Page_Rank_and_Recommendation_Systems.ipynb

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      "source": [
        "\n",
        "# DMT 2022 - Homework 2"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3ltMqfS1ph7q"
      },
      "source": [
        "\n",
        "# Homework"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MUsht5bRM9iT"
      },
      "source": [
        "The homework consists of two parts:\n",
        "\n",
        "  1. PageRank\n",
        "\n",
        "  and\n",
        "\n",
        "  2. Recommendation System\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZdyeR5JdyCki"
      },
      "source": [
        "# Group composition:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "g3zOpW7YyMlr"
      },
      "source": [
        "\n",
        "D'Erasmo, Giulio, 1859130\n",
        "\n",
        "Potì, Andrea, 2008416"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KCoIbBZcrYRH"
      },
      "source": [
        "# Part 1: PageRank\n",
        "In this part of the homework, you have to deal with the PageRank algorithm."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IxkmPDaWrYRM"
      },
      "source": [
        "## Part 1.0\n",
        "Import **ALL** the Python packages that you need for Part 1."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
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        },
        "id": "GTVP9OLGrYRN",
        "outputId": "516d0e9a-fc1b-4290-e3d4-2b2b81dd620c"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Requirement already satisfied: scikit-network in /usr/local/lib/python3.7/dist-packages (0.26.0)\n",
            "Requirement already satisfied: scipy>=1.6.3 in /usr/local/lib/python3.7/dist-packages (from scikit-network) (1.7.3)\n",
            "Requirement already satisfied: numpy>=1.21.5 in /usr/local/lib/python3.7/dist-packages (from scikit-network) (1.21.6)\n"
          ]
        }
      ],
      "source": [
        "#REMOVE_OUTPUT#\n",
        "#YOUR CODE STARTS HERE#\n",
        "!pip install scikit-network\n",
        "from sknetwork.ranking import PageRank\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "\n",
        "\n",
        "#YOUR CODE ENDS HERE#\n",
        "#THIS IS LINE 10#"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qyULCTYnrYRO"
      },
      "source": [
        "## Part 1.1\n",
        "Using the provided dataset, you must run various PageRank algorithms.\n",
        "The dataset for this part is an unweighted and undirected graph, where nodes represent characters from the \"Harry Potter\" books and an edge connects two characters in the graph if their names appeared at least one time within 14 words of one another in at least one of the books."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZarHAE1mrYRO"
      },
      "source": [
        "### 1.1.1\n",
        "Download the dataset from the Drive link (code already provided). "
      ]
    },
    {
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      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Requirement already satisfied: gdown in /usr/local/lib/python3.7/dist-packages (4.4.0)\n",
            "Requirement already satisfied: tqdm in /usr/local/lib/python3.7/dist-packages (from gdown) (4.64.0)\n",
            "Requirement already satisfied: requests[socks] in /usr/local/lib/python3.7/dist-packages (from gdown) (2.23.0)\n",
            "Requirement already satisfied: filelock in /usr/local/lib/python3.7/dist-packages (from gdown) (3.7.0)\n",
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            "Requirement already satisfied: six in /usr/local/lib/python3.7/dist-packages (from gdown) (1.15.0)\n",
            "Requirement already satisfied: chardet<4,>=3.0.2 in /usr/local/lib/python3.7/dist-packages (from requests[socks]->gdown) (3.0.4)\n",
            "Requirement already satisfied: certifi>=2017.4.17 in /usr/local/lib/python3.7/dist-packages (from requests[socks]->gdown) (2021.10.8)\n",
            "Requirement already satisfied: urllib3!=1.25.0,!=1.25.1,<1.26,>=1.21.1 in /usr/local/lib/python3.7/dist-packages (from requests[socks]->gdown) (1.24.3)\n",
            "Requirement already satisfied: idna<3,>=2.5 in /usr/local/lib/python3.7/dist-packages (from requests[socks]->gdown) (2.10)\n",
            "Requirement already satisfied: PySocks!=1.5.7,>=1.5.6 in /usr/local/lib/python3.7/dist-packages (from requests[socks]->gdown) (1.7.1)\n"
          ]
        }
      ],
      "source": [
        "#REMOVE_OUTPUT#\n",
        "!pip install --upgrade --no-cache-dir gdown"
      ]
    },
    {
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      "execution_count": null,
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      "outputs": [
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          "text": [
            "Downloading...\n",
            "From: https://drive.google.com/uc?id=11Fa9zqDPgDthm3B84My1flWN6r-ffpY0\n",
            "To: /content/harry_potter_graph1.csv\n",
            "\r  0% 0.00/11.7k [00:00<?, ?B/s]\r100% 11.7k/11.7k [00:00<00:00, 15.1MB/s]\n"
          ]
        }
      ],
      "source": [
        "#REMOVE_OUTPUT#\n",
        "!gdown 11Fa9zqDPgDthm3B84My1flWN6r-ffpY0 #download harry_potter_graph1.csv"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Lr71odinrYRQ"
      },
      "source": [
        "### 1.1.2\n",
        "Load and inspect the dataset: print the list of field names of the dataset and also the total number of rows.\n",
        "\n",
        "Print also the first and last row of the dataset."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "2nQMJWxYrYRQ",
        "outputId": "d76331b9-8db9-437e-f7cc-a710ed78a8a1"
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      "outputs": [
        {
          "output_type": "stream",
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          "text": [
            "  Harry Potter dataset Field names\n",
            "0                      character_1\n",
            "1                      character_2\n",
            "\n",
            "The number of row of the dataset are:  406\n",
            "\n",
            "First row:\n",
            "character_1     Katie Bell\n",
            "character_2    Oliver Wood\n",
            "Name: 0, dtype: object\n",
            "\n",
            "Last row:\n",
            "character_1           Mrs Norris\n",
            "character_2    Quirinus Quirrell\n",
            "Name: 405, dtype: object\n"
          ]
        }
      ],
      "source": [
        "#YOUR CODE STARTS HERE#\n",
        "# import the dataset\n",
        "Harry_Potter_graph = pd.read_csv('/content/harry_potter_graph1.csv')\n",
        "\n",
        "# print the dataset field names\n",
        "dataset_field = list(Harry_Potter_graph.columns) \n",
        "nice_print = pd.DataFrame( dataset_field )\n",
        "nice_print.rename(columns = {0: 'Harry Potter dataset Field names'}, inplace = True)\n",
        "print(nice_print)\n",
        "print()\n",
        "\n",
        "# print of the number of row\n",
        "print(\"The number of row of the dataset are: \", Harry_Potter_graph.shape[0])\n",
        "print()\n",
        "# print of the first and last row of the dataset\n",
        "print(f\"First row:\\n{Harry_Potter_graph.iloc[0]}\")\n",
        "print()\n",
        "print(f\"Last row:\\n{Harry_Potter_graph.iloc[-1]}\")\n",
        "#YOUR CODE ENDS HERE#\n",
        "#THIS IS LINE 20#"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "S3F_8xyFrYRR"
      },
      "source": [
        "### 1.1.3\n",
        "Print the sorted list of all character names (without duplicates) in ascending alphabetical order.\n",
        "\n",
        "Print also the length of this list."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
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        "id": "NZGG5YKHrYRR",
        "outputId": "4317f5a3-5124-485e-e38e-afcae8fa15b4"
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      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "List of character in the Harry Potter Graph 1:\n",
            "Adalbert Waffling\n",
            "Adrian Pucey\n",
            "Alberic Grunnion\n",
            "Albus Dumbledore\n",
            "Algie Longbottom\n",
            "Alicia Spinnet\n",
            "Angelina Johnson\n",
            "Arabella Figg\n",
            "Argus Filch\n",
            "Arsenius Jigger\n",
            "Bane\n",
            "Bathilda Bagshot\n",
            "Bertie Bott\n",
            "Blaise Zabini\n",
            "Bloody Baron\n",
            "Boa constrictor at the Zoo\n",
            "Circe\n",
            "Cliodna\n",
            "Cornelius Agrippa\n",
            "Cornelius Fudge\n",
            "Cuthbert Binns\n",
            "Dean Thomas\n",
            "Dedalus Diggle\n",
            "Dennis\n",
            "Doris Crockford\n",
            "Draco Malfoy\n",
            "Dudley Dursley\n",
            "Elfric the Eager\n",
            "Emeric Switch\n",
            "Emeric the Evil\n",
            "Enid (disambiguation)\n",
            "Fang\n",
            "Fat Friar\n",
            "Fat Lady\n",
            "Filius Flitwick\n",
            "Firenze\n",
            "Fluffy\n",
            "Fred Weasley\n",
            "Garrick Ollivander\n",
            "Gellert Grindelwald\n",
            "George Weasley\n",
            "Gordon\n",
            "Gregory Goyle\n",
            "Gregory the Smarmy\n",
            "Gringotts Head Goblin\n",
            "Griphook\n",
            "Hannah Abbott\n",
            "Harry Potter\n",
            "Hedwig\n",
            "Helena Ravenclaw\n",
            "Hengist of Woodcroft\n",
            "Hermione Granger\n",
            "Irma Pince\n",
            "James Potter I\n",
            "Jim McGuffin\n",
            "Justin Finch-Fletchley\n",
            "Katie Bell\n",
            "Keeper of the reptile house\n",
            "Lavender Brown\n",
            "Lee Jordan\n",
            "Lily J. Potter\n",
            "Lily Moon\n",
            "Lisa Turpin\n",
            "Malcolm\n",
            "Mandy Brocklehurst\n",
            "Marcus Flint\n",
            "Merlin\n",
