CS224W_Colab_1.ipynb

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  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.7.3"
    },
    "colab": {
      "name": "CS224W - Colab 1.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "toc_visible": true,
      "machine_shape": "hm",
      "include_colab_link": true
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/amayuelas/GNN_CS224W/blob/main/CS224W_Colab_1.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XuXWJLEm2UWS"
      },
      "source": [
        "# **CS224W - Colab 1**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8gzsP50bF6Gb"
      },
      "source": [
        "In this Colab, we will write a full pipeline for **learning node embeddings**.\n",
        "We will go through the following 3 steps.\n",
        "\n",
        "To start, we will load a classic graph in network science, the [Karate Club Network](https://en.wikipedia.org/wiki/Zachary%27s_karate_club). We will explore multiple graph statistics for that graph.\n",
        "\n",
        "We will then work together to transform the graph structure into a PyTorch tensor, so that we can perform machine learning over the graph.\n",
        "\n",
        "Finally, we will finish the first learning algorithm on graphs: a node embedding model. For simplicity, our model here is simpler than DeepWalk / node2vec algorithms taught in the lecture. But it's still rewarding and challenging, as we will write it from scratch via PyTorch.\n",
        "\n",
        "Now let's get started!\n",
        "\n",
        "**Note**: Make sure to **sequentially run all the cells**, so that the intermediate variables / packages will carry over to the next cell"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Nwwq0nSdmsOL"
      },
      "source": [
        "# 1 Graph Basics\n",
        "To start, we will load a classic graph in network science, the [Karate Club Network](https://en.wikipedia.org/wiki/Zachary%27s_karate_club). We will explore multiple graph statistics for that graph."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FDkpByYYfSzb"
      },
      "source": [
        "## Setup\n",
        "We will heavily use NetworkX in this Colab."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VWPkJjPAfVNW"
      },
      "source": [
        "import networkx as nx"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VqUnYT5qUZYh"
      },
      "source": [
        "## Zachary's karate club network\n",
        "\n",
        "The [Karate Club Network](https://en.wikipedia.org/wiki/Zachary%27s_karate_club) is a graph describes a social network of 34 members of a karate club and documents links between members who interacted outside the club."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VIETqEfrfy5Y",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "fedd4119-1cac-42a3-f6d9-66e6ccec26b1"
      },
      "source": [
        "G = nx.karate_club_graph()\n",
        "\n",
        "# G is an undirected graph\n",
        "type(G)"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "networkx.classes.graph.Graph"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 2
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hDvf3nm-ors4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 319
        },
        "outputId": "39e838cb-8b42-43b2-8242-df650391223f"
      },
      "source": [
        "# Visualize the graph\n",
        "nx.draw(G, with_labels = True)"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FX25Y1CrYmgN"
      },
      "source": [
        "## Question 1: What is the average degree of the karate club network? (5 Points)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AUhES1VYo3tB",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "79a94043-abd5-496e-e800-a4cdb2c65389"
      },
      "source": [
        "def average_degree(num_edges, num_nodes):\n",
        "  # TODO: Implement this function that takes number of edges\n",
        "  # and number of nodes, and returns the average node degree of \n",
        "  # the graph. Round the result to nearest integer (for example \n",
        "  # 3.3 will be rounded to 3 and 3.7 will be rounded to 4)\n",
        "\n",
