CS224W_Colab_1.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": {
    "id": "VIETqEfrfy5Y"
   },
   "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": 3,
   "metadata": {
    "id": "hDvf3nm-ors4"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 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": {
    "id": "AUhES1VYo3tB"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average degree of karate club network is 5\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 = 2*num_edges/num_nodes\n",
    "    avg_degree = int(round(avg_degree))\n",
    "\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": {
    "id": "k15XKEto1aYJ"
   },
   "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 = nx.average_clustering(G)\n",
    "    avg_cluster_coef = round(avg_cluster_coef, 2)\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": 13,
   "metadata": {
    "id": "BOGdWjNc6O7x"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The PageRank value for node 0 after one iteration is 0.22\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 = 0\n",
    "\n",
    "    ############# Your code here ############\n",
    "    ## Note: \n",
    "    ## 1: You should not use nx.pagerank\n",
    "    N = G.number_of_nodes()\n",
    "\n",
    "    for node_neighbor in G.neighbors(node_id):\n",
    "        node_deg = G.degree[node_neighbor]\n",
    "        # Notice that all nodes share the same PageRank value r0 at the first iteration\n",
    "        r1 += beta * r0/node_deg + (1-beta)*1/N\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": 32,
   "metadata": {
    "id": "XbCsq_tl-3ok"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The karate club network 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",
    "\n",
    "    #########################################\n",
    "    # Normalized version from NetworkX\n",
    "    # closeness = nx.closeness_centrality(G, node)\n",
    "    \n",
    "    # Raw version following above equation\n",
    "    # source: https://stackoverflow.com/questions/31764515/find-all-nodes-connected-to-n\n",
    "    path_length_total = 0 \n",
    "    for path in list(nx.single_source_shortest_path(G,node).values())[1:]:\n",
    "        path_length_total += len(path)-1\n",
    "\n",
    "    closeness = 1 / path_length_total\n",
    "    closeness = round(closeness, 2)\n",
    "\n",
    "    return closeness\n",
    "\n",
    "node = 5\n",
    "closeness = closeness_centrality(G, node=node)\n",
    "print(\"The karate club network 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": 8,
   "metadata": {
    "id": "ntuPVat_BAf1"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.8.1\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": 9,
   "metadata": {
    "id": "W2ySw3m-A9qF"
   },
   "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([[0.8381, 0.0362, 0.2747, 0.8694],\n",
      "        [0.4927, 0.8819, 0.9566, 0.3032],\n",
      "        [0.8369, 0.1242, 0.8061, 0.1690]])\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": 10,
   "metadata": {
    "id": "rQiOvKJJBwq4"
   },
   "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: 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",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "id": "kEtVxMFID3ZT"
   },
   "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 = 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 x len(edge_list)].\n",
    "\n",
    "    edge_index = torch.tensor([])\n",
    "\n",
    "    ############# Your code here ############\n",
    "    edge_index = torch.tensor(np.array(edge_list), dtype=torch.long)\n",
    "    edge_index = edge_index.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)))"
   ]
  },
  {
   "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",