            "Miles Bletchley\n",
            "Millicent Bulstrode\n",
            "Minerva McGonagall\n",
            "Miranda Goshawk\n",
            "Morag MacDougal\n",
            "Mr Paws\n",
            "Mr Tibbles\n",
            "Mrs Norris\n",
            "Neville Longbottom\n",
            "Newton Scamander\n",
            "Nicholas de Mimsy-Porpington\n",
            "Nicolas Flamel\n",
            "Oliver Wood\n",
            "Owner of the Railview Hotel\n",
            "Padma Patil\n",
            "Pansy Parkinson\n",
            "Parvati Patil\n",
            "Peeves\n",
            "Percy Weasley\n",
            "Perenelle Flamel\n",
            "Petunia Dursley\n",
            "Phyllida Spore\n",
            "Piers Polkiss\n",
            "Pomona Sprout\n",
            "Poppy Pomfrey\n",
            "Ptolemy\n",
            "Quentin Trimble\n",
            "Quirinus Quirrell\n",
            "Rolanda Hooch\n",
            "Ronald Weasley\n",
            "Ronan\n",
            "Rubeus Hagrid\n",
            "Sally-Anne Perks\n",
            "Seamus Finnigan\n",
            "Severus Snape\n",
            "Sirius Black\n",
            "Snowy\n",
            "Sorting Hat\n",
            "Susan Bones\n",
            "Ted\n",
            "Terence Higgs\n",
            "Terry Boot\n",
            "Theodore Nott\n",
            "Tom\n",
            "Trevor\n",
            "Tufty\n",
            "Unicorn\n",
            "Uric the Oddball\n",
            "Vernon Dursley\n",
            "Vincent Crabbe\n",
            "Vindictus Viridian\n",
            "Yvonne\n",
            "\n",
            "The total number of character are:  119\n"
          ]
        }
      ],
      "source": [
        "#YOUR CODE STARTS HERE#\n",
        "# Flatten the dataset and take the unique value\n",
        "character_names_list = sorted(pd.unique(Harry_Potter_graph.to_numpy().flatten()))\n",
        "print(\"List of character in the Harry Potter Graph 1:\")\n",
        "for char in character_names_list:\n",
        "  print(char)\n",
        "print()\n",
        "n = len(character_names_list)\n",
        "print(\"The total number of character are: \", n)\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "#YOUR CODE ENDS HERE#\n",
        "#THIS IS LINE 20#"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ExTNrAB0rYRR"
      },
      "source": [
        "### 1.1.4\n",
        "Create the adjacency matrix for the graph, assigning to each character a node identifier equal to the index that the character name has in ascending alphabetical order (remember that the first element of a list in Python has index 0)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Vqb_1UZwrYRS"
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      "outputs": [],
      "source": [
        "#YOUR CODE STARTS HERE#\n",
        "# dictiory that map id to character name\n",
        "map_character_id_character_name = {i: x for i,x in enumerate(character_names_list)}\n",
        "# reverse of the previous dictionary\n",
        "map_character_name_character_id = {x: i for i,x in enumerate(character_names_list)}\n",
        "\n",
        "# construct the Adjancy matrix\n",
        "adj = pd.crosstab(Harry_Potter_graph.character_1, Harry_Potter_graph.character_2)\n",
        "idx = character_names_list\n",
        "adj = adj.reindex(index = idx, columns=idx, fill_value=0)\n",
        "adj = adj + np.transpose(adj)\n",
        "\n",
        "adj_of_Harry_Potter_graph = adj.to_numpy()\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "#YOUR CODE ENDS HERE#\n",
        "#THIS IS LINE 20#"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lDMyeP1hrYRS"
      },
      "source": [
        "### 1.1.5\n",
        "Compute the PageRank vector for the obtained graph using a damping factor of 0.8."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "FF4p5lEHrYRT"
      },
      "outputs": [],
      "source": [
        "#YOUR CODE STARTS HERE#\n",
        "# Set the parameters for the PageRank computation\n",
        "alpha = 0.2\n",
        "damping_factor = 1. - alpha\n",
        "\n",
        "# PageRank\n",
        "pagerank = PageRank(damping_factor=damping_factor, solver=\"piteration\", \n",
        "                    n_iter=1000, tol=10**-6)\n",
        "\n",
        "# Compute Page-Rank on the entire Harry Potter graph\n",
        "pagerank_vector = pagerank.fit_transform(adj_of_Harry_Potter_graph)\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "#YOUR CODE ENDS HERE#\n",
        "#THIS IS LINE 20#"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_1ad6G92-mzf"
      },
      "source": [
        "Print the name and the PageRank score of the top-10 characters according to the PageRank score of their associated nodes."
      ]
    },
    {
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              "       Character name  Pagerank score\n",
              "0        Harry Potter        0.091486\n",
              "1      Ronald Weasley        0.037713\n",
              "2       Rubeus Hagrid        0.034323\n",
              "3    Hermione Granger        0.029205\n",
              "4    Albus Dumbledore        0.026936\n",
              "5        Draco Malfoy        0.022058\n",
              "6  Neville Longbottom        0.021599\n",
              "7       Severus Snape        0.021282\n",
              "8      Dudley Dursley        0.018598\n",
              "9      Vernon Dursley        0.015355"
            ],
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              "      <td>Harry Potter</td>\n",
              "      <td>0.091486</td>\n",
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              "      <td>Ronald Weasley</td>\n",
              "      <td>0.037713</td>\n",
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              "      <td>Rubeus Hagrid</td>\n",
              "      <td>0.034323</td>\n",
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              "      <td>Hermione Granger</td>\n",
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              "      <td>0.022058</td>\n",
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              "      <td>Neville Longbottom</td>\n",
              "      <td>0.021599</td>\n",
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              "      <td>Severus Snape</td>\n",
              "      <td>0.021282</td>\n",
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              "      <td>Dudley Dursley</td>\n",
              "      <td>0.018598</td>\n",
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              "      <th>9</th>\n",
              "      <td>Vernon Dursley</td>\n",
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              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-2557bbf8-5387-40bf-b23c-251aa0bec12f button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-2557bbf8-5387-40bf-b23c-251aa0bec12f');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {}
        }
      ],
      "source": [
        "#YOUR CODE STARTS HERE#\n",
        "k = 10\n",
        "ind = np.argpartition(pagerank_vector, -k)[-k:]\n",
        "ind  = ind[np.argsort(pagerank_vector[ind])][::-1]\n",
        "top_10 = [(map_character_id_character_name[x], np.round(pagerank_vector[x],6)) for x in ind]\n",
        "\n",
        "display(pd.DataFrame(top_10, columns = ['Character name', 'Pagerank score']))\n",
        "\n",
        "#YOUR CODE ENDS HERE#\n",
        "#THIS IS LINE 10#"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DcxLpyBq-ygQ"
      },
      "source": [
        "### 1.1.6\n",
        "Compute the Topic-specific PageRank vector for the obtained graph using a damping factor of 0.9, by considering as topic the Weasley family: a character belongs to the topic if its name contains the string `Weasley`."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "1cj7Gn9O-ygg"
      },
      "outputs": [],
      "source": [
        "#YOUR CODE STARTS HERE#\n",
        "# Set the parameters for the PageRank computation\n",
        "alpha = 0.1\n",
        "damping_factor = 1. - alpha\n",
        "\n",
        "set_of_character_ids_belonging_to_Weasley_family = [pair[0] for pair in map_character_id_character_name.items() if 'Weasley' in pair[1]]\n",
        "\n",
        "pagerank = PageRank(damping_factor=damping_factor, solver=\"piteration\",\n",
        "                      n_iter=1000, tol=10 ** -6)\n",
        "# define the topic as probability distribution over all pages.\n",
        "topic_as_map__character_id__landing_probability = {}\n",
        "num_characters_belonging_to_the_topic = len(set_of_character_ids_belonging_to_Weasley_family)\n",
        "for c_character_id_belonging_to_Weasley_family in set_of_character_ids_belonging_to_Weasley_family:\n",
        "    topic_as_map__character_id__landing_probability[c_character_id_belonging_to_Weasley_family] = 1. / num_characters_belonging_to_the_topic\n",
        "\n",
        "# Compute Page-Rank on the entire WIKIPEDIA graph\n",
        "pagerank_vector = pagerank.fit_transform(adj_of_Harry_Potter_graph,\n",
        "                                        seeds=topic_as_map__character_id__landing_probability)\n",
        "#YOUR CODE ENDS HERE#\n",
        "#THIS IS LINE 20#"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rW5fzpmE-ygj"
      },
      "source": [
        "Print the name and the PageRank score of the top-20 characters according to the Topic-specific PageRank score of their associated nodes."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 676
        },
        "id": "xcH9NXMY-ygj",
        "outputId": "a4260021-a409-4a5d-87f2-05039a882d2d"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "        Character name  Pagerank score\n",
              "0         Harry Potter        0.086388\n",
              "1       Ronald Weasley        0.075632\n",
              "2         Fred Weasley        0.048802\n",
              "3        Percy Weasley        0.048195\n",
              "4       George Weasley        0.044858\n",
              "5        Rubeus Hagrid        0.041669\n",
              "6     Hermione Granger        0.040929\n",
