LINE_1_part1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "6f2c3146664fc7e0",
   "metadata": {},
   "source": [
    "# LINE-1 IMPLEMENTATION\n",
    "\n",
    "This notebook contains the step-by-step implementation of the LINE-1 model, and the results for the experiments on BlogCatalog, Pubmed and Cora datasets.\n",
    "\n",
    "Note that the original source code from the paper can be found here: [https://github.com/tangjianpku/LINE/tree/master](https://github.com/tangjianpku/LINE/tree/master). This was also used slightly as help in this implementation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "a00a75a3fbece027",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-01-02T08:04:32.866521Z",
     "start_time": "2024-01-02T08:04:32.848843Z"
    }
   },
   "outputs": [],
   "source": [
    "import random\n",
    "import time\n",
    "from tqdm import tqdm\n",
    "import networkx as nx\n",
    "import numpy as np\n",
    "\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import pandas as pd\n",
    "import torch\n",
    "\n",
    "from sklearn.model_selection import KFold, cross_validate\n",
    "from sklearn.multiclass import OneVsRestClassifier\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.metrics import f1_score, accuracy_score, roc_auc_score\n",
    "from sklearn.preprocessing import MultiLabelBinarizer, normalize\n",
    "from torch_geometric.utils import to_networkx, from_networkx\n",
    "from torch_geometric.transforms import RandomLinkSplit"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "48af601dee204539",
   "metadata": {},
   "source": [
    "## Creation of a simple test graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "dabbf3ccc59985c",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-12-31T10:30:59.591484Z",
     "start_time": "2023-12-31T10:30:59.490303Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Creation of a random graph // Upload a graph\n",
    "G = nx.karate_club_graph()\n",
    "\n",
    "# Assignment of the labels. Each student belongs to 1 of the 2 possible clubs\n",
    "clubs = []\n",
    "print(G.nodes)\n",
    "\n",
    "for n in G.nodes:\n",
    "    c = G.nodes[n]['club']  # karate club name, can be either 'Officer' or 'Mr. Hi'\n",
    "    clubs.append(1 if c == 'Officer' else 0)\n",
    "    \n",
    "pos = nx.spring_layout(G, seed=42) # To be able to recreate the graph layout\n",
    "nx.draw_networkx(G, pos=pos, node_color = clubs, cmap='coolwarm') # Plot the graph"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d680a483c885bb2c",
   "metadata": {},
   "source": [
    "# Helper functions\n",
    "\n",
    "These are the helper functions for LINE-1 algorithm. It uses an alias table that it samples from to make computations more efficient. Addtionally, it uses a negative sampling table for the same reasons.\n",
    "\n",
    "Moreover, the code used for evaluating embeddings in node classification and link prediction can be found in this section."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "a3ab515dda3a701c",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-01-02T08:03:34.171587Z",
     "start_time": "2024-01-02T08:03:34.137955Z"
    }
   },
   "outputs": [],
   "source": [
    "def generate_alias(probs):\n",
    "    \"\"\"\n",
    "    Generates an Alias table to sample from based on some probability distribution p\n",
    "    :param probs: distribution to create the Alias table\n",
    "    :return: A (Alias table)\n",
    "    \"\"\"\n",
    "    l = len(probs)\n",
    "    L, H = [], []\n",
    "    \n",
    "    for i, p in enumerate(probs):\n",
    "        if p <= 1/l:\n",
    "            L.append((i, p))\n",
    "        else:\n",
    "            H.append((i, p))\n",
    "    \n",
    "    A = []\n",
    "    while len(L) > 0 and len(H) > 0:\n",
    "        i, p_i = L.pop()\n",
    "        h, p_h = H.pop()\n",
    "        \n",
    "        A.append((i, h, p_i))\n",
    "        if p_h - p_i > 1/l:\n",
    "            H.append((h, p_h - p_i))\n",
    "        else:\n",
    "            L.append((h, p_h - p_i))\n",
    "\n",
    "    # Handling any remaining items\n",
    "    while len(L) > 0:\n",
    "        i, p = L.pop()\n",
    "        A.append((i, i, 1/l))\n",
    "    \n",
    "    while len(H) > 0:\n",
    "        h, p = H.pop()\n",
    "        A.append((h, h, 1/l))\n",
    "    return A\n",
    "\n",
    "\n",
    "def sample_alias(A, l):\n",
    "    \"\"\"\n",
    "    Samples an outcome from the alias table over a distribution p\n",