   "execution_count": 15,
   "metadata": {
    "id": "9N8VT1f8-IJ8",
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The neg_edge_index tensor has shape torch.Size([2, 78])\n",
      "False\n",
      "True\n",
      "False\n",
      "False\n",
      "True\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "tensor([[18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18,\n",
       "         18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 13, 13, 13, 13, 13,\n",
       "         13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13,\n",
       "         13, 13, 13, 13,  6,  6,  6,  6,  6,  6,  6,  6,  6,  6,  6,  6,  6,  6,\n",
       "          6,  6,  6,  6,  6,  6],\n",
       "        [13,  6, 31, 27, 10, 14,  4, 28, 15, 12, 20, 25, 26,  0, 22, 23,  5,  2,\n",
       "         21,  8, 11, 24, 16,  1, 19, 17,  3,  7,  9, 30, 29,  6, 32, 31, 27, 10,\n",
       "         14,  4, 28, 15, 12, 20, 25, 26, 22, 23,  5, 21,  8, 11, 24, 16, 19, 17,\n",
       "          7,  9, 30, 29, 32, 31, 27, 10, 14, 28, 15, 12, 20, 25, 26, 22, 23, 33,\n",
       "          2, 21,  8, 11, 24,  1]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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",
    "    pos_set = set(G.edges())\n",
    "    visited_set = set()\n",
    "\n",
    "    ############# Your code here ############\n",
    "    node_list = list(G.nodes())\n",
    "    random.shuffle(node_list)\n",
    "    \n",
    "    for n_i in node_list:\n",
    "        for n_j in node_list:\n",
    "            if n_i == n_j \\\n",
    "            or (n_i,n_j) in pos_set or (n_j,n_i) in pos_set \\\n",
    "            or (n_i,n_j) in visited_set or (n_j, n_i) is visited_set:\n",
    "                continue\n",
    "                \n",
    "            neg_edge_list.append((n_i,n_j))\n",
    "            visited_set.add((n_i,n_j))\n",
    "            visited_set.add((n_j,n_i))\n",
    "            if len(neg_edge_list) == num_neg_samples:\n",
    "                return neg_edge_list\n",
    "\n",
    "    #########################################\n",
    "    \n",
    "    \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",
    "def is_neg_edge(edge):\n",
    "    return not(edge in pos_edge_list or (edge[1], edge[0]) in pos_edge_list)\n",
    "\n",
    "print(is_neg_edge(edge_1))\n",
    "print(is_neg_edge(edge_2))\n",
    "print(is_neg_edge(edge_3))\n",
    "print(is_neg_edge(edge_4))\n",
    "print(is_neg_edge(edge_5))\n",
    "\n",
    "\n",
    "#########################################\n",
    "neg_edge_index"
   ]
  },
  {
   "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": 14,
   "metadata": {
    "id": "Lnqn9H6s_ehX"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.8.1\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": 29,
   "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": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualize the graph\n",
    "nx.draw(G, with_labels = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "id": "9AGIfP4QEDr8"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[ 1.1557, -1.0234,  0.9199,  1.3019,  0.9390,  0.8462,  0.2809, -1.3055],\n",
      "        [ 1.6396, -1.9154, -1.8657, -0.6708,  0.0423, -0.5353,  0.6595,  0.3424],\n",
      "        [-2.1762, -1.2711,  0.3710, -0.2658, -0.1624,  1.7706,  2.3947, -1.0720],\n",
      "        [-1.2375,  1.1541,  0.8352,  1.7608,  0.0344,  1.1384,  1.6472, -0.3850]],\n",
      "       grad_fn=<EmbeddingBackward>)\n",
      "tensor([[ 1.6396, -1.9154, -1.8657, -0.6708,  0.0423, -0.5353,  0.6595,  0.3424],\n",
      "        [-1.2375,  1.1541,  0.8352,  1.7608,  0.0344,  1.1384,  1.6472, -0.3850]],\n",
      "       grad_fn=<EmbeddingBackward>)\n",
      "torch.Size([4, 8])\n",
