PCA.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Iris dataset (150 iris flowers from 3 different specifes/classes)\n",
    "- classes (3): setosa (n=50), veriscolor (n=50), virginica (n=50)\n",
    "- features (4): sepal length, sepal width, petal length, petal width\n",
    "\n",
    "other examples: https://jakevdp.github.io/PythonDataScienceHandbook/05.09-principal-component-analysis.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sepal_len</th>\n",
       "      <th>sepal_wid</th>\n",
       "      <th>petal_len</th>\n",
       "      <th>petal_wid</th>\n",
       "      <th>class</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>145</th>\n",
       "      <td>6.7</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.2</td>\n",
       "      <td>2.3</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>146</th>\n",
       "      <td>6.3</td>\n",
       "      <td>2.5</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.9</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>147</th>\n",
       "      <td>6.5</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.2</td>\n",
       "      <td>2.0</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>148</th>\n",
       "      <td>6.2</td>\n",
       "      <td>3.4</td>\n",
       "      <td>5.4</td>\n",
       "      <td>2.3</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>149</th>\n",
       "      <td>5.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.1</td>\n",
       "      <td>1.8</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     sepal_len  sepal_wid  petal_len  petal_wid           class\n",
       "145        6.7        3.0        5.2        2.3  Iris-virginica\n",
       "146        6.3        2.5        5.0        1.9  Iris-virginica\n",
       "147        6.5        3.0        5.2        2.0  Iris-virginica\n",
       "148        6.2        3.4        5.4        2.3  Iris-virginica\n",
       "149        5.9        3.0        5.1        1.8  Iris-virginica"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv(filepath_or_buffer='https://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data', \n",
    "                 header=None, sep=',')\n",
    "df.columns = ['sepal_len','sepal_wid','petal_len','petal_wid','class']\n",
    "df.dropna(how=\"all\",inplace=True) #drops the empty line at file-end\n",
    "df.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### split data table into data X and class labels Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = df.iloc[:,0:4].values\n",
    "y = df.iloc[:,4].values"
   ]
  },
  {
   "attachments": {
    "Screen%20Shot%202018-01-31%20at%2010.46.20%20PM.png": {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### our iris dataset is now stored in form of a 150x4 matrix. Each sample row, x, can be pictured as a 4-d vector.\n",
    "![Screen%20Shot%202018-01-31%20at%2010.46.20%20PM.png](attachment:Screen%20Shot%202018-01-31%20at%2010.46.20%20PM.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#standardize\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "X_std = StandardScaler().fit_transform(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.52237162, -0.37231836,  0.72101681,  0.26199559],\n",
       "       [ 0.26335492, -0.92555649, -0.24203288, -0.12413481],\n",
       "       [-0.58125401, -0.02109478, -0.14089226, -0.80115427],\n",
       "       [-0.56561105, -0.06541577, -0.6338014 ,  0.52354627]])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#singular vector decomposition (SVD) -- improves computational effeciency\n",
    "u,s,v = np.linalg.svd(X_std.T)\n",
    "u"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Components:\n",
      " [[ 0.52237162 -0.26335492  0.58125401  0.56561105]\n",
      " [ 0.37231836  0.92555649  0.02109478  0.06541577]\n",
      " [-0.72101681  0.24203288  0.14089226  0.6338014 ]\n",
      " [-0.26199559  0.12413481  0.80115427 -0.52354627]]\n",
      "Explained Variance:\n",
      " [ 2.91081808  0.92122093  0.14735328  0.02060771]\n"
     ]
    },
    {
     "data": {
      "image/png": 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4dxFJAa0WDHe/DigC/kRwtdRqM/tVsoNJajlYXcudTy1lzIDufGlSYdxxRCQJIh0tuHuN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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11715f3c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "pca = PCA(n_components=4)\n",
    "Y = pca.fit_transform(X_std)\n",
    "print(\"Components:\\n\", pca.components_)\n",
    "print(\"Explained Variance:\\n\",pca.explained_variance_)\n",
    "plt.plot(np.cumsum(pca.explained_variance_ratio_))\n",
    "plt.xlabel('number of components')\n",
    "plt.ylabel('cumulative explained variance');"
   ]
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    "- PCA's main weakness is that it tends to be highly affected by outliers in the data. For this reason, many robust variants of PCA have been developed, many of which act to iteratively discard data points that are poorly described by the initial components. Scikit-Learn contains a couple interesting variants on PCA, including RandomizedPCA and SparsePCA, both also in the sklearn.decomposition submodule."
   ]
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   "execution_count": null,
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