CS224W_Colab1.ipynb

{
 "cells": [
  {
   "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",
   "execution_count": 1,
   "metadata": {
    "id": "VWPkJjPAfVNW"
   },
   "outputs": [],
   "source": [
    "import networkx as nx"
   ]
  },
  {
   "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",
   "execution_count": 2,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "VIETqEfrfy5Y",
    "outputId": "2f9e8ba3-4b18-42be-dec1-05cb8d2837c8"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "networkx.classes.graph.Graph"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G = nx.karate_club_graph()\n",
    "\n",
    "# G is an undirected graph\n",
    "type(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 318
    },
    "id": "hDvf3nm-ors4",
    "outputId": "14023a82-fe97-4064-8673-7300e987ffd1"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualize the graph\n",
    "nx.draw(G, with_labels = True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "FX25Y1CrYmgN"
   },
   "source": [
    "## Question 1: What is the average degree of the karate club network? (5 Points)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "AUhES1VYo3tB",
    "outputId": "77a151c2-9e33-425e-a708-51b976a40b48"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average degree of karate club network is 2\n"
     ]
    }
   ],
   "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 = 0\n",
    "\n",
    "    ############# Your code here ############\n",
    "    avg_degree = round( num_edges / num_nodes)\n",
    "    #########################################\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))"
   ]
  },
  {
   "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",
   "execution_count": 5,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "k15XKEto1aYJ",
    "outputId": "0ef30024-a820-43e2-ba4c-ee4285bd4ce4"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average clustering coefficient of karate club network is 0.57\n"
     ]
    }
   ],
   "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 = 0\n",
    "\n",
    "    ############# Your code here ############\n",
    "    ## Note: \n",
    "    ## 1: Please use the appropriate NetworkX clustering function\n",
    "    avg_cluster_coef = round(nx.average_clustering(G), 2)\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))"
   ]
  },
  {
   "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",
   "execution_count": 6,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "BOGdWjNc6O7x",
    "outputId": "5f10b403-0811-4efa-b0df-a1e831779824"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The PageRank value for node 0 after one iteration is 0.13\n"
     ]
    }
   ],
   "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 can be initialized as (1 - beta) / N (number of nodes)\n",
    "    r1 = 0\n",
    "\n",
    "    ############# Your code here ############\n",
    "    ## Note: \n",
    "    ## 1: You should not use nx.pagerank\n",
    "    # loop over edges\n",
    "    r1 = (1 - beta) / len(G.nodes())\n",
    "    \n",
    "    for edge in G.edges(node_id):\n",
    "        # extract j from edge (i, j)\n",
    "        j = edge[1]\n",
    "        \n",
    "        # update r1\n",
    "        r1 += (beta * r0) /  G.degree(j)\n",
    "\n",
    "    r1 = round(r1, 2)\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))"
   ]
  },
  {
   "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",
   "execution_count": 7,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "XbCsq_tl-3ok",
    "outputId": "7520a487-4511-4252-d792-951061244595"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The node 5 has closeness centrality 0.01\n"
     ]
    }
   ],
   "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 = 0\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",
    "    # get max_degree to unnormalize\n",
    "    \n",