      "tensor([[ 1.1557, -1.0234,  0.9199,  1.3019,  0.9390,  0.8462,  0.2809, -1.3055],\n",
      "        [-1.2375,  1.1541,  0.8352,  1.7608,  0.0344,  1.1384,  1.6472, -0.3850]],\n",
      "       grad_fn=<EmbeddingBackward>)\n"
     ]
    }
   ],
   "source": [
    "# Select an embedding in emb_sample\n",
    "id = torch.LongTensor([0, 1, 2, 3])\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": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# %config Completer.use_jedi = False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "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=<EmbeddingBackward>)\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",
    "    emb = None\n",
    "\n",
    "    ############# Your code here ############\n",
    "    emb = nn.Embedding(num_nodes, embedding_dim)\n",
    "    emb.weight.data = torch.rand(num_nodes, 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))"
   ]
  },
  {
   "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",
   "execution_count": 19,
   "metadata": {
    "id": "_LCoIkarhfYD"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "id": "RDeQTNNxqH0j",
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loss for Epoch 0: 2.147944927215576\n",
      "Accuracy for is Epoch 0: 0.5\n",
      "\n",
      "Loss for Epoch 1: 2.1088569164276123\n",
      "Accuracy for is Epoch 1: 0.5\n",
      "\n",
      "Loss for Epoch 2: 2.035390615463257\n",
      "Accuracy for is Epoch 2: 0.5\n",
      "\n",
      "Loss for Epoch 3: 1.9324657917022705\n",
      "Accuracy for is Epoch 3: 0.5\n",
      "\n",
      "Loss for Epoch 4: 1.8051190376281738\n",
      "Accuracy for is Epoch 4: 0.5\n",
      "\n",
      "Loss for Epoch 5: 1.658468246459961\n",
      "Accuracy for is Epoch 5: 0.5\n",
      "\n",
      "Loss for Epoch 6: 1.4977258443832397\n",
      "Accuracy for is Epoch 6: 0.5\n",
      "\n",
      "Loss for Epoch 7: 1.3282560110092163\n",
      "Accuracy for is Epoch 7: 0.5\n",
      "\n",
      "Loss for Epoch 8: 1.1556425094604492\n",
      "Accuracy for is Epoch 8: 0.5\n",
      "\n",
      "Loss for Epoch 9: 0.9857252240180969\n",
      "Accuracy for is Epoch 9: 0.5\n",
      "\n",
      "Loss for Epoch 10: 0.8245416283607483\n",
      "Accuracy for is Epoch 10: 0.5064\n",
      "\n",
      "Loss for Epoch 11: 0.678042471408844\n",
      "Accuracy for is Epoch 11: 0.5064\n",
      "\n",
      "Loss for Epoch 12: 0.5514200925827026\n",
      "Accuracy for is Epoch 12: 0.5577\n",
      "\n",
      "Loss for Epoch 13: 0.4480952322483063\n",
      "Accuracy for is Epoch 13: 0.6667\n",
      "\n",
      "Loss for Epoch 14: 0.36887815594673157\n",
      "Accuracy for is Epoch 14: 0.8205\n",
      "\n",
      "Loss for Epoch 15: 0.31196290254592896\n",
      "Accuracy for is Epoch 15: 0.9103\n",
      "\n",
      "Loss for Epoch 16: 0.27379873394966125\n",
      "Accuracy for is Epoch 16: 0.9167\n",
      "\n",
      "Loss for Epoch 17: 0.25023719668388367\n",
      "Accuracy for is Epoch 17: 0.9167\n",
      "\n",
      "Loss for Epoch 18: 0.23738589882850647\n",
      "Accuracy for is Epoch 18: 0.9167\n",
      "\n",
      "Loss for Epoch 19: 0.23200947046279907\n",
      "Accuracy for is Epoch 19: 0.9167\n",
      "\n",
      "Loss for Epoch 20: 0.23160140216350555\n",
      "Accuracy for is Epoch 20: 0.9167\n",
      "\n",
      "Loss for Epoch 21: 0.23429836332798004\n",
      "Accuracy for is Epoch 21: 0.9167\n",
      "\n",
      "Loss for Epoch 22: 0.23875057697296143\n",
      "Accuracy for is Epoch 22: 0.9167\n",
      "\n",
      "Loss for Epoch 23: 0.24399977922439575\n",
      "Accuracy for is Epoch 23: 0.9167\n",
      "\n",
      "Loss for Epoch 24: 0.24937957525253296\n",
      "Accuracy for is Epoch 24: 0.9167\n",
      "\n",
      "Loss for Epoch 25: 0.2544391453266144\n",