              "7        Severus Snape        0.031772\n",
              "8     Albus Dumbledore        0.030667\n",
              "9   Neville Longbottom        0.028557\n",
              "10        Draco Malfoy        0.028119\n",
              "11         Argus Filch        0.018016\n",
              "12   Quirinus Quirrell        0.017652\n",
              "13     Filius Flitwick        0.016014\n",
              "14       Rolanda Hooch        0.015329\n",
              "15         Oliver Wood        0.013815\n",
              "16       Poppy Pomfrey        0.013284\n",
              "17              Peeves        0.013125\n",
              "18      Vernon Dursley        0.012436\n",
              "19     Seamus Finnigan        0.012068"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-05ba7725-ea99-4001-8789-c3de423394ea\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
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              "    .dataframe tbody tr th {\n",
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              "\n",
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              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Character name</th>\n",
              "      <th>Pagerank score</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>Harry Potter</td>\n",
              "      <td>0.086388</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>Ronald Weasley</td>\n",
              "      <td>0.075632</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>Fred Weasley</td>\n",
              "      <td>0.048802</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>Percy Weasley</td>\n",
              "      <td>0.048195</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>George Weasley</td>\n",
              "      <td>0.044858</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>Rubeus Hagrid</td>\n",
              "      <td>0.041669</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>Hermione Granger</td>\n",
              "      <td>0.040929</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>Severus Snape</td>\n",
              "      <td>0.031772</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>Albus Dumbledore</td>\n",
              "      <td>0.030667</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>Neville Longbottom</td>\n",
              "      <td>0.028557</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>Draco Malfoy</td>\n",
              "      <td>0.028119</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>Argus Filch</td>\n",
              "      <td>0.018016</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>Quirinus Quirrell</td>\n",
              "      <td>0.017652</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>Filius Flitwick</td>\n",
              "      <td>0.016014</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td>Rolanda Hooch</td>\n",
              "      <td>0.015329</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>15</th>\n",
              "      <td>Oliver Wood</td>\n",
              "      <td>0.013815</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>16</th>\n",
              "      <td>Poppy Pomfrey</td>\n",
              "      <td>0.013284</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>17</th>\n",
              "      <td>Peeves</td>\n",
              "      <td>0.013125</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>18</th>\n",
              "      <td>Vernon Dursley</td>\n",
              "      <td>0.012436</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>19</th>\n",
              "      <td>Seamus Finnigan</td>\n",
              "      <td>0.012068</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-05ba7725-ea99-4001-8789-c3de423394ea')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
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              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
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              "      fill: #1967D2;\n",
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              "    .colab-df-convert:hover {\n",
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              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
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              "      fill: #FFFFFF;\n",
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              "  </style>\n",
              "\n",
              "      <script>\n",
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              "          document.querySelector('#df-05ba7725-ea99-4001-8789-c3de423394ea button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-05ba7725-ea99-4001-8789-c3de423394ea');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {}
        }
      ],
      "source": [
        "#YOUR CODE STARTS HERE#\n",
        "k = 20\n",
        "ind = np.argpartition(pagerank_vector, -k)[-k:]\n",
        "ind  = ind[np.argsort(pagerank_vector[ind])][::-1]\n",
        "top_20 = [(map_character_id_character_name[x], np.round(pagerank_vector[x],6)) for x in ind]\n",
        "\n",
        "display(pd.DataFrame(top_20, columns = ['Character name', 'Pagerank score']))\n",
        "\n",
        "#YOUR CODE ENDS HERE#\n",
        "#THIS IS LINE 10#"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hWVFUOX1-y4k"
      },
      "source": [
        "### 1.1.7\n",
        "Compute the Personalized PageRank vector for the obtained graph using a damping factor of 0.1 for each of the *Hogwarts professors*: Albus Dumbledore, Filius Flitwick, Firenze, Minerva McGonagall, Pomona Sprout, Quirinus Quirrell, Rolanda Hooch, Severus Snape."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "BTMKagGW-y4l"
      },
      "outputs": [],
      "source": [
        "#YOUR CODE STARTS HERE#\n",
        "# Set the parameters for the PageRank computation\n",
        "alpha = 0.9\n",
        "damping_factor = 1. - alpha\n",
        "\n",
        "Professors = ['Albus Dumbledore', 'Filius Flitwick', 'Firenze', 'Minerva McGonagall', \n",
        "              'Pomona Sprout', 'Quirinus Quirrell', 'Rolanda Hooch', 'Severus Snape']\n",
        "pagerank_vectors = []\n",
        "\n",
        "for professor in Professors:\n",
        "  professor_id = map_character_name_character_id[professor]\n",
        "  # personalize PageRank\n",
        "  pagerank = PageRank(damping_factor=damping_factor, solver=\"piteration\", \n",
        "                    n_iter=1000, tol=10 ** -6)\n",
        "  # define the topic as probability distribution over all pages.\n",
        "  map__character_id__landing_probability = {}\n",
        "  map__character_id__landing_probability[professor_id] = 1.\n",
        "  # Compute Page-Rank on the entire Harry Potter Graph 1\n",
        "  pagerank_vector = pagerank.fit_transform(adj_of_Harry_Potter_graph,\n",
        "                                        seeds=map__character_id__landing_probability)\n",
        "  pagerank_vectors.append(pagerank_vector)\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "#YOUR CODE ENDS HERE#\n",
        "#THIS IS LINE 30#"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yh1B87tu-y4m"
      },
      "source": [
        "For each of the *Hogwarts professors*, print the name and the PageRank score of the top-3 characters according to the Personalized PageRank score of their associated nodes."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "A6tPqQ2F-y4m",
        "outputId": "84e41696-06e1-44fa-9431-de82fc4f75f0"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Pagerank for Professor Albus Dumbledore\n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "     Character name  Pagerank score\n",
              "0  Albus Dumbledore        0.901642\n",
              "1      Harry Potter        0.004358\n",
              "2     Rubeus Hagrid        0.004001"
            ],
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              "\n",
              "  <div id=\"df-525bb2e0-6c84-4ce3-aab8-158d9ea8775c\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <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",
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              "\n",
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              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Character name</th>\n",
              "      <th>Pagerank score</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>Albus Dumbledore</td>\n",
              "      <td>0.901642</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>Harry Potter</td>\n",
              "      <td>0.004358</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>Rubeus Hagrid</td>\n",
              "      <td>0.004001</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-525bb2e0-6c84-4ce3-aab8-158d9ea8775c')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
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            "-----------------------------\n",
            "Pagerank for Professor Filius Flitwick\n",
            "\n"
          ]
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              "    Character name  Pagerank score\n",
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            "-----------------------------\n",
            "Pagerank for Professor Firenze\n",
            "\n"
          ]
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              "  Character name  Pagerank score\n",
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            "-----------------------------\n",
            "Pagerank for Professor Minerva McGonagall\n",
            "\n"
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              "       Character name  Pagerank score\n",
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            "-----------------------------\n",
            "Pagerank for Professor Pomona Sprout\n",
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              "  Character name  Pagerank score\n",
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            "-----------------------------\n",