    "    no_of_desc = len(nx.descendants(G, node))\n",
    "    closeness = round(nx.closeness_centrality(G, node) / no_of_desc, 2)\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))"
   ]
  },
  {
   "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",
   "execution_count": 3,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "ntuPVat_BAf1",
    "outputId": "307ab4e7-9989-4662-a621-c97f9cbe48b4"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.12.1\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "print(torch.__version__)"
   ]
  },
  {
   "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",
   "execution_count": 4,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "W2ySw3m-A9qF",
    "outputId": "2c7e46b1-8546-4faa-f80c-2aee95369ba3"
   },
   "outputs": [
    {
     "name": "stdout",
     "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([[0.0790, 0.2423, 0.6790, 0.6772],\n",
      "        [0.1815, 0.4736, 0.5999, 0.4465],\n",
      "        [0.0739, 0.5486, 0.9740, 0.7859]])\n",
      "torch.Size([3, 4])\n"
     ]
    }
   ],
   "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)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "x8mp66eHBxWC"
   },
   "source": [
    "PyTorch tensor contains elements for a single data type, the `dtype`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "rQiOvKJJBwq4",
    "outputId": "262eefb9-d91d-4d0a-ce3f-bb210b297f89"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.float32\n",
      "torch.int64\n"
     ]
    }
   ],
   "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)"
   ]
  },
  {
   "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",
   "execution_count": 6,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "kEtVxMFID3ZT",
    "outputId": "d55c1904-b9b1-4d75-cbb6-43ea505da042"
   },
   "outputs": [
    {
     "name": "stdout",
     "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"
     ]
    }
   ],
   "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 = []\n",
    "\n",
    "    ############# Your code here ############\n",
    "    edge_list = [x for x in G.edges]\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 x len(edge_list)].\n",
    "\n",
    "    \n",
    "    ############# Your code here ############\n",
    "    edge_index = torch.tensor(edge_list).T\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)))"
   ]
  },
  {
   "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) can be potential negative edges in the karate club network? (10 Points)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "9N8VT1f8-IJ8",
    "outputId": "27ee01b1-db56-4cb8-c8dc-dfa6d924ecd0"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The neg_edge_index tensor has shape torch.Size([2, 78])\n",
      "Edge 1: False\n",
      "Edge 2: True\n",
      "Edge 3: False\n",
      "Edge 4: False\n",
      "Edge 5: True\n"
     ]
    }
   ],
   "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",
    "    neg_edge_list = []\n",
    "\n",
    "    ############# Your code here ############\n",
    "    counter = num_neg_samples\n",
    "    nodes = list(G.nodes)\n",
    "    for i in nodes:\n",
    "        nbr_set = set(G.neighbors(i))\n",
    "        for j in nodes[i + 1:]:\n",
    "            if j not in nbr_set:\n",
    "                # negative edge found\n",
    "                neg_edge_list.append((i, j))\n",
    "                counter -= 1\n",
    "                \n",
    "                if counter == 0:\n",
    "                    return neg_edge_list\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",
    "def check_neg_edge(edge):\n",
    "    return (edge[1] not in set(G.neighbors(edge[0])))\n",
    "\n",
    "## Note:\n",
    "## 1: For each of the 5 edges, print whether it can be negative edge\n",
    "print (f'Edge 1: {check_neg_edge(edge_1)}')\n",
    "print (f'Edge 2: {check_neg_edge(edge_2)}')\n",
