CS224W_Colab_1_2022_23.ipynb

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  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
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    "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": {
      "provenance": [],
      "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/pipaber/GNN/blob/main/CS224W_Colab_1_2022_23.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! This Colab should take roughly 1 hour to complete.\n",
        "\n",
        "**Note**: Make sure to **restart and run all** before submission, 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": 2,
      "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 which 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"
      },
      "source": [
        "G = nx.karate_club_graph()\n",
        "\n",
        "# G is an undirected graph\n",
        "type(G)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hDvf3nm-ors4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 516
        },
        "outputId": "0e869f4b-4b59-4d32-dce4-7ce1035052a9"
      },
      "source": [
        "# Visualize the graph\n",
        "nx.draw(G, with_labels = True)"
      ],
      "execution_count": 165,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "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": "8025a5fa-1baf-4cc5-f0b1-9a92d9089950"
      },
      "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",
        "  avg_degree = 2*num_edges/num_nodes\n",
        "\n",
        "  ############# Your code here ############\n",
        "\n",
        "  #########################################\n",
        "\n",
        "  return round(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": 9,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Average degree of karate club network is 5\n"
          ]
        }
      ]
    },
    {
      "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": "c030457a-5ab9-494e-8964-f07b0fe8f4ca"
      },
      "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 = nx.average_clustering(G)\n",
        "\n",
        "  ############# Your code here ############\n",
        "  ## Note:\n",
        "  ## 1: Please use the appropriate NetworkX clustering function\n",
        "\n",
        "  #########################################\n",
        "\n",
        "  return round(avg_cluster_coef,2)\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": 10,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Average clustering coefficient of karate club network is 0.57\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "nx.average_clustering(G)"
      ],
      "metadata": {
        "id": "3HQPVsAcn7Oj",
        "outputId": "22f54667-36fc-4d90-da91-88f5e46fed65",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.5706384782076823"
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ]
    },
    {
      "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",
        "Page Rank measures importance of nodes in a graph using the link structure of the web. A “vote” from an important page is worth more. Specifically, if  a page $i$ with importance $r_i$ has $d_i$ out-links, then each link gets $\\frac{r_i}{d_i}$ votes. Thus, the importance of a Page $j$, represented as $r_j$ is the sum of the votes on its in links.\n",
        "$$r_j = \\sum_{i \\rightarrow j} \\frac{r_i}{d_i}$$, where $d_i$ is the out degree of node $i$.\n",
        "\n",
        "The PageRank algorithm (used by Google) outputs a probability distribution which represent the likelihood of a random surfer clicking on links will arrive at any particular page. At each time step, the random surfer has two options\n",
        "- With prob. $\\beta$, follow a link at random\n",
        "- With prob. $1- \\beta$, jump to a random page\n",
        "\n",
        "Thus, the importance of a particular page is calculated with the following PageRank equation:\n",
        " $$r_j = \\sum_{i \\rightarrow j} \\beta \\frac{r_i}{d_i} + (1 - \\beta) \\frac{1}{N}$$\n",
        "\n",
        "Please complete the code block by implementing the above PageRank equation for node 0.\n",
        "\n",
        "Note - You can refer to more information from the slides here - http://snap.stanford.edu/class/cs224w-2020/slides/04-pagerank.pdf\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BOGdWjNc6O7x",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "600577bb-204e-4ec7-fd84-0813cb8000dc"
      },
      "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",
        "  r1 = 0\n",
        "\n",
        "  ############# Your code here ############\n",
        "  ## Note:\n",
        "  ## 1: You should not use nx.pagerank\n",
        "\n",
        "  summatory = 0\n",
        "\n",
        "  in_deg_nodes = [i[1] for i in list(G.edges) if i[0] == node_id]\n",
        "\n",
        "  for i in in_deg_nodes:\n",
        "    summatory += (beta*r0)/G.degree[i]\n",
        "\n",
        "  r1 = summatory + (1-beta)*r0\n",
        "\n",
        "  #########################################\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": 29,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The PageRank value for node 0 after one iteration is 0.12810457516339868\n"
          ]
        }
      ]
    },
    {
      "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": "bfd280ff-f4b8-4265-dbed-12b2fe05aadf"
      },
      "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",
        "\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",
        "  closeness = nx.closeness_centrality(G, u=node)\n",
        "\n",
        "  #########################################\n",
        "\n",
        "  return closeness\n",
        "\n",
        "node = 5\n",
        "closeness = closeness_centrality(G, node=node)\n",
        "print(\"The node 5 has closeness centrality {}\".format(closeness))"
      ],
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The node 5 has closeness centrality 0.38372093023255816\n"
          ]
        }
      ]
    },
    {