      "Accuracy for is Epoch 25: 0.9167\n",
      "\n",
      "Loss for Epoch 26: 0.2588857114315033\n",
      "Accuracy for is Epoch 26: 0.9167\n",
      "\n",
      "Loss for Epoch 27: 0.2625417411327362\n",
      "Accuracy for is Epoch 27: 0.9167\n",
      "\n",
      "Loss for Epoch 28: 0.2653135061264038\n",
      "Accuracy for is Epoch 28: 0.9167\n",
      "\n",
      "Loss for Epoch 29: 0.26716798543930054\n",
      "Accuracy for is Epoch 29: 0.9167\n",
      "\n",
      "Loss for Epoch 30: 0.2681153118610382\n",
      "Accuracy for is Epoch 30: 0.9167\n",
      "\n",
      "Loss for Epoch 31: 0.2681965231895447\n",
      "Accuracy for is Epoch 31: 0.9167\n",
      "\n",
      "Loss for Epoch 32: 0.2674736976623535\n",
      "Accuracy for is Epoch 32: 0.9167\n",
      "\n",
      "Loss for Epoch 33: 0.2660233974456787\n",
      "Accuracy for is Epoch 33: 0.9167\n",
      "\n",
      "Loss for Epoch 34: 0.26393091678619385\n",
      "Accuracy for is Epoch 34: 0.9167\n",
      "\n",
      "Loss for Epoch 35: 0.2612864375114441\n",
      "Accuracy for is Epoch 35: 0.9167\n",
      "\n",
      "Loss for Epoch 36: 0.2581818997859955\n",
      "Accuracy for is Epoch 36: 0.9167\n",
      "\n",
      "Loss for Epoch 37: 0.25470858812332153\n",
      "Accuracy for is Epoch 37: 0.9167\n",
      "\n",
      "Loss for Epoch 38: 0.2509552836418152\n",
      "Accuracy for is Epoch 38: 0.9167\n",
      "\n",
      "Loss for Epoch 39: 0.24700631201267242\n",
      "Accuracy for is Epoch 39: 0.9167\n",
      "\n",
      "Loss for Epoch 40: 0.24294058978557587\n",
      "Accuracy for is Epoch 40: 0.9167\n",
      "\n",
      "Loss for Epoch 41: 0.23883056640625\n",
      "Accuracy for is Epoch 41: 0.9167\n",
      "\n",
      "Loss for Epoch 42: 0.23474086821079254\n",
      "Accuracy for is Epoch 42: 0.9167\n",
      "\n",
      "Loss for Epoch 43: 0.2307279258966446\n",
      "Accuracy for is Epoch 43: 0.9167\n",
      "\n",
      "Loss for Epoch 44: 0.22683930397033691\n",
      "Accuracy for is Epoch 44: 0.9167\n",
      "\n",
      "Loss for Epoch 45: 0.22311337292194366\n",
      "Accuracy for is Epoch 45: 0.9167\n",
      "\n",
      "Loss for Epoch 46: 0.21957890689373016\n",
      "Accuracy for is Epoch 46: 0.9167\n",
      "\n",
      "Loss for Epoch 47: 0.2162557691335678\n",
      "Accuracy for is Epoch 47: 0.9167\n",
      "\n",
      "Loss for Epoch 48: 0.2131546288728714\n",
      "Accuracy for is Epoch 48: 0.9167\n",
      "\n",
      "Loss for Epoch 49: 0.21027806401252747\n",
      "Accuracy for is Epoch 49: 0.9167\n",
      "\n",
      "Loss for Epoch 50: 0.20762135088443756\n",
      "Accuracy for is Epoch 50: 0.9167\n",
      "\n",
      "Loss for Epoch 51: 0.2051733285188675\n",
      "Accuracy for is Epoch 51: 0.9231\n",
      "\n",
      "Loss for Epoch 52: 0.20291784405708313\n",
      "Accuracy for is Epoch 52: 0.9231\n",
      "\n",
      "Loss for Epoch 53: 0.2008349895477295\n",
      "Accuracy for is Epoch 53: 0.9295\n",
      "\n",
      "Loss for Epoch 54: 0.198902428150177\n",
      "Accuracy for is Epoch 54: 0.9359\n",
      "\n",
      "Loss for Epoch 55: 0.19709663093090057\n",
      "Accuracy for is Epoch 55: 0.9359\n",
      "\n",
      "Loss for Epoch 56: 0.1953941434621811\n",
      "Accuracy for is Epoch 56: 0.9359\n",
      "\n",
      "Loss for Epoch 57: 0.19377245008945465\n",
      "Accuracy for is Epoch 57: 0.9359\n",
      "\n",
      "Loss for Epoch 58: 0.19221091270446777\n",
      "Accuracy for is Epoch 58: 0.9423\n",
      "\n",
      "Loss for Epoch 59: 0.1906912624835968\n",
      "Accuracy for is Epoch 59: 0.9423\n",
      "\n",
      "Loss for Epoch 60: 0.18919803202152252\n",
      "Accuracy for is Epoch 60: 0.9423\n",
      "\n",
      "Loss for Epoch 61: 0.18771874904632568\n",