    "print (f'Edge 3: {check_neg_edge(edge_3)}')\n",
    "print (f'Edge 4: {check_neg_edge(edge_4)}')\n",
    "print (f'Edge 5: {check_neg_edge(edge_5)}')\n",
    "#########################################"
   ]
  },
  {
   "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",
   "execution_count": 24,
   "metadata": {
    "id": "Lnqn9H6s_ehX"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.12.1\n"
     ]
    }
   ],
   "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__)"
   ]
  },
  {
   "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",
   "execution_count": 25,
   "metadata": {
    "id": "aRiWGuLAx5yx"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sample embedding layer: Embedding(4, 8)\n"
     ]
    }
   ],
   "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))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "bS9qQfeujEVh"
   },
   "source": [
    "We can select items from the embedding matrix, by using Tensor indices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "id": "9AGIfP4QEDr8"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[1., 1., 1., 1., 1., 1., 1., 1.]], grad_fn=<EmbeddingBackward0>)\n",
      "tensor([[1., 1., 1., 1., 1., 1., 1., 1.],\n",
      "        [1., 1., 1., 1., 1., 1., 1., 1.]], 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"
     ]
    }
   ],
   "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))"
   ]
  },
  {
   "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",
   "execution_count": 31,
   "metadata": {
    "id": "hMszSwRPKGn1"
   },
   "outputs": [
    {
     "name": "stdout",
     "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=<EmbeddingBackward0>)\n"
     ]
    }
   ],
   "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",
    "    ############# Your code here ############\n",
    "    emb = nn.Embedding(num_embeddings=num_node, embedding_dim=embedding_dim)\n",
    "    emb.weight.data.uniform_(0, 1)\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))"
   ]
  },
  {
   "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",
   "execution_count": 33,
   "metadata": {
    "id": "_LCoIkarhfYD"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "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)"
   ]
  },
  {
   "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",
   "execution_count": 96,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 255
    },
    "collapsed": true,
    "id": "RDeQTNNxqH0j",
    "jupyter": {
     "outputs_hidden": true
    },
    "outputId": "edd565ad-1305-4d65-8109-81a527bf869f",
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([2, 78])\n",
      "torch.Size([2, 156])\n",
      "Accuracy in epoch 0: 1.0 and Loss is 0.0034290386829525232\n",
      "Accuracy in epoch 1: 1.0 and Loss is 0.00342856184579432\n",
      "Accuracy in epoch 2: 1.0 and Loss is 0.0034276561345905066\n",
      "Accuracy in epoch 3: 1.0 and Loss is 0.003426362993195653\n",
      "Accuracy in epoch 4: 1.0 and Loss is 0.0034247231669723988\n",
      "Accuracy in epoch 5: 1.0 and Loss is 0.003422768786549568\n",
      "Accuracy in epoch 6: 1.0 and Loss is 0.0034205354750156403\n",
      "Accuracy in epoch 7: 1.0 and Loss is 0.0034180586226284504\n",
      "Accuracy in epoch 8: 1.0 and Loss is 0.003415345447137952\n",
      "Accuracy in epoch 9: 1.0 and Loss is 0.003412434598430991\n",
      "Accuracy in epoch 10: 1.0 and Loss is 0.003409344470128417\n",
      "Accuracy in epoch 11: 1.0 and Loss is 0.003406096249818802\n",
      "Accuracy in epoch 12: 1.0 and Loss is 0.0034027029760181904\n",
      "Accuracy in epoch 13: 1.0 and Loss is 0.0033991807140409946\n",
      "Accuracy in epoch 14: 1.0 and Loss is 0.0033955436665564775\n",
      "Accuracy in epoch 15: 1.0 and Loss is 0.003391803940758109\n",
      "Accuracy in epoch 16: 1.0 and Loss is 0.0033879780676215887\n",