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              "      Character name  Pagerank score\n",
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            "-----------------------------\n",
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              "  Character name  Pagerank score\n",
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            "-----------------------------\n",
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            "\n"
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              "   Character name  Pagerank score\n",
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              "    }\n",
              "  </style>\n",
              "\n",
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              "          document.querySelector('#df-c49058fb-87cb-4c98-a00f-13afa2d3b3dc button.colab-df-convert');\n",
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              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-c49058fb-87cb-4c98-a00f-13afa2d3b3dc');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
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              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "-----------------------------\n"
          ]
        }
      ],
      "source": [
        "#YOUR CODE STARTS HERE#\n",
        "k = 3\n",
        "top_3_at_Professors = []\n",
        "\n",
        "for i in range(len(Professors)):\n",
        "  # fix the pagerank vector\n",
        "  pagerank_vector = pagerank_vectors[i]\n",
        "  ind = np.argpartition(pagerank_vector, -k)[-k:]\n",
        "  ind  = ind[np.argsort(pagerank_vector[ind])][::-1]\n",
        "  top_3_at_Professors.append(\n",
        "      [(map_character_id_character_name[x], np.round(pagerank_vector[x],6)) for x in ind]\n",
        "  )\n",
        "\n",
        "for i,prof in enumerate(Professors):\n",
        "  print(\"Pagerank for Professor\", prof)\n",
        "  print()\n",
        "  display(pd.DataFrame(top_3_at_Professors[i], columns = ['Character name', 'Pagerank score']))\n",
        "  print(\"-----------------------------\")\n",
        "#YOUR CODE ENDS HERE#\n",
        "#THIS IS LINE 20#"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZTo5DrCICbkA"
      },
      "source": [
        "### 1.1.8\n",
        "Compute Topic-specific PageRank for the obtained graph using a damping factor of 0.1. Imagine you are in an **online** context.\n",
        "\n",
        "The Topic is the Hogwarts professors (list of characters define in step 1.1.7)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "7d4q8tO-CbkG"
      },
      "outputs": [],
      "source": [
        "#YOUR CODE STARTS HERE#\n",
        "list__map__character_id__PersonalizedPageRank_score = []\n",
        "for pagerank_vector in pagerank_vectors:\n",
        "  list__map__character_id__PersonalizedPageRank_score.append({i: x for i,x in enumerate(pagerank_vector)})\n",
        "\n",
        "aggregated_map__character_id__PersonalizedPageRank_score = {}\n",
        "n = len(list__map__character_id__PersonalizedPageRank_score)\n",
        "for map__character_id__PersonalizedPageRank_score in list__map__character_id__PersonalizedPageRank_score:\n",
        "    for character_id, PersonalizedPageRank_score in map__character_id__PersonalizedPageRank_score.items():\n",
        "        if character_id not in aggregated_map__character_id__PersonalizedPageRank_score:\n",
        "            aggregated_map__character_id__PersonalizedPageRank_score[character_id] = 0.\n",
        "        aggregated_map__character_id__PersonalizedPageRank_score[character_id] += PersonalizedPageRank_score / n\n",
        "\n",
        "list__aggregated_map__character_id__PersonalizedPageRank_score = list(\n",
        "    aggregated_map__character_id__PersonalizedPageRank_score.items())\n",
        "\n",
        "\n",
        "\n",
        "#YOUR CODE ENDS HERE#\n",
        "#THIS IS LINE 20#"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7O_C-Ig4CbkH"
      },
      "source": [
        "Print the name and the PageRank score of the top-10 characters according to the Topic-specific PageRank score of their associated nodes."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 363
        },
        "id": "yzJNQ7RqCbkI",
        "outputId": "24e78839-4c58-4017-cfee-58023aa9fec9"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "       Character name  Pagerank score\n",
              "0    Albus Dumbledore        0.116429\n",
              "1     Filius Flitwick        0.116061\n",
              "2       Severus Snape        0.114937\n",
              "3   Quirinus Quirrell        0.113734\n",
              "4       Pomona Sprout        0.113486\n",
              "5             Firenze        0.113058\n",
              "6       Rolanda Hooch        0.112675\n",
              "7  Minerva McGonagall        0.112525\n",
              "8        Harry Potter        0.020649\n",
              "9       Rubeus Hagrid        0.008062"
            ],
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              "\n",
              "  <div id=\"df-3eaf85fd-936d-4b16-b1a5-d9c2406f06a2\">\n",
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              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Character name</th>\n",
              "      <th>Pagerank score</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>Albus Dumbledore</td>\n",
              "      <td>0.116429</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>Filius Flitwick</td>\n",
              "      <td>0.116061</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>Severus Snape</td>\n",
              "      <td>0.114937</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>Quirinus Quirrell</td>\n",
              "      <td>0.113734</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>Pomona Sprout</td>\n",
              "      <td>0.113486</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>Firenze</td>\n",
              "      <td>0.113058</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>Rolanda Hooch</td>\n",
              "      <td>0.112675</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>Minerva McGonagall</td>\n",
              "      <td>0.112525</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>Harry Potter</td>\n",
              "      <td>0.020649</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>Rubeus Hagrid</td>\n",
              "      <td>0.008062</td>\n",
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              "  </tbody>\n",
              "</table>\n",
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              "\n",
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              "          const element = document.querySelector('#df-3eaf85fd-936d-4b16-b1a5-d9c2406f06a2');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
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              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
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              "    </div>\n",
              "  </div>\n",
              "  "
            ]
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          "metadata": {}
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      ],
      "source": [
        "#YOUR CODE STARTS HERE#\n",
        "k = 10\n",
        "Aggregate_PageRank_score = np.array([x[1] for x in list__aggregated_map__character_id__PersonalizedPageRank_score])\n",
        "ind = np.argpartition(Aggregate_PageRank_score, -k)[-k:]\n",
        "ind  = ind[np.argsort(Aggregate_PageRank_score[ind])][::-1]\n",
        "top_10 = [(map_character_id_character_name[x], \n",
        "           np.round(Aggregate_PageRank_score[x],6)) for x in ind]\n",
        "display(pd.DataFrame(top_10, columns = ['Character name', 'Pagerank score']))\n",
        "#YOUR CODE ENDS HERE#\n",
        "#THIS IS LINE 10#"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Cwbz2kzQrYRY"
      },
      "source": [
        "## Part 1.2"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "se_giGbPrYRZ"
      },
      "source": [
        "### 1.2.1\n",
        "**Question 1:**\n",
        "Define in an explicit way the adjacency matrix of a graph where the node with the highest PageRank (damping factor = 0.8) is not the one with the highest inDegree.\n",
        "\n",
        "The graph must be directed, unweighted, composed by exactly one connected component, and with no more than 12 nodes.\n",
        "\n",
        "Rank all the nodes in the graph according to the PageRank score of each node: from the most important to the least important. Print this rank.\n",
        "\n",
        "Rank all the nodes in the graph according to the inDegree score of each node: from the most important to the least important. Print this rank.\n",
        "\n",
        "On another line, print the identifier of the node with the highest inDegree score and the identifier of the node with the highest PageRank score."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
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          "base_uri": "https://localhost:8080/",
          "height": 527
        },
        "id": "NorZMxfkrYRZ",
        "outputId": "339d2533-1e97-421f-ab30-8eca5d44bfa9"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Rank all the nodes in the graph according to the PageRank score:\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "   ID  PageRank Score\n",
              "0   5        0.306719\n",
              "1   0        0.246553\n",
              "2   1        0.152028\n",
              "3   4        0.133508\n",
              "4   2        0.092257\n",
              "5   3        0.068935"
            ],
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              "            + ' to learn more about interactive tables.';\n",
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          "output_type": "stream",
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          "text": [
            "Rank all the nodes in the graph according to the inDegree score:\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "   ID  inDegree Score\n",