      "Accuracy for is Epoch 61: 0.9423\n",
      "\n",
      "Loss for Epoch 62: 0.18624384701251984\n",
      "Accuracy for is Epoch 62: 0.9423\n",
      "\n",
      "Loss for Epoch 63: 0.18476662039756775\n",
      "Accuracy for is Epoch 63: 0.9423\n",
      "\n",
      "Loss for Epoch 64: 0.18328282237052917\n",
      "Accuracy for is Epoch 64: 0.9423\n",
      "\n",
      "Loss for Epoch 65: 0.18179044127464294\n",
      "Accuracy for is Epoch 65: 0.9423\n",
      "\n",
      "Loss for Epoch 66: 0.18028922379016876\n",
      "Accuracy for is Epoch 66: 0.9423\n",
      "\n",
      "Loss for Epoch 67: 0.17878024280071259\n",
      "Accuracy for is Epoch 67: 0.9423\n",
      "\n",
      "Loss for Epoch 68: 0.17726561427116394\n",
      "Accuracy for is Epoch 68: 0.9487\n",
      "\n",
      "Loss for Epoch 69: 0.17574799060821533\n",
      "Accuracy for is Epoch 69: 0.9487\n",
      "\n",
      "Loss for Epoch 70: 0.17423033714294434\n",
      "Accuracy for is Epoch 70: 0.9487\n",
      "\n",
      "Loss for Epoch 71: 0.17271563410758972\n",
      "Accuracy for is Epoch 71: 0.9487\n",
      "\n",
      "Loss for Epoch 72: 0.17120669782161713\n",
      "Accuracy for is Epoch 72: 0.9487\n",
      "\n",
      "Loss for Epoch 73: 0.16970600187778473\n",
      "Accuracy for is Epoch 73: 0.9487\n",
      "\n",
      "Loss for Epoch 74: 0.1682155877351761\n",
      "Accuracy for is Epoch 74: 0.9487\n",
      "\n",
      "Loss for Epoch 75: 0.16673704981803894\n",
      "Accuracy for is Epoch 75: 0.9487\n",
      "\n",
      "Loss for Epoch 76: 0.16527144610881805\n",
      "Accuracy for is Epoch 76: 0.9487\n",
      "\n",
      "Loss for Epoch 77: 0.16381944715976715\n",
      "Accuracy for is Epoch 77: 0.9487\n",
      "\n",
      "Loss for Epoch 78: 0.16238127648830414\n",
      "Accuracy for is Epoch 78: 0.9487\n",
      "\n",
      "Loss for Epoch 79: 0.16095681488513947\n",
      "Accuracy for is Epoch 79: 0.9487\n",
      "\n",
      "Loss for Epoch 80: 0.15954558551311493\n",
      "Accuracy for is Epoch 80: 0.9487\n",
      "\n",
      "Loss for Epoch 81: 0.1581469625234604\n",
      "Accuracy for is Epoch 81: 0.9487\n",
      "\n",
      "Loss for Epoch 82: 0.1567600965499878\n",
      "Accuracy for is Epoch 82: 0.9487\n",
      "\n",
      "Loss for Epoch 83: 0.15538407862186432\n",
      "Accuracy for is Epoch 83: 0.9487\n",
      "\n",
      "Loss for Epoch 84: 0.15401794016361237\n",
      "Accuracy for is Epoch 84: 0.9487\n",
      "\n",
      "Loss for Epoch 85: 0.15266071259975433\n",
      "Accuracy for is Epoch 85: 0.9487\n",
      "\n",
      "Loss for Epoch 86: 0.15131144225597382\n",
      "Accuracy for is Epoch 86: 0.9487\n",
      "\n",
      "Loss for Epoch 87: 0.14996932446956635\n",
      "Accuracy for is Epoch 87: 0.9487\n",
      "\n",
      "Loss for Epoch 88: 0.14863352477550507\n",
      "Accuracy for is Epoch 88: 0.9487\n",
      "\n",
      "Loss for Epoch 89: 0.14730344712734222\n",
      "Accuracy for is Epoch 89: 0.9487\n",
      "\n",
      "Loss for Epoch 90: 0.14597848057746887\n",
      "Accuracy for is Epoch 90: 0.9487\n",
      "\n",
      "Loss for Epoch 91: 0.1446581929922104\n",
      "Accuracy for is Epoch 91: 0.9487\n",
      "\n",
      "Loss for Epoch 92: 0.1433422565460205\n",
      "Accuracy for is Epoch 92: 0.9487\n",
      "\n",
      "Loss for Epoch 93: 0.14203043282032013\n",
      "Accuracy for is Epoch 93: 0.9487\n",
      "\n",
      "Loss for Epoch 94: 0.1407226026058197\n",
      "Accuracy for is Epoch 94: 0.9487\n",
      "\n",
      "Loss for Epoch 95: 0.13941873610019684\n",
      "Accuracy for is Epoch 95: 0.9487\n",
      "\n",
      "Loss for Epoch 96: 0.13811883330345154\n",
      "Accuracy for is Epoch 96: 0.9487\n",
      "\n",
      "Loss for Epoch 97: 0.13682296872138977\n",