    "    :param A: Alias table\n",
    "    :param l: length of the probability distribution\n",
    "    :return: an index based on the sampling outcome\n",
    "    \"\"\"\n",
    "    draw = np.random.randint(l)\n",
    "    i, h, p = A[draw]\n",
    "    if np.random.rand() < l * p:\n",
    "        return h\n",
    "    else:\n",
    "        return i\n",
    "\n",
    "\n",
    "def init_neg_table(G, node2int, size):\n",
    "    \"\"\"\n",
    "    Creates a table for the negative sampling of vertices according to vertex degrees \n",
    "    :param G: Graph from which to sample\n",
    "    :param size: size of the table\n",
    "    :return: Negative sampling table\n",
    "    \"\"\"\n",
    "    degrees_prob = np.zeros(G.number_of_nodes())\n",
    "    for node, d in G.degree:\n",
    "        # P_n(v) ∝ d_v ** 0.75 from the paper\n",
    "        degrees_prob[node2int[node]] = d ** 0.75\n",
    "    \n",
    "    Z = np.sum(degrees_prob)\n",
    "    neg_table = np.zeros(int(size), dtype=np.uint32)\n",
    "    \n",
    "    neg_table_id = 0\n",
    "    for i, p in enumerate(degrees_prob):\n",
    "        portion_to_fill = np.round((p/Z) * size).astype(int)\n",
    "        neg_table[neg_table_id:neg_table_id+portion_to_fill] = i\n",
    "        neg_table_id += portion_to_fill\n",
    "    return neg_table\n",
    "\n",
    "\n",
    "# ---- PREDICTION TASKS ----\n",
    "def node_classification(X, y, n_folds=5):\n",
    "    \"\"\"\n",
    "    5-fold multi-label classification using one-vs-rest logistic regression\n",
    "    :param X: source embeddings of a graph\n",
    "    :param y: the labels for each node\n",
    "    :param n_folds: number of folds for cross-validation\n",
    "    :return: accuracy, f1 macro score, f1 micro score\n",
    "    \"\"\"\n",
    "    model = LogisticRegression()\n",
    "    ovr_model = OneVsRestClassifier(model)\n",
    "    kf = KFold(n_splits=n_folds, shuffle=True)\n",
    "    eval_scores = {'acc': 'accuracy', 'f1_macro': 'f1_macro', 'f1_micro': 'f1_micro'}\n",
    "    results = cross_validate(ovr_model, X, y, cv=kf, scoring=eval_scores)\n",
    "    acc, f1_macro, f1_micro = results['test_acc'].mean(), results['test_f1_macro'].mean(), results['test_f1_micro'].mean()\n",
    "    return acc, f1_macro, f1_micro\n",
    "\n",
    "\n",
    "def predict_link(u, v, embeddings):\n",
    "    \"\"\"\n",
    "    Computes the normalized probability for an existing link between two nodes u and v based on the input\n",
    "    embeddings.\n",
    "    :param u: a node in the graph\n",
    "    :param v: a node in the graph\n",
    "    :param embeddings: trained embeddings\n",
    "    :return: sigmoid normalized probability for the existence of a link\n",
    "    \"\"\"\n",
    "    embedding1 = embeddings[u]\n",
    "    embedding2 = embeddings[v]\n",
    "    \n",
    "    # Compute inner product (dot product)\n",
    "    dot_product = np.dot(embedding1, embedding2)\n",
    "\n",
    "    # Normalize by sigmoid function\n",
    "    link_probability = 1/(1 + np.exp(-dot_product))\n",
    "    return link_probability\n",
    "\n",
    "\n",
    "def link_predictions(embeddings, edges, y_true):\n",
    "    \"\"\"\n",
    "    Computes the ROC-AUC score for a given set of test edges based on the trained embeddings.\n",
    "    :param embeddings: a models trained embeddings\n",
    "    :param node2int: a models dictionary to link a node to the correct index for embedding\n",
    "    :param edges: test edges\n",
    "    :param y_true: the labels for edges (1=true, 0=false)\n",
    "    :return: the ROC-AUC score from predictions\n",
    "    \"\"\"\n",
    "    predictions = []\n",
    "    for edge in edges:\n",
    "        predictions.append(predict_link(edge[0], edge[1], embeddings))\n",
    "    return roc_auc_score(y_true, predictions) \n",
    "\n",
    "\n",
    "# reference: https://zqfang.github.io/2021-08-12-graph-linkpredict/\n",
    "def train_test_split_graph(G):\n",
    "    \"\"\"\n",
    "    Splits a Graph into a test and train set randomly to 80-20. The test split is balanced with negative edges sampled from random vertex pairs that have no edges between them. \n",
    "    While removing edges randomly, it makes sure that no vertex is isolated.\n",
    "    :param G: a networkx graph to be split\n",
    "    :return: the train-test split as torch geometrics graphs\n",
    "    \"\"\"\n",
    "    data = from_networkx(G)\n",
    "    try:\n",
