3-node2vec.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kPt5q27L5557"
      },
      "source": [
        "# CS245 - Lab 3\n",
        "## node2vec"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "p0-YhEpP_Ds-"
      },
      "source": [
        "### Setup"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "82kmj9fIVlq0"
      },
      "source": [
        "First of all, we install the [graph2vec library](https://github.com/VHRanger/graph2vec) which offers a fast implementation of the node2vec method.\n",
        "\n",
        "If you are curious to learn how to implement fast random walks on graphs, I recommend you to [read the blog post](https://www.singlelunch.com/2019/08/01/700x-faster-node2vec-models-fastest-random-walks-on-a-graph/) which explains some of the design choices behind this library."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "Ld017NzXCo-g",
        "vscode": {
          "languageId": "python"
        }
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n",
            "Collecting nodevectors\n",
            "  Downloading nodevectors-0.1.23.tar.gz (15 kB)\n",
            "Collecting csrgraph\n",
            "  Downloading csrgraph-0.1.28.tar.gz (14 kB)\n",
            "Requirement already satisfied: gensim in /usr/local/lib/python3.7/dist-packages (from nodevectors) (3.6.0)\n",
            "Requirement already satisfied: networkx in /usr/local/lib/python3.7/dist-packages (from nodevectors) (2.6.3)\n",
            "Requirement already satisfied: numba in /usr/local/lib/python3.7/dist-packages (from nodevectors) (0.51.2)\n",
            "Requirement already satisfied: numpy in /usr/local/lib/python3.7/dist-packages (from nodevectors) (1.21.6)\n",
            "Requirement already satisfied: pandas>=1.0 in /usr/local/lib/python3.7/dist-packages (from nodevectors) (1.3.5)\n",
            "Requirement already satisfied: scipy in /usr/local/lib/python3.7/dist-packages (from nodevectors) (1.4.1)\n",
            "Requirement already satisfied: scikit-learn in /usr/local/lib/python3.7/dist-packages (from nodevectors) (1.0.2)\n",
            "Requirement already satisfied: pytz>=2017.3 in /usr/local/lib/python3.7/dist-packages (from pandas>=1.0->nodevectors) (2022.1)\n",
            "Requirement already satisfied: python-dateutil>=2.7.3 in /usr/local/lib/python3.7/dist-packages (from pandas>=1.0->nodevectors) (2.8.2)\n",
            "Requirement already satisfied: six>=1.5 in /usr/local/lib/python3.7/dist-packages (from python-dateutil>=2.7.3->pandas>=1.0->nodevectors) (1.15.0)\n",
            "Requirement already satisfied: tqdm in /usr/local/lib/python3.7/dist-packages (from csrgraph->nodevectors) (4.64.0)\n",
            "Requirement already satisfied: smart-open>=1.2.1 in /usr/local/lib/python3.7/dist-packages (from gensim->nodevectors) (6.0.0)\n",
            "Requirement already satisfied: llvmlite<0.35,>=0.34.0.dev0 in /usr/local/lib/python3.7/dist-packages (from numba->nodevectors) (0.34.0)\n",
            "Requirement already satisfied: setuptools in /usr/local/lib/python3.7/dist-packages (from numba->nodevectors) (57.4.0)\n",
            "Requirement already satisfied: threadpoolctl>=2.0.0 in /usr/local/lib/python3.7/dist-packages (from scikit-learn->nodevectors) (3.1.0)\n",
            "Requirement already satisfied: joblib>=0.11 in /usr/local/lib/python3.7/dist-packages (from scikit-learn->nodevectors) (1.1.0)\n",
            "Building wheels for collected packages: nodevectors, csrgraph\n",
            "  Building wheel for nodevectors (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "  Created wheel for nodevectors: filename=nodevectors-0.1.23-py3-none-any.whl size=17950 sha256=56a6e86941dadec754641b78c64a93d5ce98a44da0aaacb4c2d5af786ffe8246\n",
            "  Stored in directory: /root/.cache/pip/wheels/6e/6a/11/ac8620f101db6248c3cd436636eb17f6f7430cd1ac3a3068dc\n",
            "  Building wheel for csrgraph (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "  Created wheel for csrgraph: filename=csrgraph-0.1.28-py3-none-any.whl size=17632 sha256=328e6af90ef183679771431039dd866df23d7b29eeca00448ca1bd68d7791185\n",
            "  Stored in directory: /root/.cache/pip/wheels/3d/0a/58/36a63805f1cd719cbcc5a3c4c109604985a809e7d81bac1649\n",
            "Successfully built nodevectors csrgraph\n",
            "Installing collected packages: csrgraph, nodevectors\n",
            "Successfully installed csrgraph-0.1.28 nodevectors-0.1.23\n"
          ]
        }
      ],
      "source": [
        "!pip install nodevectors"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pUCNE4-5Wc8b"
      },
      "source": [