      "Accuracy for is Epoch 97: 0.9487\n",
      "\n",
      "Loss for Epoch 98: 0.13553138077259064\n",
      "Accuracy for is Epoch 98: 0.9487\n",
      "\n",
      "Loss for Epoch 99: 0.1342441439628601\n",
      "Accuracy for is Epoch 99: 0.9487\n",
      "\n",
      "Loss for Epoch 100: 0.13296158611774445\n",
      "Accuracy for is Epoch 100: 0.9487\n",
      "\n",
      "Loss for Epoch 101: 0.13168387115001678\n",
      "Accuracy for is Epoch 101: 0.9423\n",
      "\n",
      "Loss for Epoch 102: 0.130411297082901\n",
      "Accuracy for is Epoch 102: 0.9487\n",
      "\n",
      "Loss for Epoch 103: 0.129144087433815\n",
      "Accuracy for is Epoch 103: 0.9551\n",
      "\n",
      "Loss for Epoch 104: 0.12788257002830505\n",
      "Accuracy for is Epoch 104: 0.9551\n",
      "\n",
      "Loss for Epoch 105: 0.12662696838378906\n",
      "Accuracy for is Epoch 105: 0.9615\n",
      "\n",
      "Loss for Epoch 106: 0.12537755072116852\n",
      "Accuracy for is Epoch 106: 0.9615\n",
      "\n",
      "Loss for Epoch 107: 0.12413457781076431\n",
      "Accuracy for is Epoch 107: 0.9615\n",
      "\n",
      "Loss for Epoch 108: 0.12289825826883316\n",
      "Accuracy for is Epoch 108: 0.9615\n",
      "\n",
      "Loss for Epoch 109: 0.12166883796453476\n",
      "Accuracy for is Epoch 109: 0.9615\n",
      "\n",
      "Loss for Epoch 110: 0.12044652551412582\n",
      "Accuracy for is Epoch 110: 0.9615\n",
      "\n",
      "Loss for Epoch 111: 0.11923151463270187\n",
      "Accuracy for is Epoch 111: 0.9615\n",
      "\n",
      "Loss for Epoch 112: 0.11802396923303604\n",
      "Accuracy for is Epoch 112: 0.9615\n",
      "\n",
      "Loss for Epoch 113: 0.11682412773370743\n",
      "Accuracy for is Epoch 113: 0.9615\n",
      "\n",
      "Loss for Epoch 114: 0.1156320795416832\n",
      "Accuracy for is Epoch 114: 0.9615\n",
      "\n",
      "Loss for Epoch 115: 0.11444801092147827\n",
      "Accuracy for is Epoch 115: 0.9615\n",
      "\n",
      "Loss for Epoch 116: 0.1132720559835434\n",
      "Accuracy for is Epoch 116: 0.9615\n",
      "\n",
      "Loss for Epoch 117: 0.11210435628890991\n",
      "Accuracy for is Epoch 117: 0.9615\n",
      "\n",
      "Loss for Epoch 118: 0.11094501614570618\n",
      "Accuracy for is Epoch 118: 0.9615\n",
      "\n",
      "Loss for Epoch 119: 0.10979419201612473\n",
      "Accuracy for is Epoch 119: 0.9615\n",
      "\n",
      "Loss for Epoch 120: 0.10865195840597153\n",
      "Accuracy for is Epoch 120: 0.9615\n",
      "\n",
      "Loss for Epoch 121: 0.10751840472221375\n",
      "Accuracy for is Epoch 121: 0.9615\n",
      "\n",
      "Loss for Epoch 122: 0.10639370232820511\n",
      "Accuracy for is Epoch 122: 0.9615\n",
      "\n",
      "Loss for Epoch 123: 0.1052778959274292\n",
      "Accuracy for is Epoch 123: 0.9615\n",
      "\n",
      "Loss for Epoch 124: 0.10417106747627258\n",
      "Accuracy for is Epoch 124: 0.9679\n",
      "\n",
      "Loss for Epoch 125: 0.10307332873344421\n",
      "Accuracy for is Epoch 125: 0.9679\n",
      "\n",
      "Loss for Epoch 126: 0.10198475420475006\n",
      "Accuracy for is Epoch 126: 0.9679\n",
      "\n",
      "Loss for Epoch 127: 0.1009054183959961\n",
      "Accuracy for is Epoch 127: 0.9679\n",
      "\n",
      "Loss for Epoch 128: 0.09983537346124649\n",
      "Accuracy for is Epoch 128: 0.9679\n",
      "\n",
      "Loss for Epoch 129: 0.09877471625804901\n",
      "Accuracy for is Epoch 129: 0.9679\n",
      "\n",
      "Loss for Epoch 130: 0.09772349894046783\n",
      "Accuracy for is Epoch 130: 0.9679\n",
      "\n",
      "Loss for Epoch 131: 0.09668177366256714\n",
      "Accuracy for is Epoch 131: 0.9679\n",
      "\n",
      "Loss for Epoch 132: 0.0956496000289917\n",