      "Accuracy in epoch 17: 1.0 and Loss is 0.00338406371884048\n",
      "Accuracy in epoch 18: 1.0 and Loss is 0.0033800809178501368\n",
      "Accuracy in epoch 19: 1.0 and Loss is 0.003376033389940858\n",
      "Accuracy in epoch 20: 1.0 and Loss is 0.0033719372004270554\n",
      "Accuracy in epoch 21: 1.0 and Loss is 0.003367791650816798\n",
      "Accuracy in epoch 22: 1.0 and Loss is 0.003363600466400385\n",
      "Accuracy in epoch 23: 1.0 and Loss is 0.003359367838129401\n",
      "Accuracy in epoch 24: 1.0 and Loss is 0.0033551042433828115\n",
      "Accuracy in epoch 25: 1.0 and Loss is 0.0033508222550153732\n",
      "Accuracy in epoch 26: 1.0 and Loss is 0.0033465097658336163\n",
      "Accuracy in epoch 27: 1.0 and Loss is 0.0033421714324504137\n",
      "Accuracy in epoch 28: 1.0 and Loss is 0.0033378207590430975\n",
      "Accuracy in epoch 29: 1.0 and Loss is 0.0033334547188133\n",
      "Accuracy in epoch 30: 1.0 and Loss is 0.003329081693664193\n",
      "Accuracy in epoch 31: 1.0 and Loss is 0.0033246909733861685\n",
      "Accuracy in epoch 32: 1.0 and Loss is 0.003320298856124282\n",
      "Accuracy in epoch 33: 1.0 and Loss is 0.003315892070531845\n",
      "Accuracy in epoch 34: 1.0 and Loss is 0.0033114950638264418\n",
      "Accuracy in epoch 35: 1.0 and Loss is 0.0033070866484194994\n",
      "Accuracy in epoch 36: 1.0 and Loss is 0.003302682191133499\n",
      "Accuracy in epoch 37: 1.0 and Loss is 0.003298274939879775\n",
      "Accuracy in epoch 38: 1.0 and Loss is 0.0032938681542873383\n",
      "Accuracy in epoch 39: 1.0 and Loss is 0.003289462998509407\n",
      "Accuracy in epoch 40: 1.0 and Loss is 0.003285060403868556\n",
      "Accuracy in epoch 41: 1.0 and Loss is 0.003280660370364785\n",
      "Accuracy in epoch 42: 1.0 and Loss is 0.0032762743066996336\n",
      "Accuracy in epoch 43: 1.0 and Loss is 0.003271880093961954\n",
      "Accuracy in epoch 44: 1.0 and Loss is 0.0032675021793693304\n",
      "Accuracy in epoch 45: 1.0 and Loss is 0.0032631284557282925\n",
      "Accuracy in epoch 46: 1.0 and Loss is 0.0032587568275630474\n",
      "Accuracy in epoch 47: 1.0 and Loss is 0.0032543991692364216\n",
      "Accuracy in epoch 48: 1.0 and Loss is 0.0032500438392162323\n",
      "Accuracy in epoch 49: 1.0 and Loss is 0.003245693864300847\n",
      "Accuracy in epoch 50: 1.0 and Loss is 0.003241355996578932\n",
      "Accuracy in epoch 51: 1.0 and Loss is 0.0032370234839618206\n",
      "Accuracy in epoch 52: 1.0 and Loss is 0.0032327042426913977\n",
      "Accuracy in epoch 53: 1.0 and Loss is 0.003228386165574193\n",
      "Accuracy in epoch 54: 1.0 and Loss is 0.003224083920940757\n",
      "Accuracy in epoch 55: 1.0 and Loss is 0.003219792153686285\n",
      "Accuracy in epoch 56: 1.0 and Loss is 0.003215502481907606\n",
      "Accuracy in epoch 57: 1.0 and Loss is 0.003211231669411063\n",
      "Accuracy in epoch 58: 1.0 and Loss is 0.0032069587614387274\n",
      "Accuracy in epoch 59: 1.0 and Loss is 0.0032027000561356544\n",
      "Accuracy in epoch 60: 1.0 and Loss is 0.0031984581146389246\n",
      "Accuracy in epoch 61: 1.0 and Loss is 0.003194214077666402\n",
      "Accuracy in epoch 62: 1.0 and Loss is 0.003189985640347004\n",
      "Accuracy in epoch 63: 1.0 and Loss is 0.003185765817761421\n",
      "Accuracy in epoch 64: 1.0 and Loss is 0.003181556472554803\n",
      "Accuracy in epoch 65: 1.0 and Loss is 0.003177359700202942\n",
      "Accuracy in epoch 66: 1.0 and Loss is 0.0031731645576655865\n",
      "Accuracy in epoch 67: 1.0 and Loss is 0.003168985713273287\n",
      "Accuracy in epoch 68: 1.0 and Loss is 0.0031648126896470785\n",
      "Accuracy in epoch 69: 1.0 and Loss is 0.003160653403028846\n",
      "Accuracy in epoch 70: 1.0 and Loss is 0.0031565011013299227\n",
      "Accuracy in epoch 71: 1.0 and Loss is 0.0031523576471954584\n",