        "We now import the library, and create a small wrapper class which will expose only the few hyperparameters we will need to tune in this Lab"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "id": "QiIPtudrGlTf",
        "vscode": {
          "languageId": "python"
        }
      },
      "outputs": [],
      "source": [
        "from nodevectors import Node2Vec\n",
        "import networkx as nx\n",
        "\n",
        "class Node2VecNew(Node2Vec):\n",
        "    \"\"\"\n",
        "    Parameters\n",
        "    ----------\n",
        "    p : float\n",
        "        p parameter of node2vec\n",
        "    q : float\n",
        "        q parameter of node2vec\n",
        "    d : int\n",
        "        dimensionality of the embedding vectors\n",
        "    \"\"\"\n",
        "    def __init__(self, p=1, q=1, d=32):\n",
        "        super().__init__(n_components=d,\n",
        "                         walklen=10,\n",
        "                         epochs=50,\n",
        "                         return_weight=1.0/p,\n",
        "                         neighbor_weight=1.0/q,\n",
        "                         threads=0,\n",
        "                         w2vparams={'window': 4,\n",
        "                                    'negative': 5, \n",
        "                                    'iter': 10,\n",
        "                                    'ns_exponent': 0.5,\n",
        "                                    'batch_words': 128})"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qwtlO4_m_LbQ"
      },
      "source": [
        "Lastly, let's import some of the common libraries needed for our task."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "id": "twk-K-jilWK7",
        "vscode": {
          "languageId": "python"
        }
      },
      "outputs": [],
      "source": [
        "import pandas as pd\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kAYRX2PMm0L6"
      },
      "source": [
        "### Example"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "id": "2PsVt5f2CsmP",
        "vscode": {
          "languageId": "python"
        }
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Making walks... "
          ]
        },
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/numba/np/ufunc/parallel.py:363: NumbaWarning: The TBB threading layer requires TBB version 2019.5 or later i.e., TBB_INTERFACE_VERSION >= 11005. Found TBB_INTERFACE_VERSION = 9107. The TBB threading layer is disabled.\n",
            "  warnings.warn(problem)\n"
          ]
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Done, T=3.25\n",
            "Mapping Walk Names... Done, T=0.23\n",
            "Training W2V... Done, T=0.41\n"
          ]
        }
      ],
      "source": [
        "# Load the Zachary's Karate Club as a NetworkX Graph object\n",
        "KCG = nx.karate_club_graph()\n",
        "\n",
        "# Fit embedding model to the Karate Club graph\n",
        "n2v = Node2VecNew(1, 1, 2)\n",
        "n2v.fit(KCG)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "id": "ZEjzhwEiC1HD",
        "vscode": {
          "languageId": "python"
        }
      },
      "outputs": [],
      "source": [
        "embeddings = []\n",
        "for node in KCG.nodes:\n",
        "    embedding = list(n2v.predict(node))\n",
        "    club = KCG.nodes[node]['club']\n",
        "    embeddings.append(embedding + [club])\n",
        "\n",
        "# Construct a pandas dataframe with the 2D embeddings from node2vec,\n",
        "# plus the club name that each node belongs to after the split\n",
        "df = pd.DataFrame(embeddings, columns=['x', 'y', 'club'])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "id": "fJBTilMGLInb",
        "vscode": {
          "languageId": "python"
        }
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7f33d8300810>"
            ]
          },
          "execution_count": 6,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Nodes who stayed with the Mr. Hi will be plotted in red, while nodes\n",
        "# who moved with the Officer will be plotted in blue\n",
        "colors = ['red' if x == 'Mr. Hi' else 'blue' for x in df.club]\n",
        "df.plot.scatter(x='x', y='y', s=50, c=colors)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "e6vmpmj6Ylph"
      },
      "source": [
        "If our example trained correctly, you should notice a clear separation between the blue and red nodes.  Solely from the graph structure, node2vec could predict how the Zachary's Karate Club split!\n",
        "\n",
        "Tune the hyperparameters ```p``` and ```q```, and notice how they affect the resulting embeddings."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vbmr23B2rJKR"