      "Accuracy for is Epoch 132: 0.9679\n",
      "\n",
      "Loss for Epoch 133: 0.09462698549032211\n",
      "Accuracy for is Epoch 133: 0.9679\n",
      "\n",
      "Loss for Epoch 134: 0.09361404180526733\n",
      "Accuracy for is Epoch 134: 0.9679\n",
      "\n",
      "Loss for Epoch 135: 0.09261077642440796\n",
      "Accuracy for is Epoch 135: 0.9679\n",
      "\n",
      "Loss for Epoch 136: 0.09161720424890518\n",
      "Accuracy for is Epoch 136: 0.9679\n",
      "\n",
      "Loss for Epoch 137: 0.09063336998224258\n",
      "Accuracy for is Epoch 137: 0.9679\n",
      "\n",
      "Loss for Epoch 138: 0.08965928107500076\n",
      "Accuracy for is Epoch 138: 0.9679\n",
      "\n",
      "Loss for Epoch 139: 0.0886949896812439\n",
      "Accuracy for is Epoch 139: 0.9744\n",
      "\n",
      "Loss for Epoch 140: 0.0877404659986496\n",
      "Accuracy for is Epoch 140: 0.9808\n",
      "\n",
      "Loss for Epoch 141: 0.08679573237895966\n",
      "Accuracy for is Epoch 141: 0.9808\n",
      "\n",
      "Loss for Epoch 142: 0.08586079627275467\n",
      "Accuracy for is Epoch 142: 0.9808\n",
      "\n",
      "Loss for Epoch 143: 0.08493565022945404\n",
      "Accuracy for is Epoch 143: 0.9808\n",
      "\n",
      "Loss for Epoch 144: 0.08402028679847717\n",
      "Accuracy for is Epoch 144: 0.9808\n",
      "\n",
      "Loss for Epoch 145: 0.08311468362808228\n",
      "Accuracy for is Epoch 145: 0.9808\n",
      "\n",
      "Loss for Epoch 146: 0.08221884816884995\n",
      "Accuracy for is Epoch 146: 0.9808\n",
      "\n",
      "Loss for Epoch 147: 0.0813327506184578\n",
      "Accuracy for is Epoch 147: 0.9808\n",
      "\n",
      "Loss for Epoch 148: 0.08045636117458344\n",
      "Accuracy for is Epoch 148: 0.9808\n",
      "\n",
      "Loss for Epoch 149: 0.07958965748548508\n",
      "Accuracy for is Epoch 149: 0.9808\n",
      "\n",
      "Loss for Epoch 150: 0.07873261719942093\n",
      "Accuracy for is Epoch 150: 0.9808\n",
      "\n",
      "Loss for Epoch 151: 0.077885203063488\n",
      "Accuracy for is Epoch 151: 0.9808\n",
      "\n",
      "Loss for Epoch 152: 0.07704736292362213\n",
      "Accuracy for is Epoch 152: 0.9808\n",
      "\n",
      "Loss for Epoch 153: 0.07621905952692032\n",
      "Accuracy for is Epoch 153: 0.9808\n",
      "\n",
      "Loss for Epoch 154: 0.07540027797222137\n",
      "Accuracy for is Epoch 154: 0.9808\n",
      "\n",
      "Loss for Epoch 155: 0.07459094375371933\n",
      "Accuracy for is Epoch 155: 0.9808\n",
      "\n",
      "Loss for Epoch 156: 0.0737910121679306\n",
      "Accuracy for is Epoch 156: 0.9808\n",
      "\n",
      "Loss for Epoch 157: 0.07300044596195221\n",
      "Accuracy for is Epoch 157: 0.9808\n",
      "\n",
      "Loss for Epoch 158: 0.07221918553113937\n",
      "Accuracy for is Epoch 158: 0.9808\n",
      "\n",
      "Loss for Epoch 159: 0.07144718617200851\n",
      "Accuracy for is Epoch 159: 0.9808\n",
      "\n",
      "Loss for Epoch 160: 0.07068437337875366\n",
      "Accuracy for is Epoch 160: 0.9872\n",
      "\n",
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      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loss for Epoch 196: 0.048775676637887955\n",
      "Accuracy for is Epoch 196: 1.0\n",
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      "Accuracy for is Epoch 394: 1.0\n",
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loss for Epoch 395: 0.01341076847165823\n",
      "Accuracy for is Epoch 395: 1.0\n",
      "\n",
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      "\n",
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      "\n",
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      "\n",
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      "\n",