        "  deg = num_edges * 2\n",
        "\n",
        "  avg_degree = int(round(deg / num_nodes,1))\n",
        "\n",
        "  return avg_degree\n",
        "\n",
        "num_edges = G.number_of_edges()\n",
        "num_nodes = G.number_of_nodes()\n",
        "avg_degree = average_degree(num_edges, num_nodes)\n",
        "print(\"Average degree of karate club network is {}\".format(avg_degree))"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Average degree of karate club network is 4\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Fk02fD4vYmZI"
      },
      "source": [
        "## Question 2: What is the average clustering coefficient of the karate club network? (5 Points)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "k15XKEto1aYJ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "a9fba668-d4e3-4976-c1ee-678fd5cf8b1b"
      },
      "source": [
        "def average_clustering_coefficient(G):\n",
        "  # TODO: Implement this function that takes a nx.Graph\n",
        "  # and returns the average clustering coefficient. Round \n",
        "  # the result to 2 decimal places (for example 3.333 will\n",
        "  # be rounded to 3.33 and 3.7571 will be rounded to 3.76)\n",
        "\n",
        "  avg_cluster_coef = round(nx.average_clustering(G),2)\n",
        "\n",
        "  ############# Your code here ############\n",
        "  ## Note: \n",
        "  ## 1: Please use the appropriate NetworkX clustering function\n",
        "\n",
        "  #########################################\n",
        "\n",
        "  return avg_cluster_coef\n",
        "\n",
        "avg_cluster_coef = average_clustering_coefficient(G)\n",
        "print(\"Average clustering coefficient of karate club network is {}\".format(avg_cluster_coef))"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Average clustering coefficient of karate club network is 0.57\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zghQ-AhXYmP4"
      },
      "source": [
        "## Question 3: What is the PageRank value for node 0 (node with id 0) after one PageRank iteration? (5 Points)\n",
        "\n",
        "Please complete the code block by implementing the PageRank equation: $r_j = \\sum_{i \\rightarrow j} \\beta \\frac{r_i}{d_i} + (1 - \\beta) \\frac{1}{N}$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BOGdWjNc6O7x",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "33cea1d9-35d8-4f9f-ca3d-370dc313b241"
      },
      "source": [
        "def one_iter_pagerank(G, beta, r0, node_id):\n",
        "  # TODO: Implement this function that takes a nx.Graph, beta, r0 and node id.\n",
        "  # The return value r1 is one interation PageRank value for the input node.\n",
        "  # Please round r1 to 2 decimal places.\n",
        "\n",
        "  nodes_i = [i for j,i in G.edges(node_id)]\n",
        "  r1 = sum([beta*(r0/G.degree(i)) + (1-beta) * (1/G.number_of_nodes()) for i in nodes_i])\n",
        "  r1 = round(r1,2)\n",
        "\n",
        "  return r1\n",
        "\n",
        "beta = 0.8\n",
        "r0 = 1 / G.number_of_nodes()\n",
        "node = 0\n",
        "r1 = one_iter_pagerank(G, beta, r0, node)\n",
        "print(\"The PageRank value for node 0 after one iteration is {}\".format(r1))"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "The PageRank value for node 0 after one iteration is 0.22\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "icTcOULeYmIu"
      },
      "source": [
        "## Question 4: What is the (raw) closeness centrality for the karate club network node 5? (5 Points)\n",
        "\n",
        "The equation for closeness centrality is $c(v) = \\frac{1}{\\sum_{u \\neq v}\\text{shortest path length between } u \\text{ and } v}$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XbCsq_tl-3ok",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "818ec26d-ca9c-447f-ddc9-63fac7d0df78"
      },
      "source": [
        "def closeness_centrality(G, node=5):\n",
        "  # TODO: Implement the function that calculates closeness centrality \n",
        "  # for a node in karate club network. G is the input karate club \n",