      "Accuracy in epoch 72: 1.0 and Loss is 0.0031482286285609007\n",
      "Accuracy in epoch 73: 1.0 and Loss is 0.003144105663523078\n",
      "Accuracy in epoch 74: 1.0 and Loss is 0.0031399959698319435\n",
      "Accuracy in epoch 75: 1.0 and Loss is 0.0031358946580439806\n",
      "Accuracy in epoch 76: 1.0 and Loss is 0.003131801960989833\n",
      "Accuracy in epoch 77: 1.0 and Loss is 0.0031277143862098455\n",
      "Accuracy in epoch 78: 1.0 and Loss is 0.0031236433424055576\n",
      "Accuracy in epoch 79: 1.0 and Loss is 0.0031195799820125103\n",
      "Accuracy in epoch 80: 1.0 and Loss is 0.0031155268661677837\n",
      "Accuracy in epoch 81: 1.0 and Loss is 0.0031114802695810795\n",
      "Accuracy in epoch 82: 1.0 and Loss is 0.003107447177171707\n",
      "Accuracy in epoch 83: 1.0 and Loss is 0.0031034238636493683\n",
      "Accuracy in epoch 84: 1.0 and Loss is 0.0030994080007076263\n",
      "Accuracy in epoch 85: 1.0 and Loss is 0.003095401218160987\n",
      "Accuracy in epoch 86: 1.0 and Loss is 0.0030914018861949444\n",
      "Accuracy in epoch 87: 1.0 and Loss is 0.003087418619543314\n",
      "Accuracy in epoch 88: 1.0 and Loss is 0.0030834381468594074\n",
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      "Accuracy in epoch 375: 1.0 and Loss is 0.002236258005723357\n",
      "Accuracy in epoch 376: 1.0 and Loss is 0.002234070561826229\n",
      "Accuracy in epoch 377: 1.0 and Loss is 0.0022318868432193995\n",
      "Accuracy in epoch 378: 1.0 and Loss is 0.0022297101095318794\n",
      "Accuracy in epoch 379: 1.0 and Loss is 0.0022275410592556\n",
      "Accuracy in epoch 380: 1.0 and Loss is 0.0022253647912293673\n",
      "Accuracy in epoch 381: 1.0 and Loss is 0.0022232001647353172\n",
      "Accuracy in epoch 382: 1.0 and Loss is 0.0022210434544831514\n",
      "Accuracy in epoch 383: 1.0 and Loss is 0.0022188855800777674\n",
      "Accuracy in epoch 384: 1.0 and Loss is 0.0022167316637933254\n",
      "Accuracy in epoch 385: 1.0 and Loss is 0.0022145784460008144\n",
      "Accuracy in epoch 386: 1.0 and Loss is 0.00221243011765182\n",
      "Accuracy in epoch 387: 1.0 and Loss is 0.0022102922666817904\n",
      "Accuracy in epoch 388: 1.0 and Loss is 0.0022081525530666113\n",
      "Accuracy in epoch 389: 1.0 and Loss is 0.00220601842738688\n",
      "Accuracy in epoch 390: 1.0 and Loss is 0.002203887328505516\n",
      "Accuracy in epoch 391: 1.0 and Loss is 0.002201762283220887\n",
      "Accuracy in epoch 392: 1.0 and Loss is 0.002199634676799178\n",
      "Accuracy in epoch 393: 1.0 and Loss is 0.0021975194104015827\n",
      "Accuracy in epoch 394: 1.0 and Loss is 0.0021954018156975508\n",
      "Accuracy in epoch 395: 1.0 and Loss is 0.0021932886447757483\n",
      "Accuracy in epoch 396: 1.0 and Loss is 0.002191187348216772\n",
      "Accuracy in epoch 397: 1.0 and Loss is 0.002189077902585268\n",
      "Accuracy in epoch 398: 1.0 and Loss is 0.0021869800984859467\n",
      "Accuracy in epoch 399: 1.0 and Loss is 0.0021848822943866253\n",
      "Accuracy in epoch 400: 1.0 and Loss is 0.002182788448408246\n",
      "Accuracy in epoch 401: 1.0 and Loss is 0.002180699724704027\n",
      "Accuracy in epoch 402: 1.0 and Loss is 0.002178616588935256\n",
      "Accuracy in epoch 403: 1.0 and Loss is 0.0021765350829809904\n",
      "Accuracy in epoch 404: 1.0 and Loss is 0.002174453577026725\n",
      "Accuracy in epoch 405: 1.0 and Loss is 0.0021723771933466196\n",
      "Accuracy in epoch 406: 1.0 and Loss is 0.0021703136153519154\n",
      "Accuracy in epoch 407: 1.0 and Loss is 0.0021682404913008213\n",
      "Accuracy in epoch 408: 1.0 and Loss is 0.002166184363886714\n",
      "Accuracy in epoch 409: 1.0 and Loss is 0.002164121950045228\n",
      "Accuracy in epoch 410: 1.0 and Loss is 0.0021620620973408222\n",
      "Accuracy in epoch 411: 1.0 and Loss is 0.0021600089967250824\n",