      "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",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "a9e473de-f0cb-48fd-96be-7d46ece4d947"
      },
      "source": [
        "import torch\n",
        "print(torch.__version__)"
      ],
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "2.2.1+cu121\n"
          ]
        }
      ]
    },
    {
      "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",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "4715eb51-c66a-4066-ccbb-011912fb6aec"
      },
      "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": 33,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "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([[0.4677, 0.5218, 0.8721, 0.9888],\n",
            "        [0.5375, 0.4288, 0.6120, 0.5621],\n",
            "        [0.9678, 0.1501, 0.2332, 0.8240]])\n",
            "torch.Size([3, 4])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "x8mp66eHBxWC"
      },
      "source": [
        "PyTorch tensor contains elements for a single data type, the `dtype`."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rQiOvKJJBwq4",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "b9a676db-00aa-4349-dd01-c8ecb3582e7a"
      },
      "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": 34,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "torch.float32\n",
            "torch.int64\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "I9EfegIRDkk2"
      },
      "source": [
        "## Question 5: Get 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"
      },
      "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",
        "\n",
        "  ############# Your code here ############\n",
        "\n",
        "  edge_list = list(G.edges)\n",
        "\n",
        "  #########################################\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, len(edge_list)].\n",
        "\n",
        "\n",
        "  ############# Your code here ############\n",
        "\n",
        "  edge_index = torch.tensor(edge_list).T\n",
        "\n",
        "  #########################################\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": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UBL-ZmdHWqIu"
      },
      "source": [
        "## Question 6: Please implement following function that samples negative edges. Then answer which edges (edge_1 to edge_5) are the negative edges in the karate club network? (10 Points)\n",
        "\n",
        "\"Negative\" edges refer to the edges/links that do not exist in the graph. The term \"negative\" is borrowed from \"negative sampling\" in link prediction. It has nothing to do with the edge weights.\n",
        "\n",
        "For example, given an edge (src, dst), you should check that neither (src, dst) nor (dst, src) are edges in the Graph. If these hold true, then it is a negative edge."
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "G.number_of_nodes()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "h4YRp52QIurT",
        "outputId": "9b1e1074-3f34-427c-e472-7fdf0dde53cf"
      },
      "execution_count": 49,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "34"
            ]
          },
          "metadata": {},
          "execution_count": 49
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9N8VT1f8-IJ8",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "697a0e07-1656-4c6a-f701-5c3105199910"
      },
      "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 loops 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",
        "\n",
        "  ############# Your code here ############\n",
        "\n",
        "  neg_edge_list = []\n",
        "\n",
        "  max_index = G.number_of_nodes()\n",
        "\n",
        "  edges_ingraph = G.edges\n",
        "\n",
        "  n_sampled = 0\n",
        "\n",
        "  while n_sampled < num_neg_samples:\n",
        "\n",
        "    sample = (random.randint(0,max_index), random.randint(0,max_index))\n",
        "\n",
        "    if sample in edges_ingraph:\n",
        "      pass\n",
        "\n",
        "    elif (sample not in edges_ingraph) and (sample[0] != sample[1]):\n",
        "      n_sampled += 1\n",
        "      neg_edge_list.append(sample)\n",
        "\n",
        "\n",
        "  #########################################\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",
        "############# Your code here ############\n",
        "## Note:\n",
        "## 1: For each of the 5 edges, print whether it can be negative edge\n",
        "\n",
        "ll = [edge_1, edge_2, edge_3, edge_5, edge_5]\n",
        "\n",
        "[print(f\"{i} Not a negative edge\") if i in G.edges else print(f\"{i} is a negative edge\") for i in ll]\n",
        "\n",
        "\n",
        "#########################################"
      ],
      "execution_count": 68,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The neg_edge_index tensor has shape torch.Size([2, 78])\n",
            "(7, 1) Not a negative edge\n",
            "(1, 33) is a negative edge\n",
            "(33, 22) Not a negative edge\n",
            "(4, 2) is a negative edge\n",
            "(4, 2) is a negative edge\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[None, None, None, None, None]"
            ]
          },
          "metadata": {},
          "execution_count": 68
        }
      ]
    },
    {
      "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",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "633ae94e-6b0d-44e8-e9ba-1445b9a5ae7b"
      },
      "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": 69,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "2.2.1+cu121\n"
          ]
        }
      ]
    },
    {
      "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",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "bd5a063e-0827-41d9-c663-6a80a9cdb55c"
      },
      "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": 76,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Sample embedding layer: Embedding(4, 8)\n"