        "  # network and node is the node id in the graph. Please round the \n",
        "  # closeness centrality result to 2 decimal places.\n",
        "\n",
        "  closeness = (1/G.number_of_nodes()) * nx.algorithms.centrality.closeness_centrality(G,node, \n",
        "                                                            wf_improved=False)\n",
        "\n",
        "  ## Note:\n",
        "  ## 1: You can use networkx closeness centrality function.\n",
        "  ## 2: Notice that networkx closeness centrality returns the normalized \n",
        "  ## closeness directly, which is different from the raw (unnormalized) \n",
        "  ## one that we learned in the lecture.\n",
        "\n",
        "  #########################################\n",
        "\n",
        "  return round(closeness,2)\n",
        "\n",
        "node = 5\n",
        "closeness = closeness_centrality(G, node=node)\n",
        "print(\"The karate club network has closeness centrality {}\".format(closeness))"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "The karate club network has closeness centrality 0.01\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-MxvowibYl4x"
      },
      "source": [
        "# 2 Graph to Tensor\n",
        "We will then work together to transform the graph $G$ into a PyTorch tensor, so that we can perform machine learning over the graph."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eDA8PosrA-9V"
      },
      "source": [
        "## Setup\n",
        "Check if PyTorch is properly installed"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ntuPVat_BAf1",
        "outputId": "c6233f03-2af6-4930-fe7c-538e83565238",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "import torch\n",
        "print(torch.__version__)"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "1.7.0+cu101\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fko_2wSKYlun"
      },
      "source": [
        "## PyTorch tensor basics\n",
        "\n",
        "We can generate PyTorch tensor with all zeros, ones or random values."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "W2ySw3m-A9qF",
        "outputId": "f26f6803-b0d6-45d5-9b15-04fd9c49405b",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "# Generate 3 x 4 tensor with all ones\n",
        "ones = torch.ones(3, 4)\n",
        "print(ones)\n",
        "\n",
        "# Generate 3 x 4 tensor with all zeros\n",
        "zeros = torch.zeros(3, 4)\n",
        "print(zeros)\n",
        "\n",
        "# Generate 3 x 4 tensor with random values on the interval [0, 1)\n",
        "random_tensor = torch.rand(3, 4)\n",
        "print(random_tensor)\n",
        "\n",
        "# Get the shape of the tensor\n",
        "print(ones.shape)"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "tensor([[1., 1., 1., 1.],\n",
            "        [1., 1., 1., 1.],\n",
            "        [1., 1., 1., 1.]])\n",
            "tensor([[0., 0., 0., 0.],\n",
            "        [0., 0., 0., 0.],\n",
            "        [0., 0., 0., 0.]])\n",
            "tensor([[0.3634, 0.5413, 0.4224, 0.1270],\n",
            "        [0.8890, 0.9445, 0.3290, 0.6647],\n",
            "        [0.3028, 0.2170, 0.7591, 0.1821]])\n",
            "torch.Size([3, 4])\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "x8mp66eHBxWC"
      },
      "source": [
        "PyTorch tensor contains elements for a single data type, the `dtype`."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rQiOvKJJBwq4",
        "outputId": "26e520bc-edcb-4e62-8526-e080e5988214",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "# Create a 3 x 4 tensor with all 32-bit floating point zeros\n",
        "zeros = torch.zeros(3, 4, dtype=torch.float32)\n",
        "print(zeros.dtype)\n",
        "\n",
        "# Change the tensor dtype to 64-bit integer\n",
        "zeros = zeros.type(torch.long)\n",
        "print(zeros.dtype)"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "torch.float32\n",
            "torch.int64\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "I9EfegIRDkk2"
      },
      "source": [