              "0   0               5\n",
              "1   5               3\n",
              "2   1               2\n",
              "3   2               2\n",
              "4   4               2\n",
              "5   3               1"
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          "metadata": {}
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        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "ID of highest inDegree score: 5\n",
            "ID of highest PageRank score: 0\n"
          ]
        }
      ],
      "source": [
        "#YOUR CODE STARTS HERE#\n",
        "Explicit_Adj = [[0,0,0,0,0,1],[1,0,1,0,0,1],[1,1,0,0,0,0],[1,0,1,0,1,0],[1,0,0,1,0,1],[1,1,0,0,1,0]]\n",
        "Adj_mat = np.array(Explicit_Adj)\n",
        "in_degree_vector = np.sum(Adj_mat, axis = 0)\n",
        "\n",
        "# dumping factor = 0.8\n",
        "alpha = 0.2\n",
        "damping_factor = 1. - alpha\n",
        "\n",
        "# PageRank\n",
        "pagerank = PageRank(damping_factor=damping_factor, solver=\"piteration\", \n",
        "                    n_iter=1000, tol=10**-6)\n",
        "\n",
        "# Compute Page-Rank on the entire Harry Potter graph\n",
        "pagerank_vector = pagerank.fit_transform(Adj_mat)\n",
        "\n",
        "map_id_pagerank_score = [ (i, x) for i,x in enumerate(pagerank_vector) ]\n",
        "map_id_inDegree  = [ (i, x) for i,x in enumerate(in_degree_vector)] \n",
        "\n",
        "ranked_according_to_pagerank_scores = sorted(map_id_pagerank_score, key=lambda x: x[1], reverse = True)\n",
        "ranked_according_to_inDegree_scores = sorted(map_id_inDegree, key=lambda x: x[1], reverse = True)\n",
        "\n",
        "print(\"Rank all the nodes in the graph according to the PageRank score:\")\n",
        "display(pd.DataFrame(ranked_according_to_pagerank_scores, columns = ['ID','PageRank Score']))\n",
        "print(\"Rank all the nodes in the graph according to the inDegree score:\")\n",
        "display(pd.DataFrame(ranked_according_to_inDegree_scores, columns = ['ID','inDegree Score']))\n",
        "print(f\"ID of highest inDegree score: {ranked_according_to_pagerank_scores[0][0]}\")\n",
        "print(f\"ID of highest PageRank score: {ranked_according_to_inDegree_scores[0][0]}\")\n",
        "#YOUR CODE ENDS HERE#\n",
        "#THIS IS LINE 30#"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KisyJ9B9rYRa"
      },
      "source": [
        "### 1.2.2\n",
        "**Question 2:**\n",
        "Given a graph with `n` nodes, what is the Topic-specific PageRank vector that is obtained when running the Topic-specific PageRank algorithm with damping factor `0`? Is the result dependent on graph topology? **Use at most 3 sentences.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pm3WzBBacQVP"
      },
      "source": [
        "----------YOUR TEXT STARTS HERE----------\n",
        "\n",
        "The Pagerank matrix $P = (1-\\alpha)P^{RW} + \\alpha U$ where $P^{RW}$ contain the information about the topology of the graph (infact is $A_{i,j}/(\\#1s \\text{ in line i})$, with $A$ the adjacency matrix), so if the dumping factor is zero, the alpha value is 1, erasing the dependency from the graph topology.\n",
        "\n",
        "If we want to bias toward a Topic, let $S$ the set of document belonging to the specific topic, $N$ the number of nodes and U the matrix such that $U_{i,j} = 1/|S|$ if $i \\in S$ or $U_{i,j} = 0$ otherwise.\n",
        "\n",
        "Then $P^{RW} = U$ and the $j$-th element of the pagerank vector is: $(πP^{PR})_j = \\frac{1}{|S|}\\sum_{i = 1}^N π_i = \\frac{1}{|S|} \\cdot 1:= \\pi_j$ for all j $\\in S$ and $\\pi_j = 0$ otherwise. \n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XUikJP59ebgQ"
      },
      "source": [
        "# Part 2: Recommendation System\n",
        "In this part of the homework, you have to improve the performance of various recommendation-systems by using non-trivial algorithms and also by performing the tuning of the hyper-parameters."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Nsh93bnylqAX"
      },
      "source": [
        "## Part 2.0\n",
        "Import here **ALL** the Python packages that you need for Part 2."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "puYHRVRFlwQk",
        "outputId": "6c64a46a-625e-432d-b670-e74d2bb08fe1"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Requirement already satisfied: scikit-surprise in /usr/local/lib/python3.7/dist-packages (1.1.1)\n",
            "Requirement already satisfied: six>=1.10.0 in /usr/local/lib/python3.7/dist-packages (from scikit-surprise) (1.15.0)\n",
            "Requirement already satisfied: scipy>=1.0.0 in /usr/local/lib/python3.7/dist-packages (from scikit-surprise) (1.7.3)\n",
            "Requirement already satisfied: numpy>=1.11.2 in /usr/local/lib/python3.7/dist-packages (from scikit-surprise) (1.21.6)\n",
            "Requirement already satisfied: joblib>=0.11 in /usr/local/lib/python3.7/dist-packages (from scikit-surprise) (1.1.0)\n"
          ]
        }
      ],
      "source": [
        "#REMOVE_OUTPUT#\n",
        "#YOUR CODE STARTS HERE#\n",
        "!pip install scikit-surprise\n",
        "from surprise import Dataset, Reader \n",
        "from surprise.model_selection import KFold, cross_validate, GridSearchCV, RandomizedSearchCV\n",
        "import pandas as pd; import numpy as np; from itertools import product\n",
        "import surprise.prediction_algorithms as pa\n",
        "import multiprocessing ; from scipy.stats import randint\n",
        "#YOUR CODE ENDS HERE#\n",
        "#THIS IS LINE 10#"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rk-JaiE_hB8h"
      },
      "source": [
        "## Part 2.1\n",
        "Apply **all** algorithms for recommendation made available by “Surprise” libraries on the provided dataset **with their default configuration**, and use **ALL** CPU-cores available on the remote machine by specifying the value in an **explicit** way with an integer number.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Mz5AtR_6ge6h"
      },
      "source": [
        "### 2.1.1\n",
        "Download the dataset from the Drive link (code already provided). "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "xoz3kpEZge6q",
        "outputId": "7eabc4d3-d8bf-4379-e8a4-719a2994be81"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Requirement already satisfied: gdown in /usr/local/lib/python3.7/dist-packages (4.4.0)\n",
            "Requirement already satisfied: filelock in /usr/local/lib/python3.7/dist-packages (from gdown) (3.7.0)\n",
            "Requirement already satisfied: requests[socks] in /usr/local/lib/python3.7/dist-packages (from gdown) (2.23.0)\n",
            "Requirement already satisfied: tqdm in /usr/local/lib/python3.7/dist-packages (from gdown) (4.64.0)\n",
            "Requirement already satisfied: beautifulsoup4 in /usr/local/lib/python3.7/dist-packages (from gdown) (4.6.3)\n",
            "Requirement already satisfied: six in /usr/local/lib/python3.7/dist-packages (from gdown) (1.15.0)\n",
            "Requirement already satisfied: idna<3,>=2.5 in /usr/local/lib/python3.7/dist-packages (from requests[socks]->gdown) (2.10)\n",
            "Requirement already satisfied: chardet<4,>=3.0.2 in /usr/local/lib/python3.7/dist-packages (from requests[socks]->gdown) (3.0.4)\n",
            "Requirement already satisfied: certifi>=2017.4.17 in /usr/local/lib/python3.7/dist-packages (from requests[socks]->gdown) (2021.10.8)\n",
            "Requirement already satisfied: urllib3!=1.25.0,!=1.25.1,<1.26,>=1.21.1 in /usr/local/lib/python3.7/dist-packages (from requests[socks]->gdown) (1.24.3)\n",
            "Requirement already satisfied: PySocks!=1.5.7,>=1.5.6 in /usr/local/lib/python3.7/dist-packages (from requests[socks]->gdown) (1.7.1)\n"
          ]
        }
      ],
      "source": [
        "#REMOVE_OUTPUT#\n",
        "!pip install --upgrade --no-cache-dir gdown"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "rt-6KfMvge6s",
        "outputId": "ef46e0a1-9a4e-4732-c312-86e8875734c2"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Downloading...\n",
            "From: https://drive.google.com/uc?id=1MKE_PY0v30CP_rs3sNzwkmo6QvKAVn_J\n",
            "To: /content/ratings_hw2.csv\n",
            "\r  0% 0.00/1.23M [00:00<?, ?B/s]\r100% 1.23M/1.23M [00:00<00:00, 112MB/s]\n"
          ]
        }
      ],
      "source": [
        "#REMOVE_OUTPUT#\n",
        "!gdown 1MKE_PY0v30CP_rs3sNzwkmo6QvKAVn_J #download ratings_hw2.csv"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MeJlxd5BZjRI"
      },
      "source": [
        "### 2.1.2\n",
        "Load and inspect the dataset: \n",
        "1. Print the list of fields names.\n",
        "2. For each field, print the minimum and maximum values.\n",
        "3. Print also the value of the first and last row of the dataset.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "WTSwJXbkZqp5",
        "outputId": "b0d4dc10-a113-426a-b6bd-abc99c936911"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "  Ratings dataset Field names\n",
            "0                     User_ID\n",
            "1                     Item_ID\n",
            "2                      Rating\n",
            "\n",
            "For <User_ID> field: \n",
            "Min value: 1\n",
            "Max value: 943\n",
            "For <Item_ID> field: \n",
            "Min value: 1\n",
            "Max value: 1682\n",
            "For <Rating> field: \n",
            "Min value: 3.0\n",
            "Max value: 5.0\n",
            "\n",
            "First row:\n",
            "User_ID    276.0\n",
            "Item_ID    559.0\n",
            "Rating       4.5\n",
            "Name: 0, dtype: float64\n",
            "\n",
            "Last row:\n",
            "User_ID    758.0\n",
            "Item_ID    319.0\n",
            "Rating       4.5\n",
            "Name: 96368, dtype: float64\n"
          ]
        }
      ],
      "source": [
        "#YOUR CODE STARTS HERE#\n",
        "# import the dataset\n",
        "ratings_dataset = pd.read_csv('/content/ratings_hw2.csv')\n",
        "# print the dataset field names\n",
