\n",
       "        }\n",
       "\n",
       "        fb.style.display = \"block\";\n",
       "        if (correct) {\n",
       "            ths.className = \"Input-text\";\n",
       "            ths.classList.add(\"correctButton\");\n",
       "            fb.className = \"Feedback\";\n",
       "            fb.classList.add(\"correct\");\n",
       "        } else {\n",
       "            ths.className = \"Input-text\";\n",
       "            ths.classList.add(\"incorrectButton\");\n",
       "            fb.className = \"Feedback\";\n",
       "            fb.classList.add(\"incorrect\");\n",
       "        }\n",
       "\n",
       "        // What follows is for the saved responses stuff\n",
       "        var outerContainer = fb.parentElement.parentElement;\n",
       "        var responsesContainer = document.getElementById(\"responses\" + outerContainer.id);\n",
       "        if (responsesContainer) {\n",
       "            console.log(submission);\n",
       "            var qnum = document.getElementById(\"quizWrap\"+id).dataset.qnum;\n",
       "            //console.log(\"Question \" + qnum);\n",
       "            //console.log(id, \", got numcorrect=\",fb.dataset.numcorrect);\n",
       "            var responses=JSON.parse(responsesContainer.dataset.responses);\n",
       "            console.log(responses);\n",
       "            if (submission == ths.value){\n",
       "                responses[qnum]= submission;\n",
       "            } else {\n",
       "                responses[qnum]= ths.value + \"(\" + submission +\")\";\n",
       "            }\n",
       "            responsesContainer.setAttribute('data-responses', JSON.stringify(responses));\n",
       "            printResponses(responsesContainer);\n",
       "        }\n",
       "        // End code to preserve responses\n",
       "\n",
       "        if (typeof MathJax != 'undefined') {\n",
       "            var version = MathJax.version;\n",
       "            console.log('MathJax version', version);\n",
       "            if (version[0] == \"2\") {\n",
       "                MathJax.Hub.Queue([\"Typeset\", MathJax.Hub]);\n",
       "            } else if (version[0] == \"3\") {\n",
       "                MathJax.typeset([fb]);\n",
       "            }\n",
       "        } else {\n",
       "            console.log('MathJax not detected');\n",
       "        }\n",
       "        return false;\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "function isValid(el, charC) {\n",
       "    //console.log(\"Input char: \", charC);\n",
       "    if (charC == 46) {\n",
       "        if (el.value.indexOf('.') === -1) {\n",
       "            return true;\n",
       "        } else if (el.value.indexOf('/') != -1) {\n",
       "            var parts = el.value.split('/');\n",
       "            if (parts[1].indexOf('.') === -1) {\n",
       "                return true;\n",
       "            }\n",
       "        }\n",
       "        else {\n",
       "            return false;\n",
       "        }\n",
       "    } else if (charC == 47) {\n",
       "        if (el.value.indexOf('/') === -1) {\n",
       "            if ((el.value != \"\") && (el.value != \".\")) {\n",
       "                return true;\n",
       "            } else {\n",
       "                return false;\n",
       "            }\n",
       "        } else {\n",
       "            return false;\n",
       "        }\n",
       "    } else if (charC == 45) {\n",
       "        var edex = el.value.indexOf('e');\n",
       "        if (edex == -1) {\n",
       "            edex = el.value.indexOf('E');\n",
       "        }\n",
       "\n",
       "        if (el.value == \"\") {\n",
       "            return true;\n",
       "        } else if (edex == (el.value.length - 1)) { // If just after e or E\n",
       "            return true;\n",
       "        } else {\n",
       "            return false;\n",
       "        }\n",
       "    } else if (charC == 101) { // \"e\"\n",
       "        if ((el.value.indexOf('e') === -1) && (el.value.indexOf('E') === -1) && (el.value.indexOf('/') == -1)) {\n",
       "            // Prev symbol must be digit or decimal point:\n",
       "            if (el.value.slice(-1).search(/\\d/) >= 0) {\n",
       "                return true;\n",
       "            } else if (el.value.slice(-1).search(/\\./) >= 0) {\n",
       "                return true;\n",
       "            } else {\n",