        "## Question 5: Getting the edge list of the karate club network and transform it into `torch.LongTensor`. What is the `torch.sum` value of `pos_edge_index` tensor? (10 Points)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kEtVxMFID3ZT",
        "outputId": "4c862198-f639-4e2c-fe73-cbcec43bf178",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "def graph_to_edge_list(G):\n",
        "  # TODO: Implement the function that returns the edge list of\n",
        "  # an nx.Graph. The returned edge_list should be a list of tuples\n",
        "  # where each tuple is a tuple representing an edge connected \n",
        "  # by two nodes.\n",
        "\n",
        "  edge_list = list(G.edges())\n",
        "\n",
        "  return edge_list\n",
        "\n",
        "def edge_list_to_tensor(edge_list):\n",
        "  # TODO: Implement the function that transforms the edge_list to\n",
        "  # tensor. The input edge_list is a list of tuples and the resulting\n",
        "  # tensor should have the shape [2 x len(edge_list)].\n",
        "\n",
        "  edge_index = torch.tensor(edge_list)\n",
        "  edge_index = torch.transpose(edge_index,0,1)\n",
        "\n",
        "  return edge_index\n",
        "\n",
        "pos_edge_list = graph_to_edge_list(G)\n",
        "pos_edge_index = edge_list_to_tensor(pos_edge_list)\n",
        "print(\"The pos_edge_index tensor has shape {}\".format(pos_edge_index.shape))\n",
        "print(\"The pos_edge_index tensor has sum value {}\".format(torch.sum(pos_edge_index)))"
      ],
      "execution_count": 122,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "The pos_edge_index tensor has shape torch.Size([2, 78])\n",
            "The pos_edge_index tensor has sum value 2535\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UBL-ZmdHWqIu"
      },
      "source": [
        "## Question 6: Please implement following function that samples negative edges. Then you will answer which edges (edge_1 to edge_5) can be negative ones in the karate club network? (10 Points)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9N8VT1f8-IJ8",
        "outputId": "880f864f-5dd3-4a6a-e767-82ed29657039",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "import random\n",
        "\n",
        "def sample_negative_edges(G, num_neg_samples):\n",
        "  # TODO: Implement the function that returns a list of negative edges.\n",
        "  # The number of sampled negative edges is num_neg_samples. You do not\n",
        "  # need to consider the corner case when the number of possible negative edges\n",
        "  # is less than num_neg_samples. It should be ok as long as your implementation \n",
        "  # works on the karate club network. In this implementation, self loop should \n",
        "  # not be considered as either a positive or negative edge. Also, notice that \n",
        "  # the karate club network is an undirected graph, if (0, 1) is a positive \n",
        "  # edge, do you think (1, 0) can be a negative one?\n",
        "\n",
        "  neg_edge_list = []\n",
        "\n",
        "  while len(neg_edge_list) != num_neg_samples:\n",
        "\n",
        "    # Select 2 nodes at random\n",
        "    n1 = random.randint(min(G.nodes()), max(G.nodes()))\n",
        "    n2 = random.randint(min(G.nodes()), max(G.nodes()))\n",
        "\n",
        "    # Check if the edge exist\n",
        "    if ((n1,n2) not in G.edges()) and (n1!=n2) and \\\n",
        "    ((n1,n2) not in neg_edge_list) and ((n2,n1) not in neg_edge_list):\n",
        "      neg_edge_list.append((n1,n2))\n",
        "\n",
        "  return neg_edge_list\n",
        "\n",
        "# Sample 78 negative edges\n",
        "neg_edge_list = sample_negative_edges(G, len(pos_edge_list))\n",
        "\n",
        "# Transform the negative edge list to tensor\n",
        "neg_edge_index = edge_list_to_tensor(neg_edge_list)\n",
        "print(\"The neg_edge_index tensor has shape {}\".format(neg_edge_index.shape))\n",
        "\n",
        "# Which of following edges can be negative ones?\n",
        "edge_1 = (7, 1)\n",
        "edge_2 = (1, 33)\n",
        "edge_3 = (33, 22)\n",
        "edge_4 = (0, 4)\n",
        "edge_5 = (4, 2)\n",
        "\n",