        "dataset_fields = list(ratings_dataset.columns) \n",
        "nice_print = pd.DataFrame( dataset_fields )\n",
        "nice_print.rename(columns = {0: 'Ratings dataset Field names'}, inplace = True)\n",
        "print(nice_print)\n",
        "print()\n",
        "# print of the number of row\n",
        "for field in dataset_fields:\n",
        "  print(f\"For <{field}> field: \")\n",
        "  print(f\"Min value: {ratings_dataset[field].min()}\", f\"Max value: {ratings_dataset[field].max()}\", sep = '\\n')\n",
        "# print of the first and last row of the dataset\n",
        "print()\n",
        "print(f\"First row:\\n{ratings_dataset.iloc[0]}\")\n",
        "print()\n",
        "print(f\"Last row:\\n{ratings_dataset.iloc[-1]}\")\n",
        "#YOUR CODE ENDS HERE#\n",
        "#THIS IS LINE 20#"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kt6pXlGxZq1g"
      },
      "source": [
        "### 2.1.3\n",
        "Load the dataset into the appropriate scikit-surprise structure."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "3c8vPdgwZr77"
      },
      "outputs": [],
      "source": [
        "#YOUR CODE STARTS HERE#\n",
        "file_path = '/content/ratings_hw2.csv'\n",
        "reader = Reader(line_format='user item rating', sep=',', rating_scale=[3, 5], skip_lines=1)\n",
        "data = Dataset.load_from_file(file_path, reader=reader)\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "#YOUR CODE ENDS HERE#\n",
        "#THIS IS LINE 10#"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9rqpaEKvZupX"
      },
      "source": [
        "### 2.1.4\n",
        "Initialize a `scikit-surprise` `KFold` object with 5-folds. Set the random_state to **42**."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "A05Rgv64Zvde"
      },
      "outputs": [],
      "source": [
        "#YOUR CODE STARTS HERE#\n",
        "kf = KFold(n_splits=5, random_state=42)\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "#YOUR CODE ENDS HERE#\n",
        "#THIS IS LINE 10#"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "72kpxJnjZv40"
      },
      "source": [
        "### 2.1.5\n",
        "Define **all** the algorithms you are going to use"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "VUTQOaEYZ0LY"
      },
      "outputs": [],
      "source": [
        "#YOUR CODE STARTS HERE#\n",
        "# Basic algorithms\n",
        "NormalPredictor = pa.random_pred.NormalPredictor\n",
        "BaselineOnly = pa.baseline_only.BaselineOnly\n",
        "# k-NN inspired algorithms\n",
        "KNNBasic = pa.knns.KNNBasic\n",
        "KNNWithMeans = pa.knns.KNNWithMeans\n",
        "KNNWithZScore = pa.knns.KNNWithZScore\n",
        "KNNBaseline = pa.knns.KNNBaseline\n",
        "# Matrix Factorization-based algorithms\n",
        "SVD = pa.matrix_factorization.SVD\n",
        "SVDpp = pa.matrix_factorization.SVDpp\n",
        "NMF = pa.matrix_factorization.NMF\n",
        "# Slope One\n",
        "SlopeOne = pa.slope_one.SlopeOne\n",
        "# Co-clustering\n",
        "CoClustering = pa.co_clustering.CoClustering\n",
        "\n",
        "#YOUR CODE ENDS HERE#\n",
        "#THIS IS LINE 20#"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qBoF_e5reRQR"
      },
      "source": [
        "### 2.1.6\n",
        "Define the parameter configurations for each selected algorithm."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "lyxdQmr6e-sZ"
      },
      "outputs": [],
      "source": [
        "#YOUR CODE STARTS HERE#\n",
        "# BaselineOnly algorithm\n",
        "baseline_predictor_options = {   \n",
        "  'method': \"sgd\", \n",
        "  'learning_rate': 0.005,  \n",
        "  'n_epochs': 50,  \n",
        "  'reg': 0.02,  \n",
        "}\n",
        "# k-NN inspired algorithms \n",
        "MAXIMUM_number_of_neighbors_to_consider = 40 \n",
        "min_number_of_neighbors_to_consider = 1  \n",
        "similarity_options = {\n",
        "   'name': \"cosine\",  \n",
        "   'user_based': True,  \n",
        "   'min_support': 3, \n",
        "}\n",
        "# Matrix Factorization-based algorithms \n",
        "# N.B SVD, SVD++, NMF have different default parameters\n",
        "number_of_factors = [100,20,15] \n",
        "number_of_epochs = [20,20,50]\n",
        "use_together_with_baseline_estimator = [True,False]  \n",
        "learning_rate = [.005, .007]  \n",
        "lambda_parameter = [.02, 0.06] \n",
        "# Co-clustering\n",
        "number_of_cluster = 3\n",
        "number_of_item_cluster = 3\n",
        "\n",
        "\n",
        "#YOUR CODE ENDS HERE#\n",
        "#THIS IS LINE 30#"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9PF4-s-VZ0pD"
      },
      "source": [
        "### 2.1.7\n",
        "Print the number of CPU cores belonging to the machine on which Colab is running."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "g4TbBIC_fDfE",
        "outputId": "4a588caa-4f5a-4c76-f6c5-35c2c8967d58"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The number of CPU cores are: 2\n"
          ]
        }
      ],
      "source": [
        "#YOUR CODE STARTS HERE#\n",
        "import multiprocessing\n",
        "\n",
        "# Count the number of cores in a computer\n",
        "cores = multiprocessing.cpu_count() \n",
        "print(\"The number of CPU cores are:\", cores)\n",
        "\n",
        "\n",
        "#YOUR CODE ENDS HERE#\n",
        "#THIS IS LINE 10#"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "l_nMGmT3u_WD"
      },
      "source": [
        "Run a **5-Folds**-cross-validation for all the selected algorithms, using the parameters configuration that you selected for each algorithm.\n",
        "Make sure that the cross-validation gives in output the metric measures for each split, as well as fit and test times."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "83ZbCXhmu_yC",
        "outputId": "3be523f5-48db-4df3-db07-304eb798eb9e"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Evaluating RMSE, MAE of algorithm NormalPredictor on 5 split(s).\n",
            "\n",
            "                  Fold 1  Fold 2  Fold 3  Fold 4  Fold 5  Mean    Std     \n",
            "RMSE (testset)    0.7593  0.7595  0.7613  0.7590  0.7541  0.7586  0.0024  \n",
            "MAE (testset)     0.6102  0.6088  0.6123  0.6097  0.6038  0.6089  0.0028  \n",
            "Fit time          0.26    0.22    0.27    0.27    0.13    0.23    0.05    \n",
            "Test time         0.54    0.64    0.48    0.64    0.31    0.52    0.12    \n",
            "Evaluating RMSE, MAE of algorithm BaselineOnly on 5 split(s).\n",
            "\n",
            "                  Fold 1  Fold 2  Fold 3  Fold 4  Fold 5  Mean    Std     \n",
            "RMSE (testset)    0.4719  0.4730  0.4680  0.4681  0.4714  0.4705  0.0021  \n",
            "MAE (testset)     0.3731  0.3734  0.3692  0.3696  0.3721  0.3715  0.0017  \n",
            "Fit time          0.75    0.73    0.74    0.72    0.40    0.67    0.13    \n",
            "Test time         0.19    0.17    0.18    0.17    0.12    0.16    0.02    \n",
            "Evaluating RMSE, MAE of algorithm KNNBasic on 5 split(s).\n",
            "\n",
            "                  Fold 1  Fold 2  Fold 3  Fold 4  Fold 5  Mean    Std     \n",
            "RMSE (testset)    0.5093  0.5125  0.5053  0.5075  0.5086  0.5086  0.0024  \n",
            "MAE (testset)     0.4040  0.4059  0.3986  0.4007  0.4021  0.4022  0.0025  \n",
            "Fit time          1.23    2.06    2.29    2.00    1.22    1.76    0.45    \n",
            "Test time         5.53    6.31    5.78    4.76    3.32    5.14    1.04    \n",
            "Evaluating RMSE, MAE of algorithm KNNWithMeans on 5 split(s).\n",
            "\n",
            "                  Fold 1  Fold 2  Fold 3  Fold 4  Fold 5  Mean    Std     \n",
            "RMSE (testset)    0.4784  0.4793  0.4737  0.4747  0.4783  0.4769  0.0023  \n",
            "MAE (testset)     0.3779  0.3782  0.3732  0.3739  0.3767  0.3760  0.0020  \n",
            "Fit time          1.43    2.05    2.42    1.92    1.24    1.81    0.43    \n",
            "Test time         5.95    6.40    6.38    5.03    3.23    5.40    1.19    \n",
            "Evaluating RMSE, MAE of algorithm KNNWithZScore on 5 split(s).\n",
            "\n",
            "                  Fold 1  Fold 2  Fold 3  Fold 4  Fold 5  Mean    Std     \n",
            "RMSE (testset)    0.4783  0.4786  0.4736  0.4742  0.4779  0.4765  0.0022  \n",
            "MAE (testset)     0.3760  0.3759  0.3719  0.3721  0.3748  0.3741  0.0018  \n",
            "Fit time          1.47    2.56    2.09    2.28    1.33    1.94    0.47    \n",
            "Test time         5.99    6.65    6.74    5.32    3.40    5.62    1.22    \n",
            "Evaluating RMSE, MAE of algorithm KNNBaseline on 5 split(s).\n",
            "\n",
            "                  Fold 1  Fold 2  Fold 3  Fold 4  Fold 5  Mean    Std     \n",
            "RMSE (testset)    0.4674  0.4690  0.4636  0.4638  0.4678  0.4663  0.0022  \n",
            "MAE (testset)     0.3682  0.3692  0.3644  0.3646  0.3677  0.3668  0.0020  \n",
            "Fit time          1.92    2.91    3.16    2.55    2.12    2.53    0.46    \n",
            "Test time         6.62    7.39    6.96    5.56    3.42    5.99    1.42    \n",
            "Evaluating RMSE, MAE of algorithm SVD on 5 split(s).\n",
            "\n",
            "                  Fold 1  Fold 2  Fold 3  Fold 4  Fold 5  Mean    Std     \n",
            "RMSE (testset)    0.4767  0.4780  0.4734  0.4735  0.4769  0.4757  0.0019  \n",
            "MAE (testset)     0.3773  0.3782  0.3741  0.3751  0.3768  0.3763  0.0015  \n",
            "Fit time          9.84    10.13   10.53   9.83    5.97    9.26    1.67    \n",
            "Test time         0.33    0.47    0.27    0.24    0.17    0.30    0.10    \n",
            "Evaluating RMSE, MAE of algorithm SVDpp on 5 split(s).\n",
            "\n",
            "                  Fold 1  Fold 2  Fold 3  Fold 4  Fold 5  Mean    Std     \n",
            "RMSE (testset)    0.4722  0.4733  0.4684  0.4688  0.4714  0.4708  0.0019  \n",