      "Accuracy in epoch 412: 1.0 and Loss is 0.0021579645108431578\n",
      "Accuracy in epoch 413: 1.0 and Loss is 0.0021559211891144514\n",
      "Accuracy in epoch 414: 1.0 and Loss is 0.0021538783330470324\n",
      "Accuracy in epoch 415: 1.0 and Loss is 0.0021518419962376356\n",
      "Accuracy in epoch 416: 1.0 and Loss is 0.002149806823581457\n",
      "Accuracy in epoch 417: 1.0 and Loss is 0.002147773513570428\n",
      "Accuracy in epoch 418: 1.0 and Loss is 0.0021457471884787083\n",
      "Accuracy in epoch 419: 1.0 and Loss is 0.0021437250543385744\n",
      "Accuracy in epoch 420: 1.0 and Loss is 0.0021416994277387857\n",
      "Accuracy in epoch 421: 1.0 and Loss is 0.002139688702300191\n",
      "Accuracy in epoch 422: 1.0 and Loss is 0.0021376728545874357\n",
      "Accuracy in epoch 423: 1.0 and Loss is 0.002135662827640772\n",
      "Accuracy in epoch 424: 1.0 and Loss is 0.002133661648258567\n",
      "Accuracy in epoch 425: 1.0 and Loss is 0.0021316595375537872\n",
      "Accuracy in epoch 426: 1.0 and Loss is 0.0021296602208167315\n",
      "Accuracy in epoch 427: 1.0 and Loss is 0.0021276683546602726\n",
      "Accuracy in epoch 428: 1.0 and Loss is 0.0021256746258586645\n",
      "Accuracy in epoch 429: 1.0 and Loss is 0.0021236841566860676\n",
      "Accuracy in epoch 430: 1.0 and Loss is 0.0021216925233602524\n",
      "Accuracy in epoch 431: 1.0 and Loss is 0.0021197150927037\n",
      "Accuracy in epoch 432: 1.0 and Loss is 0.002117738826200366\n",
      "Accuracy in epoch 433: 1.0 and Loss is 0.002115759765729308\n",
      "Accuracy in epoch 434: 1.0 and Loss is 0.0021137897856533527\n",
      "Accuracy in epoch 435: 1.0 and Loss is 0.0021118265576660633\n",
      "Accuracy in epoch 436: 1.0 and Loss is 0.002109858440235257\n",
      "Accuracy in epoch 437: 1.0 and Loss is 0.002107899868860841\n",
      "Accuracy in epoch 438: 1.0 and Loss is 0.0021059459540992975\n",
      "Accuracy in epoch 439: 1.0 and Loss is 0.002103992272168398\n",
      "Accuracy in epoch 440: 1.0 and Loss is 0.002102033933624625\n",
      "Accuracy in epoch 441: 1.0 and Loss is 0.0021000925917178392\n",
      "Accuracy in epoch 442: 1.0 and Loss is 0.002098145429044962\n",
      "Accuracy in epoch 443: 1.0 and Loss is 0.002096201293170452\n",
      "Accuracy in epoch 444: 1.0 and Loss is 0.0020942639093846083\n",
      "Accuracy in epoch 445: 1.0 and Loss is 0.0020923323463648558\n",
      "Accuracy in epoch 446: 1.0 and Loss is 0.0020904007833451033\n",
      "Accuracy in epoch 447: 1.0 and Loss is 0.002088474575430155\n",
      "Accuracy in epoch 448: 1.0 and Loss is 0.002086549997329712\n",
      "Accuracy in epoch 449: 1.0 and Loss is 0.002084628213196993\n",
      "Accuracy in epoch 450: 1.0 and Loss is 0.0020827099215239286\n",
      "Accuracy in epoch 451: 1.0 and Loss is 0.002080797916278243\n",
      "Accuracy in epoch 452: 1.0 and Loss is 0.0020788891706615686\n",
      "Accuracy in epoch 453: 1.0 and Loss is 0.0020769794937223196\n",
      "Accuracy in epoch 454: 1.0 and Loss is 0.0020750719122588634\n",
      "Accuracy in epoch 455: 1.0 and Loss is 0.002073173876851797\n",
      "Accuracy in epoch 456: 1.0 and Loss is 0.0020712700206786394\n",
      "Accuracy in epoch 457: 1.0 and Loss is 0.00206938199698925\n",
      "Accuracy in epoch 458: 1.0 and Loss is 0.002067487221211195\n",
      "Accuracy in epoch 459: 1.0 and Loss is 0.002065599663183093\n",
      "Accuracy in epoch 460: 1.0 and Loss is 0.002063716994598508\n",
      "Accuracy in epoch 461: 1.0 and Loss is 0.002061831997707486\n",
      "Accuracy in epoch 462: 1.0 and Loss is 0.0020599556155502796\n",
      "Accuracy in epoch 463: 1.0 and Loss is 0.0020580748096108437\n",
      "Accuracy in epoch 464: 1.0 and Loss is 0.0020562035497277975\n",
      "Accuracy in epoch 465: 1.0 and Loss is 0.0020543367136269808\n",