      "Loss for Epoch 480: 0.00975179672241211\n",
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      "\n",
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      "\n",
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      "\n",
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      "\n",
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      "\n",
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      "\n",
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      "\n",
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      "\n",
      "Loss for Epoch 490: 0.009437916800379753\n",
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      "\n",
      "Loss for Epoch 491: 0.009407526813447475\n",
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      "\n",
      "Loss for Epoch 492: 0.009377307258546352\n",
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      "\n",
      "Loss for Epoch 493: 0.009347268380224705\n",
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      "\n",
      "Loss for Epoch 494: 0.009317400865256786\n",
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      "\n",
      "Loss for Epoch 495: 0.009287706576287746\n",
      "Accuracy for is Epoch 495: 1.0\n",
      "\n",
      "Loss for Epoch 496: 0.009258183650672436\n",
      "Accuracy for is Epoch 496: 1.0\n",
      "\n",
      "Loss for Epoch 497: 0.009228819981217384\n",
      "Accuracy for is Epoch 497: 1.0\n",
      "\n",
      "Loss for Epoch 498: 0.009199636057019234\n",
      "Accuracy for is Epoch 498: 1.0\n",
      "\n",
      "Loss for Epoch 499: 0.009170610457658768\n",
      "Accuracy for is Epoch 499: 1.0\n",
      "\n"
     ]
    }
   ],
   "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",
    "    ############# Your code here ############\n",
    "    pred = [1 if item>0.5 else 0 for item in pred]\n",
    "    num_match = (np.array(pred) == np.array(train_label)).sum()\n",
    "    accu = num_match / len(train_label)\n",
    "    accu = round(accu, 4)\n",
    "    #########################################\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",
    "\n",
    "    ############# Your code here ############\n",
    "        optimizer.zero_grad()\n",
    "        \n",
    "        # (1) Get the embeddings of the nodes in train_edge\n",
    "        emb_set_u = emb(train_edge[0])\n",
    "        emb_set_v = emb(train_edge[1])\n",
    "        \n",
    "        # (2) Dot product the embeddings between each node pair\n",
    "        dot_prod = torch.sum(emb_set_u * emb_set_v, dim=-1)\n",
    "        \n",
    "        # (3) Feed the dot product result into sigmoid\n",
    "        sig = sigmoid(dot_prod)\n",
    "        \n",
    "        # (4) Feed the sigmoid output into the loss_fn\n",
    "        loss = loss_fn(sig, train_label)\n",
    "        \n",
    "        loss.backward()  # Derive gradients.\n",
    "        optimizer.step()  # Update parameters based on gradients.\n",
    "        \n",
    "        \n",
    "        print(f\"Loss for Epoch {i}: {loss}\")\n",
    "        print(f\"Accuracy for is Epoch {i}: {accuracy(sig, train_label)}\")\n",
    "        print()\n",
    "        \n",
    "    #########################################\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)"
   ]
  },
  {
   "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": 21,
   "metadata": {
    "id": "MtNgl4VhYKow"
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": {
   "collapsed_sections": [],
   "machine_shape": "hm",
   "name": "CS224W - Colab 1.ipynb",
   "provenance": [],
   "toc_visible": true
  },
  "kernelspec": {
   "display_name": "Python [conda env:Graph_env] *",
   "language": "python",
   "name": "conda-env-Graph_env-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}