            "MAE (testset)     0.3745  0.3745  0.3706  0.3713  0.3730  0.3728  0.0016  \n",
            "Fit time          308.15  308.15  309.07  307.74  150.55  276.73  63.09   \n",
            "Test time         5.03    6.34    5.06    5.01    2.56    4.80    1.23    \n",
            "Evaluating RMSE, MAE of algorithm NMF on 5 split(s).\n",
            "\n",
            "                  Fold 1  Fold 2  Fold 3  Fold 4  Fold 5  Mean    Std     \n",
            "RMSE (testset)    0.5073  0.5074  0.4987  0.5018  0.5047  0.5040  0.0033  \n",
            "MAE (testset)     0.4079  0.4077  0.3996  0.4034  0.4053  0.4048  0.0030  \n",
            "Fit time          9.79    10.04   10.80   9.20    5.38    9.04    1.90    \n",
            "Test time         0.24    0.48    0.23    0.23    0.14    0.26    0.11    \n",
            "Evaluating RMSE, MAE of algorithm SlopeOne on 5 split(s).\n",
            "\n",
            "                  Fold 1  Fold 2  Fold 3  Fold 4  Fold 5  Mean    Std     \n",
            "RMSE (testset)    0.4758  0.4771  0.4727  0.4719  0.4758  0.4747  0.0020  \n",
            "MAE (testset)     0.3742  0.3751  0.3708  0.3704  0.3733  0.3728  0.0019  \n",
            "Fit time          1.14    1.68    1.71    1.89    1.04    1.49    0.34    \n",
            "Test time         4.61    4.79    4.60    3.68    2.16    3.97    0.98    \n",
            "Evaluating RMSE, MAE of algorithm CoClustering on 5 split(s).\n",
            "\n",
            "                  Fold 1  Fold 2  Fold 3  Fold 4  Fold 5  Mean    Std     \n",
            "RMSE (testset)    0.5431  0.5405  0.5358  0.5379  0.5469  0.5408  0.0039  \n",
            "MAE (testset)     0.4419  0.4383  0.4343  0.4369  0.4430  0.4389  0.0032  \n",
            "Fit time          1.40    1.41    1.51    1.43    0.84    1.32    0.24    \n",
            "Test time         0.19    0.18    0.20    0.18    0.13    0.18    0.03    \n"
          ]
        }
      ],
      "source": [
        "#YOUR CODE STARTS HERE#\n",
        "NormalPredictor = NormalPredictor()\n",
        "BaselineOnly = BaselineOnly(bsl_options=baseline_predictor_options)\n",
        "KNNBasic = KNNBasic(k=MAXIMUM_number_of_neighbors_to_consider, min_k=min_number_of_neighbors_to_consider, sim_options=similarity_options)\n",
        "KNNWithMeans = KNNWithMeans(k=MAXIMUM_number_of_neighbors_to_consider, min_k=min_number_of_neighbors_to_consider, sim_options=similarity_options)\n",
        "KNNWithZScore = KNNWithZScore(k=MAXIMUM_number_of_neighbors_to_consider, min_k=min_number_of_neighbors_to_consider, sim_options=similarity_options)\n",
        "KNNBaseline = KNNBaseline(k=MAXIMUM_number_of_neighbors_to_consider, min_k=min_number_of_neighbors_to_consider, sim_options=similarity_options, bsl_options = baseline_predictor_options)\n",
        "SVD = SVD(n_factors=number_of_factors[0],biased=use_together_with_baseline_estimator[0],n_epochs=number_of_epochs[0],lr_all=learning_rate[0],reg_all=lambda_parameter[0])\n",
        "SVDpp = SVDpp(n_factors=number_of_factors[1],n_epochs=number_of_epochs[1],lr_all=learning_rate[1],reg_all=lambda_parameter[1])\n",
        "NMF = NMF(n_factors=number_of_factors[2],n_epochs=number_of_epochs[2],biased=use_together_with_baseline_estimator[1], reg_pu = lambda_parameter[1], reg_qi = lambda_parameter[1])\n",
        "SlopeOne = SlopeOne()\n",
        "CoClustering = CoClustering(n_cltr_u = number_of_cluster, n_cltr_i = number_of_item_cluster, n_epochs = number_of_epochs[0])\n",
        "# vectors of the methods\n",
        "algorithms = [NormalPredictor,BaselineOnly,KNNBasic,KNNWithMeans,KNNWithZScore,KNNBaseline,SVD,SVDpp,NMF,SlopeOne,CoClustering]\n",
        "cross_validate_at_algorithm = []\n",
        "# run the cross validation\n",
        "for current_algo in algorithms: \n",
        "  cross_validate_at_algorithm.append(cross_validate(current_algo, data, measures=['RMSE','MAE'], cv=kf, n_jobs = cores, verbose=True))\n",
        "#YOUR CODE ENDS HERE#\n",
        "#THIS IS LINE 20#"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lBnOS1InfF4T"
      },
      "source": [
        "### 2.1.8\n",
        "Rank all recommendation algorithms you tested according to the mean of the Mean Absolute Error metric value: from the best to the worst algorithm."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 394
        },
        "id": "tz3cg5gVZ-C2",
        "outputId": "34259cb4-6ef6-49bb-b0cd-1add254f9993"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "          Algorithm     MAE\n",
              "0       KNNBaseline  0.3668\n",
              "1      BaselineOnly  0.3715\n",
              "2             SVDpp  0.3728\n",
              "3          SlopeOne  0.3728\n",
              "4     KNNWithZScore  0.3741\n",
              "5      KNNWithMeans  0.3760\n",
              "6               SVD  0.3763\n",
              "7          KNNBasic  0.4022\n",
              "8               NMF  0.4048\n",
              "9      CoClustering  0.4389\n",
              "10  NormalPredictor  0.6089"
            ],
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              "      <th></th>\n",
              "      <th>Algorithm</th>\n",
              "      <th>MAE</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>KNNBaseline</td>\n",
              "      <td>0.3668</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>BaselineOnly</td>\n",
              "      <td>0.3715</td>\n",
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              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>SVDpp</td>\n",
              "      <td>0.3728</td>\n",
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              "      <th>3</th>\n",
              "      <td>SlopeOne</td>\n",
              "      <td>0.3728</td>\n",
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              "      <th>4</th>\n",
              "      <td>KNNWithZScore</td>\n",
              "      <td>0.3741</td>\n",
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              "      <th>5</th>\n",
              "      <td>KNNWithMeans</td>\n",
              "      <td>0.3760</td>\n",
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              "      <th>6</th>\n",
              "      <td>SVD</td>\n",
              "      <td>0.3763</td>\n",
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              "      <th>7</th>\n",
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              "      <th>9</th>\n",
              "      <td>CoClustering</td>\n",
              "      <td>0.4389</td>\n",
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              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>NormalPredictor</td>\n",
              "      <td>0.6089</td>\n",
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              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {}
        }
      ],
      "source": [
        "#YOUR CODE STARTS HERE#\n",
        "# collect the model name\n",
        "name_algorithms = ['NormalPredictor','BaselineOnly','KNNBasic','KNNWithMeans','KNNWithZScore',\n",
        "              'KNNBaseline','SVD','SVDpp','NMF','SlopeOne','CoClustering']\n",
        "# collect the Mean Absolute Error\n",
        "MAE_scores = [ sum(x['test_mae'])/len(x['test_mae']) for x in cross_validate_at_algorithm ]\n",
        "# rank the method based on the MAE score\n",
        "Algorithm_and_score = [ (name_algorithms[i],round(x,4)) for i,x in enumerate(MAE_scores)]\n",
        "ranked_best_to_worst_according_to_MAE_scores = sorted(Algorithm_and_score, key=lambda x: x[1])\n",
        "\n",
        "# display the ranked\n",
        "display(pd.DataFrame(ranked_best_to_worst_according_to_MAE_scores, columns = ['Algorithm', 'MAE']))\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "#YOUR CODE ENDS HERE#\n",
        "#THIS IS LINE 30#"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JSWFJqVOaH8n"
      },
      "source": [
        "## Part 2.2"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iPPOwfZxh71A"
      },
      "source": [
        "You will be given several scenarios and different requirements for each of them. By respecting the requirements, you will have to:\n",
        "1. Setup and print a suitable parameter configurations list;\n",
        "2. Perform an optimization process to find the best configuration of parameters and print it\n",
        "3. Use the same dataset as in part 1.1."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "l4LAnGIwm2AY"
      },
      "source": [
        "### 2.2.1\n",
        "**Question 1:**\n",
        "The company A-DMT wants to check **23** possible configurations for the `SVD` recommendation algorithm. The number of parameters specified for the various configurations must be at least 2 and no more than 5.\n",
        "\n",
        "The company wants to obtain the best configuration among all the 23 configurations, considering the Root Mean Squared Error metric calculated on a cross-validation of **3** folds.\n",
        "\n",
        "1. Define and print the configurations' dictionary that will be used for the parameter optimization.\n",
        "2. Find an `SVD` model configuration that offers the best possible performance within the constraints provided by the company. Print this configuration.\n",
        "\n",
        "The resulting solution must outperform the default `SVD` configuration according to the Mean Absolute Error metric.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 546
        },
        "id": "PStUReWfcO5M",
        "outputId": "21100d07-2f37-4fdc-a429-50288a675eb2"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "The configurations' dictionary is:\n",
            "{'n_epochs': [80, 100, 120], 'n_factors': [20, 30, 50], 'lr_all': [0.002, 0.007, 0.009], 'biased': [False, True], 'reg_all': [0.02, 0.06]}\n",
            "\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "[Parallel(n_jobs=2)]: Using backend LokyBackend with 2 concurrent workers.\n",
            "[Parallel(n_jobs=2)]: Done   1 tasks      | elapsed:   20.1s\n",
            "[Parallel(n_jobs=2)]: Done   4 tasks      | elapsed:   40.7s\n",
            "[Parallel(n_jobs=2)]: Done   9 tasks      | elapsed:  1.5min\n",