        "neg_edges = [edge_1, edge_2, edge_3, edge_4, edge_5]\n",
        "\n",
        "# Check if negative edges\n",
        "for edge in neg_edges:\n",
        "  n1,n2 = edge\n",
        "  if ((n1,n2) not in G.edges()) and (n1!=n2):\n",
        "    print(\"{} is a NEGATIVE edge\".format(edge))\n",
        "  else:\n",
        "    print(\"{} is a NOT NEGATIVE edge\".format(edge))"
      ],
      "execution_count": 123,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "The neg_edge_index tensor has shape torch.Size([2, 78])\n",
            "(7, 1) is a NOT NEGATIVE edge\n",
            "(1, 33) is a NEGATIVE edge\n",
            "(33, 22) is a NOT NEGATIVE edge\n",
            "(0, 4) is a NOT NEGATIVE edge\n",
            "(4, 2) is a NEGATIVE edge\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Wk9Q-a-9qGsw"
      },
      "source": [
        "# 3 Node Emebedding Learning\n",
        "\n",
        "Finally, we will finish the first learning algorithm on graphs: a node embedding model.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NDBxRQcZ_dUH"
      },
      "source": [
        "## Setup"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Lnqn9H6s_ehX",
        "outputId": "19c19653-be32-4c70-b2a7-c918f8412a25",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "import torch\n",
        "import torch.nn as nn\n",
        "import matplotlib.pyplot as plt\n",
        "from sklearn.decomposition import PCA\n",
        "\n",
        "print(torch.__version__)"
      ],
      "execution_count": 124,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "1.7.0+cu101\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6gomAf8vxq0R"
      },
      "source": [
        "To write our own node embedding learning methods, we'll heavily use the [`nn.Embedding`](https://pytorch.org/docs/stable/generated/torch.nn.Embedding.html) module in PyTorch. Let's see how to use `nn.Embedding`:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "aRiWGuLAx5yx",
        "outputId": "279c3a41-f157-4da0-d673-93ad42fe2d89",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "# Initialize an embedding layer\n",
        "# Suppose we want to have embedding for 4 items (e.g., nodes)\n",
        "# Each item is represented with 8 dimensional vector\n",
        "\n",
        "emb_sample = nn.Embedding(num_embeddings=4, embedding_dim=8)\n",
        "print('Sample embedding layer: {}'.format(emb_sample))"
      ],
      "execution_count": 125,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Sample embedding layer: Embedding(4, 8)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bS9qQfeujEVh"
      },
      "source": [
        "We can select items from the embedding matrix, by using Tensor indices"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9AGIfP4QEDr8",
        "outputId": "772405a6-a9d0-4bf0-87ce-104ee699e05c",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "# Select an embedding in emb_sample\n",
        "id = torch.LongTensor([1])\n",
        "print(emb_sample(id))\n",
        "\n",
        "# Select multiple embeddings\n",
        "ids = torch.LongTensor([1, 3])\n",
        "print(emb_sample(ids))\n",
        "\n",
        "# Get the shape of the embedding weight matrix\n",
        "shape = emb_sample.weight.data.shape\n",
        "print(shape)\n",
        "\n",
        "# Overwrite the weight to tensor with all ones\n",
        "emb_sample.weight.data = torch.ones(shape)\n",
        "\n",
        "# Let's check if the emb is indeed initilized\n",
        "ids = torch.LongTensor([0, 3])\n",
        "print(emb_sample(ids))"
      ],
      "execution_count": 126,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "tensor([[ 0.0101,  0.8362,  1.2051, -0.0683, -0.4875, -0.4971,  1.4690,  0.0375]],\n",
            "       grad_fn=<EmbeddingBackward>)\n",
            "tensor([[ 0.0101,  0.8362,  1.2051, -0.0683, -0.4875, -0.4971,  1.4690,  0.0375],\n",
            "        [ 0.6357, -0.7775, -0.0557, -0.0443,  2.0859,  0.1051,  0.0199, -0.6802]],\n",
            "       grad_fn=<EmbeddingBackward>)\n",
            "torch.Size([4, 8])\n",
            "tensor([[1., 1., 1., 1., 1., 1., 1., 1.],\n",
