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": 7,
   "metadata": {
    "id": "BOGdWjNc6O7x"
   },
   "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 = 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\n",
    "        \n",
    "    r1 += (1-beta)*1/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
}