            "[Parallel(n_jobs=2)]: Done  14 tasks      | elapsed:  2.2min\n",
            "[Parallel(n_jobs=2)]: Done  21 tasks      | elapsed:  3.4min\n",
            "[Parallel(n_jobs=2)]: Done  28 tasks      | elapsed:  4.6min\n",
            "[Parallel(n_jobs=2)]: Done  37 tasks      | elapsed:  6.2min\n",
            "[Parallel(n_jobs=2)]: Done  46 tasks      | elapsed:  8.1min\n",
            "[Parallel(n_jobs=2)]: Done  57 tasks      | elapsed:  9.7min\n",
            "[Parallel(n_jobs=2)]: Done  69 out of  69 | elapsed: 12.0min finished\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Evaluating MAE of algorithm SVD on 3 split(s).\n",
            "\n",
            "                  Fold 1  Fold 2  Fold 3  Mean    Std     \n",
            "MAE (testset)     0.3642  0.3636  0.3629  0.3635  0.0005  \n",
            "Fit time          26.51   26.77   13.90   22.39   6.01    \n",
            "Test time         0.38    0.41    0.23    0.34    0.08    \n",
            "\n",
            "BEST_PARAMETERS: \n",
            "{'n_epochs': 120, 'n_factors': 50, 'lr_all': 0.009, 'biased': True, 'reg_all': 0.06}\n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "                       SVD       MAE\n",
              "0  SVD_basic_configuration  0.376300\n",
              "1     SVD_GS_configuration  0.363546"
            ],
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              "      <th></th>\n",
              "      <th>SVD</th>\n",
              "      <th>MAE</th>\n",
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              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>SVD_basic_configuration</td>\n",
              "      <td>0.376300</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>SVD_GS_configuration</td>\n",
              "      <td>0.363546</td>\n",
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              "  </tbody>\n",
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              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
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              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
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              "            + ' to learn more about interactive tables.';\n",
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              "  "
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          "metadata": {}
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      ],
      "source": [
        "#YOUR CODE STARTS HERE#\n",
        "grid_of_parameters = {\n",
        "   'n_epochs' : [80,100,120],\n",
        "   'n_factors': [20,30,50], \n",
        "   'lr_all': [0.002, 0.007, 0.009],\n",
        "   'biased': [False, True],  \n",
        "   'reg_all': [0.02,0.06] \n",
        "}\n",
        "print(f\"\\nThe configurations' dictionary is:\\n{grid_of_parameters}\\n\") \n",
        "# KFold\n",
        "kf = KFold(n_splits=3, random_state=42)\n",
        "# Number of configuration\n",
        "n_conf = 23\n",
        "SVD = pa.matrix_factorization.SVD\n",
        "rs = RandomizedSearchCV(SVD, param_distributions=grid_of_parameters, n_iter=n_conf,\n",
        "                        measures=['rmse'], cv=kf, n_jobs=cores, joblib_verbose=10)\n",
        "rs.fit(data)\n",
        "best_algo_cv = cross_validate(rs.best_estimator['rmse'], data, measures=['MAE'], cv=kf, n_jobs = cores, verbose=True)\n",
        "# combination of parameters that gave the best RMSE score\n",
        "print()\n",
        "print(\"BEST_PARAMETERS: \")\n",
        "print(rs.best_params['rmse'])\n",
        "print()\n",
        "# display the result\n",
        "match_df = pd.DataFrame([('SVD_basic_configuration', Algorithm_and_score[6][1]), \n",
        "                         ('SVD_GS_configuration', sum(best_algo_cv['test_mae'])/len(best_algo_cv['test_mae']))], \n",
        "                        columns = ['SVD', 'MAE'])\n",
        "display(match_df)\n",
        "#YOUR CODE ENDS HERE#\n",
        "#THIS IS LINE 30#"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KSQgSFvVm4YS"
      },
      "source": [
        "### 2.2.2\n",
        "**Question 2:**\n",
        "The company B-DMT wants to receive a set of possible configurations for `KNNBaseline` recommendation algorithm. The number of configurations must be more than 8 and not more than 36, the number of parameters for each configuration must be exactly 3, and the number of values for each parameter must be between 2 and 6.\n",
        "\n",
        "The company wants to get the best configuration among all configurations, considering the Mean Squared Error metric calculated on a cross-validation of **5** folds.\n",
        "\n",
        "1. Print the number of chosen configurations.\n",
        "2. Define and print the configurations' dictionary with the sets of values for each parameter whose cartesian product gives the chosen configurations.\n",
        "3. Find a `KNNBaseline` model configuration that offers the best possible performance within the constraints provided by the company. Print this configuration.\n",
        "\n",
        "The resulting solution must outperform the default `KNNBaseline` configuration according to the Mean Absolute Error metric."
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#YOUR CODE STARTS HERE#\n",
        "# Parameter configuration\n",
        "grid_of_parameters = {\n",
        "   'k': [30, 40, 50],        \n",
        "   'min_k': [1, 3, 5],           \n",
        "   'sim_options': {                  \n",
        "       'name': ['pearson_baseline', 'cosine']}}\n",
        "# Number of choosen configuration\n",
        "parameter = [grid_of_parameters['k'],grid_of_parameters['min_k'], grid_of_parameters['sim_options']['name']]\n",
        "print(\"The number of configuration are:\", len([x for x in product(*parameter)]))\n",
        "print(f\"\\nThe configurations' dictionary is:\\n{grid_of_parameters}\\n\") \n",
        "# KFold + GridSearch\n",
        "kf = KFold(n_splits=5, random_state=42)\n",
        "KNNBaseline = pa.knns.KNNBaseline\n",
        "gs = GridSearchCV(KNNBaseline, param_grid=grid_of_parameters,measures=['mse'],\n",
        "                 cv=kf, n_jobs=2, joblib_verbose=10)\n",
        "gs.fit(data)\n",
        "best_algo_cv = cross_validate(gs.best_estimator['mse'], data, measures=['MAE'], cv=kf, n_jobs = cores, verbose=True)\n",
        "# combination of parameters that gave the best RMSE score\n",
        "print(\"\\nBEST_PARAMETERS: \")\n",
        "print(gs.best_params['mse'])\n",
        "print()\n",
        "# display the result\n",
        "match_df = pd.DataFrame([('KNNBASELINE_basic_configuration', Algorithm_and_score[5][1]), \n",
        "                         ('KNNBASELINE_GS_configuration', sum(best_algo_cv['test_mae'])/len(best_algo_cv['test_mae']))], \n",
        "                        columns = ['KNNBASELINE', 'MAE'])\n",
        "display(match_df)\n",
        "\n",
        "#YOUR CODE ENDS HERE#\n",
        "#THIS IS LINE 30#"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 598
        },
        "id": "oyCJs2g6E7mu",
        "outputId": "274035e9-8909-4023-9961-57603b2f2ac1"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The number of configuration are: 18\n",
            "\n",
            "The configurations' dictionary is:\n",
            "{'k': [30, 40, 50], 'min_k': [1, 3, 5], 'sim_options': {'name': ['pearson_baseline', 'cosine']}}\n",
            "\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "[Parallel(n_jobs=2)]: Using backend LokyBackend with 2 concurrent workers.\n",
            "[Parallel(n_jobs=2)]: Done   1 tasks      | elapsed:    9.0s\n",
            "[Parallel(n_jobs=2)]: Done   4 tasks      | elapsed:   21.9s\n",
            "[Parallel(n_jobs=2)]: Done   9 tasks      | elapsed:   44.8s\n",
            "[Parallel(n_jobs=2)]: Done  14 tasks      | elapsed:  1.1min\n",
            "[Parallel(n_jobs=2)]: Done  21 tasks      | elapsed:  1.6min\n",
            "[Parallel(n_jobs=2)]: Done  28 tasks      | elapsed:  2.2min\n",
            "[Parallel(n_jobs=2)]: Done  37 tasks      | elapsed:  2.9min\n",
            "[Parallel(n_jobs=2)]: Done  46 tasks      | elapsed:  3.6min\n",
            "[Parallel(n_jobs=2)]: Done  57 tasks      | elapsed:  4.4min\n",
            "[Parallel(n_jobs=2)]: Done  68 tasks      | elapsed:  5.3min\n",
            "[Parallel(n_jobs=2)]: Done  81 tasks      | elapsed:  6.4min\n",
            "[Parallel(n_jobs=2)]: Done  90 out of  90 | elapsed:  7.1min finished\n"
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        {
          "output_type": "stream",
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          "text": [
            "Evaluating MAE of algorithm KNNBaseline on 5 split(s).\n",
            "\n",
            "                  Fold 1  Fold 2  Fold 3  Fold 4  Fold 5  Mean    Std     \n",
            "MAE (testset)     0.3617  0.3630  0.3586  0.3589  0.3619  0.3608  0.0017  \n",
            "Fit time          1.67    2.21    2.15    2.52    1.40    1.99    0.40    \n",
            "Test time         6.32    7.04    6.81    5.43    3.65    5.85    1.23    \n",
            "\n",
            "BEST_PARAMETERS: \n",
            "{'k': 40, 'min_k': 5, 'sim_options': {'name': 'pearson_baseline', 'user_based': True}}\n",
            "\n"
          ]
        },
        {
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            "text/plain": [
              "                       KNNBASELINE       MAE\n",
              "0  KNNBASELINE_basic_configuration  0.366800\n",
              "1     KNNBASELINE_GS_configuration  0.360821"
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              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-8f8284cc-a710-4e57-ab63-8c76b1bda7a9 button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-8f8284cc-a710-4e57-ab63-8c76b1bda7a9');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
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              "  </div>\n",
              "  "
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