            "        [1., 1., 1., 1., 1., 1., 1., 1.]], grad_fn=<EmbeddingBackward>)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8MjBuDKaKIsM"
      },
      "source": [
        "Now, it's your time to create node embedding matrix for the graph we have!\n",
        "- We want to have **16 dimensional** vector for each node in the karate club network.\n",
        "- We want to initalize the matrix under **uniform distribution**, in the range of $[0, 1)$. We suggest you using [`torch.rand`](https://pytorch.org/docs/stable/generated/torch.rand.html)."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hMszSwRPKGn1",
        "outputId": "17ee2e79-729f-469d-95d8-0b76ec88d36c",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "# Please do not change / reset the random seed\n",
        "torch.manual_seed(1)\n",
        "\n",
        "def create_node_emb(num_node=34, embedding_dim=16):\n",
        "  # TODO: Implement this function that will create the node embedding matrix.\n",
        "  # A torch.nn.Embedding layer will be returned. You do not need to change \n",
        "  # the values of num_node and embedding_dim. The weight matrix of returned \n",
        "  # layer should be initialized under uniform distribution. \n",
        "\n",
        "  emb = nn.Embedding(num_embeddings=num_node, embedding_dim=embedding_dim)\n",
        "  emb.weight.data = torch.rand(emb.weight.data.shape)\n",
        "\n",
        "  return emb\n",
        "\n",
        "emb = create_node_emb()\n",
        "ids = torch.LongTensor([0, 3])\n",
        "\n",
        "# Print the embedding layer\n",
        "print(\"Embedding: {}\".format(emb))\n",
        "\n",
        "# An example that gets the embeddings for node 0 and 3\n",
        "print(emb(ids))"
      ],
      "execution_count": 127,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Embedding: Embedding(34, 16)\n",
            "tensor([[0.2114, 0.7335, 0.1433, 0.9647, 0.2933, 0.7951, 0.5170, 0.2801, 0.8339,\n",
            "         0.1185, 0.2355, 0.5599, 0.8966, 0.2858, 0.1955, 0.1808],\n",
            "        [0.7486, 0.6546, 0.3843, 0.9820, 0.6012, 0.3710, 0.4929, 0.9915, 0.8358,\n",
            "         0.4629, 0.9902, 0.7196, 0.2338, 0.0450, 0.7906, 0.9689]],\n",
            "       grad_fn=<EmbeddingBackward>)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4QfoANibTzyh"
      },
      "source": [
        "## Visualize the initial node embeddings\n",
        "One good way to understand an embedding matrix, is to visualize it in a 2D space.\n",
        "Here, we have implemented an embedding visualization function for you.\n",
        "We first do PCA to reduce the dimensionality of embeddings to a 2D space.\n",
        "Then visualize each point, colored by the community it belongs to."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_LCoIkarhfYD",
        "outputId": "60a472d6-60d6-4550-f77f-d8e18d04ac31",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 374
        }
      },
      "source": [
        "def visualize_emb(emb):\n",
        "  X = emb.weight.data.numpy()\n",
        "  pca = PCA(n_components=2)\n",
        "  components = pca.fit_transform(X)\n",
        "  plt.figure(figsize=(6, 6))\n",
        "  club1_x = []\n",
        "  club1_y = []\n",
        "  club2_x = []\n",
        "  club2_y = []\n",
        "  for node in G.nodes(data=True):\n",
        "    if node[1]['club'] == 'Mr. Hi':\n",
        "      club1_x.append(components[node[0]][0])\n",
        "      club1_y.append(components[node[0]][1])\n",
        "    else:\n",
        "      club2_x.append(components[node[0]][0])\n",
        "      club2_y.append(components[node[0]][1])\n",
        "  plt.scatter(club1_x, club1_y, color=\"red\", label=\"Mr. Hi\")\n",
        "  plt.scatter(club2_x, club2_y, color=\"blue\", label=\"Officer\")\n",
        "  plt.legend()\n",
        "  plt.show()\n",
        "\n",
        "# Visualize the initial random embeddding\n",
        "visualize_emb(emb)"
      ],
      "execution_count": 128,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bQIyuEz9ANb2"
      },
      "source": [