          ]
        }
      ]
    },
    {
      "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",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "81182e6c-77ea-46d6-cf57-e37fd3a1befd"
      },
      "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": 73,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor([[-0.8110, -0.8199, -0.2571,  0.0340, -0.1790, -0.6079, -0.4750,  0.8072]],\n",
            "       grad_fn=<EmbeddingBackward0>)\n",
            "tensor([[-0.8110, -0.8199, -0.2571,  0.0340, -0.1790, -0.6079, -0.4750,  0.8072],\n",
            "        [ 0.9062, -0.7981, -1.3247, -1.2062,  1.7870,  1.5165, -1.2992, -0.4539]],\n",
            "       grad_fn=<EmbeddingBackward0>)\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=<EmbeddingBackward0>)\n"
          ]
        }
      ]
    },
    {
      "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",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "678f0866-5966-4555-f584-ecb44edd7239"
      },
      "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",
        "\n",
        "\n",
        "  ############# Your code here ############\n",
        "\n",
        "  emb = nn.Embedding(num_embeddings=num_node, embedding_dim=embedding_dim)\n",
        "\n",
        "  #########################################\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": 161,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Embedding: Embedding(34, 16)\n",
            "tensor([[-1.5256, -0.7502, -0.6540, -1.6095, -0.1002, -0.6092, -0.9798, -1.6091,\n",
            "         -0.7121,  0.3037, -0.7773, -0.2515, -0.2223,  1.6871,  0.2284,  0.4676],\n",
            "        [-0.9274,  0.5451,  0.0663, -0.4370,  0.7626,  0.4415,  1.1651,  2.0154,\n",
            "          0.1374,  0.9386, -0.1860, -0.6446,  1.5392, -0.8696, -3.3312, -0.7479]],\n",
            "       grad_fn=<EmbeddingBackward0>)\n"
          ]
        }
      ]
    },
    {
      "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 we visualize each point, colored by the community it belongs to."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_LCoIkarhfYD",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 522
        },
        "outputId": "50537b3a-e2ae-412b-be58-c71596d136a3"
      },
      "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": 162,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 600x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "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)\n",
        "\n",
        "We want to optimize our embeddings for the task of classifying edges as positive or negative. Given an edge and the embeddings for each node, the dot product of the embeddings, followed by a sigmoid, should give us the likelihood of that edge being either positive (output of sigmoid > 0.5) or negative (output of sigmoid < 0.5).\n",
        "\n",
        "Note that we're using the functions you wrote in the previous questions, _as well as the variables initialized in previous cells_. If you're running into issues, make sure your answers to questions 1-6 are correct."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RDeQTNNxqH0j"
      },
      "source": [
        "from torch.optim import SGD\n",
        "import torch.nn as nn\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",
        "  ############# Your code here ############\n",
        "\n",
        "  preds = (pred >= 0.5).int()\n",
        "  correct_predictions = (preds == label)\n",
        "  accu = correct_predictions.sum().item() / len(label)\n",
        "\n",
        "\n",
        "  #########################################\n",
        "\n",
        "  return round(accu, 4)\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",
        "  # (6) Update the embeddings using the loss and optimizer\n",
        "  # (as a sanity check, the loss should decrease during training)\n",
        "\n",
        "  epochs = 5000\n",
        "  learning_rate = 0.1\n",
        "\n",
        "  optimizer = SGD(emb.parameters(), lr=learning_rate, momentum=0.9)\n",
        "\n",
        "  train_label = train_label.float()\n",
        "\n",
        "  loss_t = []\n",
        "  acc = []\n",
        "\n",
        "  for i in range(epochs):\n",
        "\n",
        "    ############# Your code here ############\n",
        "    optimizer.zero_grad()\n",
        "\n",
        "\n",
        "    train_embeds = emb(train_edge)\n",
        "\n",
        "    dot_prod = train_embeds[0].mm(train_embeds[1].T).diag()\n",
        "\n",
        "    ss = sigmoid(dot_prod)\n",
        "\n",
        "    loss = loss_fn(ss, train_label)\n",
        "\n",
        "    loss_t.append(loss)\n",
        "\n",
        "    loss.backward()\n",
        "    optimizer.step()\n",
        "\n",
        "    accu = accuracy(ss, train_label)\n",
        "    acc.append(accu)\n",
        "\n",
        "    print(f\"Current loss: {loss}\\nCurrent accuracy: {accu}\")\n",
        "\n",
        "  return loss_t, acc\n",
        "\n",
        "    #########################################\n",
        "\n",
        "loss_fn = nn.BCELoss()\n",
        "sigmoid = nn.Sigmoid()\n",
        "\n",
        "print(pos_edge_index.shape)\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",
        "print(train_edge.shape)\n",
        "\n",
        "emb = create_node_emb(num_node=train_edge.shape[1])\n",
        "\n",
        "res = train(emb, loss_fn, sigmoid, train_label, train_edge)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "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",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 522
        },
        "outputId": "ec9f7bf1-38c2-4220-fcb5-fda7418bf355"
      },
      "source": [
        "# Visualize the final learned embedding\n",
        "visualize_emb(emb)"
      ],
      "execution_count": 164,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 600x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "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."
      ]
    }
  ]
}