       "                return false;\n",
       "            }\n",
       "        } else {\n",
       "            return false;\n",
       "        }\n",
       "    } else {\n",
       "        if (charC > 31 && (charC < 48 || charC > 57))\n",
       "            return false;\n",
       "    }\n",
       "    return true;\n",
       "}\n",
       "\n",
       "function numeric_keypress(evnt) {\n",
       "    var charC = (evnt.which) ? evnt.which : evnt.keyCode;\n",
       "\n",
       "    if (charC == 13) {\n",
       "        check_numeric(this, evnt);\n",
       "    } else {\n",
       "        return isValid(this, charC);\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "function make_numeric(qa, outerqDiv, qDiv, aDiv, id) {\n",
       "\n",
       "\n",
       "\n",
       "    //console.log(answer);\n",
       "\n",
       "\n",
       "    outerqDiv.className = \"NumericQn\";\n",
       "    aDiv.style.display = 'block';\n",
       "\n",
       "    var lab = document.createElement(\"label\");\n",
       "    lab.className = \"InpLabel\";\n",
       "    lab.textContent = \"Type numeric answer here:\";\n",
       "    aDiv.append(lab);\n",
       "\n",
       "    var inp = document.createElement(\"input\");\n",
       "    inp.type = \"text\";\n",
       "    //inp.id=\"input-\"+id;\n",
       "    inp.id = id + \"-0\";\n",
       "    inp.className = \"Input-text\";\n",
       "    inp.setAttribute('data-answers', JSON.stringify(qa.answers));\n",
       "    if (\"precision\" in qa) {\n",
       "        inp.setAttribute('data-precision', qa.precision);\n",
       "    }\n",
       "    aDiv.append(inp);\n",
       "    //console.log(inp);\n",
       "\n",
       "    //inp.addEventListener(\"keypress\", check_numeric);\n",
       "    //inp.addEventListener(\"keypress\", numeric_keypress);\n",
       "    /*\n",
       "    inp.addEventListener(\"keypress\", function(event) {\n",
       "        return numeric_keypress(this, event);\n",
       "    }\n",
       "                        );\n",
       "                        */\n",
       "    //inp.onkeypress=\"return numeric_keypress(this, event)\";\n",
       "    inp.onkeypress = numeric_keypress;\n",
       "    inp.onpaste = event => false;\n",
       "\n",
       "    inp.addEventListener(\"focus\", function (event) {\n",
       "        this.value = \"\";\n",
       "        return false;\n",
       "    }\n",
       "    );\n",
       "\n",
       "\n",
       "}\n",
       "function jaxify(string) {\n",
       "    var mystring = string;\n",
       "\n",
       "    var count = 0;\n",
       "    var loc = mystring.search(/([^\\\\]|^)(\\$)/);\n",
       "\n",
       "    var count2 = 0;\n",
       "    var loc2 = mystring.search(/([^\\\\]|^)(\\$\\$)/);\n",
       "\n",
       "    //console.log(loc);\n",
       "\n",
       "    while ((loc >= 0) || (loc2 >= 0)) {\n",
       "\n",
       "        /* Have to replace all the double $$ first with current implementation */\n",
       "        if (loc2 >= 0) {\n",
       "            if (count2 % 2 == 0) {\n",
       "                mystring = mystring.replace(/([^\\\\]|^)(\\$\\$)/, \"$1\\\\[\");\n",
       "            } else {\n",
       "                mystring = mystring.replace(/([^\\\\]|^)(\\$\\$)/, \"$1\\\\]\");\n",
       "            }\n",
       "            count2++;\n",
       "        } else {\n",
       "            if (count % 2 == 0) {\n",
       "                mystring = mystring.replace(/([^\\\\]|^)(\\$)/, \"$1\\\\(\");\n",
       "            } else {\n",
       "                mystring = mystring.replace(/([^\\\\]|^)(\\$)/, \"$1\\\\)\");\n",
       "            }\n",
       "            count++;\n",
       "        }\n",
       "        loc = mystring.search(/([^\\\\]|^)(\\$)/);\n",
       "        loc2 = mystring.search(/([^\\\\]|^)(\\$\\$)/);\n",
       "        //console.log(mystring,\", loc:\",loc,\", loc2:\",loc2);\n",
       "    }\n",
       "\n",
       "    //console.log(mystring);\n",
       "    return mystring;\n",
       "}\n",
       "\n",
       "\n",
       "function show_questions(json, mydiv) {\n",
       "    console.log('show_questions');\n",
       "    //var mydiv=document.getElementById(myid);\n",
       "    var shuffle_questions = mydiv.dataset.shufflequestions;\n",
       "    var num_questions = mydiv.dataset.numquestions;\n",
       "    var shuffle_answers = mydiv.dataset.shuffleanswers;\n",
       "    var max_width = mydiv.dataset.maxwidth;\n",
       "\n",