        "## Question 7: Training the embedding! What is the best performance you can get? Please report both the best loss and accuracy on Gradescope. (20 Points)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RDeQTNNxqH0j",
        "outputId": "9c85bc02-b53a-471e-e7a6-9c6e652a2ca0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 130
        }
      },
      "source": [
        "from torch.optim import SGD\n",
        "\n",
        "def accuracy(pred, label):\n",
        "  # TODO: Implement the accuracy function. This function takes the \n",
        "  # pred tensor (the resulting tensor after sigmoid) and the label \n",
        "  # tensor (torch.LongTensor). Predicted value greater than 0.5 will \n",
        "  # be classified as label 1. Else it will be classified as label 0.\n",
        "  # The returned accuracy should be rounded to 4 decimal places. \n",
        "  # For example, accuracy 0.82956 will be rounded to 0.8296.\n",
        "\n",
        "  accu = 0.0\n",
        "\n",
        "  pred_label = (pred >= 0.5) * 1\n",
        "  accu = sum((label == pred_label) * 1.0) / len(label)\n",
        "\n",
        "  return accu\n",
        "\n",
        "def train(emb, loss_fn, sigmoid, train_label, train_edge):\n",
        "  # TODO: Train the embedding layer here. You can also change epochs and \n",
        "  # learning rate. In general, you need to implement: \n",
        "  # (1) Get the embeddings of the nodes in train_edge\n",
        "  # (2) Dot product the embeddings between each node pair\n",
        "  # (3) Feed the dot product result into sigmoid\n",
        "  # (4) Feed the sigmoid output into the loss_fn\n",
        "  # (5) Print both loss and accuracy of each epoch \n",
        "  # (as a sanity check, the loss should decrease during training)\n",
        "\n",
        "  epochs = 500\n",
        "  learning_rate = 0.1\n",
        "\n",
        "  optimizer = SGD(emb.parameters(), lr=learning_rate, momentum=0.9)\n",
        "\n",
        "  for i in range(epochs):\n",
        "    #TODO\n",
        "\n",
        "loss_fn = nn.BCELoss()\n",
        "sigmoid = nn.Sigmoid()\n",
        "\n",
        "# Generate the positive and negative labels\n",
        "pos_label = torch.ones(pos_edge_index.shape[1], )\n",
        "neg_label = torch.zeros(neg_edge_index.shape[1], )\n",
        "\n",
        "# Concat positive and negative labels into one tensor\n",
        "train_label = torch.cat([pos_label, neg_label], dim=0)\n",
        "\n",
        "# Concat positive and negative edges into one tensor\n",
        "# Since the network is very small, we do not split the edges into val/test sets\n",
        "train_edge = torch.cat([pos_edge_index, neg_edge_index], dim=1)\n",
        "\n",
        "train(emb, loss_fn, sigmoid, train_label, train_edge)"
      ],
      "execution_count": 172,
      "outputs": [
        {
          "output_type": "error",
          "ename": "IndentationError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;36m  File \u001b[0;32m\"<ipython-input-172-48de965d814a>\"\u001b[0;36m, line \u001b[0;32m36\u001b[0m\n\u001b[0;31m    loss_fn = nn.BCELoss()\u001b[0m\n\u001b[0m                          ^\u001b[0m\n\u001b[0;31mIndentationError\u001b[0m\u001b[0;31m:\u001b[0m expected an indented block\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WX2PSXnTDiNi"
      },
      "source": [
        "## Visualize the final node embeddings\n",
        "Visualize your final embedding here! \n",
        "You can visually compare the figure with the previous embedding figure. \n",
        "After training, you should oberserve that the two classes are more evidently separated. \n",
        "This is a great sanitity check for your implementation as well."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MtNgl4VhYKow"
      },
      "source": [
        "# Visualize the final learned embedding\n",
        "visualize_emb(emb)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FTNyrAoSVeq9"
      },
      "source": [
        "# Submission"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "E_E7J_GkVhY_"
      },
      "source": [
        "In order to get credit, you must go submit your answers on Gradescope."
      ]
    }
  ]
}