      },
      "source": [
        "### Your Task"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "x15OQeyys1xd"
      },
      "source": [
        "Now we will study the behavior of node2vec on [barbell graphs](https://en.wikipedia.org/wiki/Barbell_graph).\n",
        "\n",
        "Below you can see a toy example of a barbell graph generated with NetworkX."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "id": "xUYxs4E8aHgG",
        "vscode": {
          "languageId": "python"
        }
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "toy_barbell = nx.barbell_graph(7, 0)\n",
        "nx.draw_kamada_kawai(toy_barbell)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "G7K3-57FyD8D"
      },
      "source": [
        "\n",
        "\n",
        "\n",
        "Generate a larger barbell graph, where each complete graph has exactly 1000 nodes, and the path length between the complete graphs is equal to 1 (i.e., all the nodes in the barbell graph belong to either one of the two complete graphs, and the connecting path does not have any internal node).\n",
        "\n",
        "Then, learn node2vec embeddings on this graph, setting ```p = 1, q = 1``` and ```d = 10```."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "id": "k_rmp-SvaIOt",
        "vscode": {
          "languageId": "python"
        }
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Making walks... Done, T=0.75\n",
            "Mapping Walk Names... Done, T=1.84\n",
            "Training W2V... Done, T=26.78\n"
          ]
        }
      ],
      "source": [
        "# YOUR CODE HERE\n",
        "barbell_1 = nx.barbell_graph(1000, 0)\n",
        "\n",
        "n2v_1 = Node2VecNew(1, 1, 10)\n",
        "n2v_1.fit(barbell_1)\n",
        "\n",
        "embeddings_1 = []\n",
        "for node in barbell_1.nodes:\n",
        "    embedding = list(n2v_1.predict(node))\n",
        "    embeddings_1.append(embedding)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fyxZBVwhzLQe"
      },
      "source": [
        "Write a function that takes as input a node id ```n``` in the graph (e.g., ```5```) and returns a list containing the cosine similarity between the node2vec vector of the input node ```n``` and all the nodes in the given barbell graph (including the similarity with ```n``` itself)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "id": "aq7advtkjXSp",
        "vscode": {
          "languageId": "python"
        }
      },
      "outputs": [],
      "source": [
        "# YOUR CODE HERE\n",
        "from scipy.spatial import distance\n",
        "\n",
        "def similarity(n, embeddings):\n",
        "    similarity = []\n",
        "    for embedding in embeddings:\n",
        "        similarity.append(1 - distance.cosine(embedding, embeddings[n]))\n",
        "    return similarity"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zw1oNDDD2dZO"
      },
      "source": [
        "Generate another barbell graph, this time adding a path of length 51 between the two complete graphs. To find out how, refer to the NetworkX documentation: [https://networkx.github.io/documentation/stable/reference/generated/networkx.generators.classic.barbell_graph.html#networkx.generators.classic.barbell_graph](https://networkx.github.io/documentation/stable/reference/generated/networkx.generators.classic.barbell_graph.html#networkx.generators.classic.barbell_graph)\n",
        "\n",
        "Learn the node2vec embeddings for the nodes of this new graph, using the same hyperparameters as before."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "id": "OlPg6k6z65Gk",
        "vscode": {
          "languageId": "python"
        }
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Making walks... Done, T=0.49\n",
            "Mapping Walk Names... Done, T=0.98\n",
            "Training W2V... Done, T=27.78\n"
          ]
        }
      ],
      "source": [
        "# YOUR CODE HERE\n",
        "barbell_2 = nx.barbell_graph(1000, 50)\n",
        "\n",
        "n2v_2 = Node2VecNew(1, 1, 10)\n",
        "n2v_2.fit(barbell_2)\n",
        "\n",
        "embeddings_2 = []\n",
        "for node in barbell_2.nodes:\n",
        "    embedding = list(n2v_2.predict(node))\n",
        "    embeddings_2.append(embedding)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SIrXJyVNP2AI"
      },
      "source": [
        "Once you have working code for each cell above, **save a version in Kaggle and share your notebook**!"
      ]
    }
  ],
  "metadata": {
    "language_info": {
      "name": "python"
    },
    "orig_nbformat": 4
  },
  "nbformat": 4,
  "nbformat_minor": 0
}