       "    if (num_questions > json.length) {\n",
       "        num_questions = json.length;\n",
       "    }\n",
       "\n",
       "    var questions;\n",
       "    if ((num_questions < json.length) || (shuffle_questions == \"True\")) {\n",
       "        //console.log(num_questions+\",\"+json.length);\n",
       "        questions = getRandomSubarray(json, num_questions);\n",
       "    } else {\n",
       "        questions = json;\n",
       "    }\n",
       "\n",
       "    //console.log(\"SQ: \"+shuffle_questions+\", NQ: \" + num_questions + \", SA: \", shuffle_answers);\n",
       "\n",
       "    // Iterate over questions\n",
       "    questions.forEach((qa, index, array) => {\n",
       "        //console.log(qa.question); \n",
       "\n",
       "        var id = makeid(8);\n",
       "        //console.log(id);\n",
       "\n",
       "\n",
       "        // Create Div to contain question and answers\n",
       "        var iDiv = document.createElement('div');\n",
       "        //iDiv.id = 'quizWrap' + id + index;\n",
       "        iDiv.id = 'quizWrap' + id;\n",
       "        iDiv.className = 'Quiz';\n",
       "        iDiv.setAttribute('data-qnum', index);\n",
       "        iDiv.style.maxWidth  =max_width+\"px\";\n",
       "        mydiv.appendChild(iDiv);\n",
       "        // iDiv.innerHTML=qa.question;\n",
       "        \n",
       "        var outerqDiv = document.createElement('div');\n",
       "        outerqDiv.id = \"OuterquizQn\" + id + index;\n",
       "        // Create div to contain question part\n",
       "        var qDiv = document.createElement('div');\n",
       "        qDiv.id = \"quizQn\" + id + index;\n",
       "        \n",
       "        if (qa.question) {\n",
       "            iDiv.append(outerqDiv);\n",
       "\n",
       "            //qDiv.textContent=qa.question;\n",
       "            qDiv.innerHTML = jaxify(qa.question);\n",
       "            outerqDiv.append(qDiv);\n",
       "        }\n",
       "\n",
       "        // Create div for code inside question\n",
       "        var codeDiv;\n",
       "        if (\"code\" in qa) {\n",
       "            codeDiv = document.createElement('div');\n",
       "            codeDiv.id = \"code\" + id + index;\n",
       "            codeDiv.className = \"QuizCode\";\n",
       "            var codePre = document.createElement('pre');\n",
       "            codeDiv.append(codePre);\n",
       "            var codeCode = document.createElement('code');\n",
       "            codePre.append(codeCode);\n",
       "            codeCode.innerHTML = qa.code;\n",
       "            outerqDiv.append(codeDiv);\n",
       "            //console.log(codeDiv);\n",
       "        }\n",
       "\n",
       "\n",
       "        // Create div to contain answer part\n",
       "        var aDiv = document.createElement('div');\n",
       "        aDiv.id = \"quizAns\" + id + index;\n",
       "        aDiv.className = 'Answer';\n",
       "        iDiv.append(aDiv);\n",
       "\n",
       "        //console.log(qa.type);\n",
       "\n",
       "        var num_correct;\n",
       "        if ((qa.type == \"multiple_choice\") || (qa.type == \"many_choice\") ) {\n",
       "            num_correct = make_mc(qa, shuffle_answers, outerqDiv, qDiv, aDiv, id);\n",
       "            if (\"answer_cols\" in qa) {\n",
       "                //aDiv.style.gridTemplateColumns = 'auto '.repeat(qa.answer_cols);\n",
       "                aDiv.style.gridTemplateColumns = 'repeat(' + qa.answer_cols + ', 1fr)';\n",
       "            }\n",
       "        } else if (qa.type == \"numeric\") {\n",
       "            //console.log(\"numeric\");\n",
       "            make_numeric(qa, outerqDiv, qDiv, aDiv, id);\n",
       "        }\n",
       "\n",
       "\n",
       "        //Make div for feedback\n",
       "        var fb = document.createElement(\"div\");\n",
       "        fb.id = \"fb\" + id;\n",
       "        //fb.style=\"font-size: 20px;text-align:center;\";\n",
       "        fb.className = \"Feedback\";\n",
       "        fb.setAttribute(\"data-answeredcorrect\", 0);\n",
       "        fb.setAttribute(\"data-numcorrect\", num_correct);\n",
       "        iDiv.append(fb);\n",
       "\n",
       "\n",
       "    });\n",
       "    var preserveResponses = mydiv.dataset.preserveresponses;\n",
       "    console.log(preserveResponses);\n",
       "    console.log(preserveResponses == \"true\");\n",