      "Accuracy in epoch 466: 1.0 and Loss is 0.0020524703431874514\n",
      "Accuracy in epoch 467: 1.0 and Loss is 0.002050610026344657\n",
      "Accuracy in epoch 468: 1.0 and Loss is 0.0020487483125180006\n",
      "Accuracy in epoch 469: 1.0 and Loss is 0.002046892186626792\n",
      "Accuracy in epoch 470: 1.0 and Loss is 0.0020450400188565254\n",
      "Accuracy in epoch 471: 1.0 and Loss is 0.0020431873854249716\n",
      "Accuracy in epoch 472: 1.0 and Loss is 0.0020413410384207964\n",
      "Accuracy in epoch 473: 1.0 and Loss is 0.0020394970197230577\n",
      "Accuracy in epoch 474: 1.0 and Loss is 0.002037658588960767\n",
      "Accuracy in epoch 475: 1.0 and Loss is 0.002035822719335556\n",
      "Accuracy in epoch 476: 1.0 and Loss is 0.0020339859183877707\n",
      "Accuracy in epoch 477: 1.0 and Loss is 0.002032154705375433\n",
      "Accuracy in epoch 478: 1.0 and Loss is 0.0020303241908550262\n",
      "Accuracy in epoch 479: 1.0 and Loss is 0.002028494607657194\n",
      "Accuracy in epoch 480: 1.0 and Loss is 0.0020266762003302574\n",
      "Accuracy in epoch 481: 1.0 and Loss is 0.002024857560172677\n",
      "Accuracy in epoch 482: 1.0 and Loss is 0.0020230396185070276\n",
      "Accuracy in epoch 483: 1.0 and Loss is 0.0020212261006236076\n",
      "Accuracy in epoch 484: 1.0 and Loss is 0.002019414911046624\n",
      "Accuracy in epoch 485: 1.0 and Loss is 0.0020176060497760773\n",
      "Accuracy in epoch 486: 1.0 and Loss is 0.00201580673456192\n",
      "Accuracy in epoch 487: 1.0 and Loss is 0.002014002064242959\n",
      "Accuracy in epoch 488: 1.0 and Loss is 0.002012204844504595\n",
      "Accuracy in epoch 489: 1.0 and Loss is 0.0020104029681533575\n",
      "Accuracy in epoch 490: 1.0 and Loss is 0.0020086218137294054\n",
      "Accuracy in epoch 491: 1.0 and Loss is 0.0020068304147571325\n",
      "Accuracy in epoch 492: 1.0 and Loss is 0.002005040878430009\n",
      "Accuracy in epoch 493: 1.0 and Loss is 0.002003255533054471\n",
      "Accuracy in epoch 494: 1.0 and Loss is 0.002001476474106312\n",
      "Accuracy in epoch 495: 1.0 and Loss is 0.0019996999762952328\n",
      "Accuracy in epoch 496: 1.0 and Loss is 0.001997926039621234\n",
      "Accuracy in epoch 497: 1.0 and Loss is 0.001996157458052039\n",
      "Accuracy in epoch 498: 1.0 and Loss is 0.0019943846855312586\n",
      "Accuracy in epoch 499: 1.0 and Loss is 0.001992621459066868\n"
     ]
    }
   ],
   "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",
    "    pred = (pred > 0.5) * 1.0\n",
    "    acc = ((pred == label) * 1.0).mean()\n",
    "    #########################################\n",
    "\n",
    "    return torch.round(acc, decimals=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 = 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",
    "\n",
    "        ############# Your code here ############\n",
    "        pred = sigmoid((emb(train_edge[0]) * emb(train_edge[1])).sum(1))\n",
    "        optimizer.zero_grad()\n",
    "        loss = loss_fn(pred, train_label)\n",
    "        loss.backward()\n",
    "        optimizer.step()\n",
    "        \n",
    "        acc = accuracy(pred, train_label)\n",
    "        print (f'Accuracy in epoch {i}: {acc} and Loss is {loss}')\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",
    "train(emb, loss_fn, sigmoid, train_label, train_edge)"
   ]
  },
  {
   "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",
   "execution_count": 97,
   "metadata": {
    "id": "MtNgl4VhYKow"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualize the final learned embedding\n",
    "visualize_emb(emb)"
   ]
  },
  {
   "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."
   ]
  }
 ],
 "metadata": {
  "colab": {
   "machine_shape": "hm",
   "provenance": []
  },
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.10.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}