       "    if (preserveResponses == \"true\") {\n",
       "        console.log(preserveResponses);\n",
       "        // Create Div to contain record of answers\n",
       "        var iDiv = document.createElement('div');\n",
       "        iDiv.id = 'responses' + mydiv.id;\n",
       "        iDiv.className = 'JCResponses';\n",
       "        // Create a place to store responses as an empty array\n",
       "        iDiv.setAttribute('data-responses', '[]');\n",
       "\n",
       "        // Dummy Text\n",
       "        iDiv.innerHTML=\"<b>Select your answers and then follow the directions that will appear here.</b>\"\n",
       "        //iDiv.className = 'Quiz';\n",
       "        mydiv.appendChild(iDiv);\n",
       "    }\n",
       "//console.log(\"At end of show_questions\");\n",
       "    if (typeof MathJax != 'undefined') {\n",
       "        console.log(\"MathJax version\", MathJax.version);\n",
       "        var version = MathJax.version;\n",
       "        setTimeout(function(){\n",
       "            var version = MathJax.version;\n",
       "            console.log('After sleep, MathJax version', version);\n",
       "            if (version[0] == \"2\") {\n",
       "                MathJax.Hub.Queue([\"Typeset\", MathJax.Hub]);\n",
       "            } else if (version[0] == \"3\") {\n",
       "                MathJax.typeset([mydiv]);\n",
       "            }\n",
       "        }, 500);\n",
       "if (typeof version == 'undefined') {\n",
       "        } else\n",
       "        {\n",
       "            if (version[0] == \"2\") {\n",
       "                MathJax.Hub.Queue([\"Typeset\", MathJax.Hub]);\n",
       "            } else if (version[0] == \"3\") {\n",
       "                MathJax.typeset([mydiv]);\n",
       "            } else {\n",
       "                console.log(\"MathJax not found\");\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "    return false;\n",
       "}\n",
       "/* This is to handle asynchrony issues in loading Jupyter notebooks\n",
       "           where the quiz has been previously run. The Javascript was generally\n",
       "           being run before the div was added to the DOM. I tried to do this\n",
       "           more elegantly using Mutation Observer, but I didn't get it to work.\n",
       "\n",
       "           Someone more knowledgeable could make this better ;-) */\n",
       "\n",
       "        function try_show() {\n",
       "          if(document.getElementById(\"YtRottUUXPPU\")) {\n",
       "            show_questions(questionsYtRottUUXPPU,  YtRottUUXPPU); \n",
       "          } else {\n",
       "             setTimeout(try_show, 200);\n",
       "          }\n",
       "        };\n",
       "    \n",
       "        {\n",
       "        // console.log(element);\n",
       "\n",
       "        //console.log(\"YtRottUUXPPU\");\n",
       "        // console.log(document.getElementById(\"YtRottUUXPPU\"));\n",
       "\n",
       "        try_show();\n",
       "        }\n",
       "        "
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display_quiz(\"examples3.json\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "MgArG2NQjaM3"
   },
   "source": [
    "## Conclusion\n",
    "\n",
    "You have now learned what clustering means, what the different types of clustering are, how to cluster a given dataset using the k-means algorithm, how to use various methods for determining the optimal number of clusters K, and finally, how to do a basic analysis of the resulting clusters."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Appendix \n",
    "A link to an additional resource to help with the understanding of the concepts presented in this train. \n",
    "\n",
    "> - [How to choose the number of clusters K?](http://www2.stat.duke.edu/~rcs46/lectures_2017/10-unsupervise/10-specify-clusters.pdf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#  \n",
    "\n",
    "<div align=\"center\" style=\" font-size: 80%; text-align: center; margin: 0 auto\">\n",
    "<img src=\"https://raw.githubusercontent.com/Explore-AI/Pictures/master/ExploreAI_logos/EAI_Blue_Dark.png\"  style=\"width:200px\";/>\n",
    "</div>"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "name": "12_kmeans_clustering.ipynb",
   "provenance": []
  },
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.4"
  }
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 "nbformat": 4,
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}