    "        data.y = data.group_belonging\n",
    "    except:\n",
    "        data.y = data.club  # this only happens with karate club\n",
    "    data.x = torch.arange(G.number_of_nodes()).unsqueeze(1)\n",
    "    \n",
    "    transform = RandomLinkSplit(num_val=0, num_test=0.5, is_undirected=True, add_negative_train_samples=False)\n",
    "    train_data, _, test_data = transform(data)\n",
    "    return train_data, test_data\n",
    "\n",
    "\n",
    "# SILVIA'S METHOD\n",
    "def multi_label_classification(X, y, n_folds=5):\n",
    "    kf = KFold(n_splits=n_folds, shuffle=True)\n",
    "    micro_f1_scores = []\n",
    "    macro_f1_scores = []\n",
    "    \n",
    "    for train_index, test_index in kf.split(X):\n",
    "        X_train, X_test = X[train_index], X[test_index]\n",
    "        y_train, y_test = y[train_index], y[test_index]\n",
    "\n",
    "        # Predictions\n",
    "        model = OneVsRestClassifier(LogisticRegression())\n",
    "        model.fit(X_train, y_train)\n",
    "        y_pred = model.predict(X_test)\n",
    "\n",
    "        micro_f1 = f1_score(y_test, y_pred, average='micro')\n",
    "        macro_f1 = f1_score(y_test, y_pred, average='macro')\n",
    "\n",
    "        micro_f1_scores.append(micro_f1)\n",
    "        macro_f1_scores.append(macro_f1)\n",
    "    \n",
    "    # Calculate mean scores over all folds\n",
    "    mean_micro_f1 = np.mean(micro_f1_scores)\n",
    "    mean_macro_f1 = np.mean(macro_f1_scores)\n",
    "\n",
    "    return mean_micro_f1, mean_macro_f1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2d686fb51100f5c6",
   "metadata": {},
   "source": [
    "# Start of the model for Karate Club Network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "45b48bc2511fd2f2",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-12-31T10:31:13.425457Z",
     "start_time": "2023-12-31T10:31:13.294162Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Num nodes: 34 Edges: 78\n"
     ]
    }
   ],
   "source": [
    "neg_table_size = 1e8  # default, same as in the original source code\n",
    "num_nodes = G.number_of_nodes()\n",
    "num_edges = G.number_of_edges()\n",
    "\n",
    "node2int = {node: i for i, node in enumerate(G.nodes())}\n",
    "\n",
    "edges = [[node2int[u], node2int[v]] for u, v in G.edges()]\n",
    "edges_prob = np.array([G[u][v].get(\"weight\", 1) for u, v in G.edges()])\n",
    "edges_prob = edges_prob/np.sum(edges_prob)\n",
    "\n",
    "# Create sampling tables for the algorithm\n",
    "neg_table = init_neg_table(G, node2int, neg_table_size)\n",
    "alias_table = generate_alias(edges_prob)\n",
    "print('Num nodes:', num_nodes, 'Edges:', num_edges)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "2670282275e9ab36",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-12-31T10:31:15.115010Z",
     "start_time": "2023-12-31T10:31:15.102520Z"
    }
   },
   "outputs": [],
   "source": [
    "# hyperparameters from the paper\n",
    "dim = 128\n",
    "alpha = 0.025\n",
    "neg_samples = 5\n",
    "T = 1e6\n",
    "\n",
    "np.random.seed(42)\n",
    "# starting embedding, uniform [-0.5, 0.5]\n",
    "init_embeddings = (np.random.random((num_nodes, dim)) - 0.5)/dim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "47bed49bcf340190",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-12-31T10:31:29.243802Z",
     "start_time": "2023-12-31T10:31:29.230973Z"
    }
   },
   "outputs": [],
   "source": [
    "def update(u_i, u_j, alpha, acc_gradient, local_label):\n",
    "    \"\"\"\n",
    "    The update equation for the SGD in the LINE-1 algorithm\n",
    "    :param u_i: source representation for vertex i\n",
    "    :param u_j: source representation for vertex j\n",
    "    :param alpha: learning rate\n",
    "    :param acc_gradient: accumulated gradient\n",
    "    :param local_label: label in the local graph (1=connected, 0=not connected)\n",
    "    :return: \n",
    "    \"\"\"\n",
    "    f_line = 1/(1 + np.exp(-(u_i @ u_j)))  # sigmoid\n",
    "    g = (local_label - f_line) * alpha\n",
    "    \n",
    "    acc_gradient += g * u_j\n",
    "    u_j += g * u_i\n",
    "    return \n",
    "\n",
    "\n",
    "def train_line(embeddings, alpha_0, num_samples, edges, alias_table, neg_samples, neg_table):\n",
    "    \"\"\"\n",
    "    Trains a LINE-1 algorithm embeddings via Edge Sampling with a minibatch size of 1\n",
    "    :param embeddings: vertex embeddings to train\n",
    "    :param alpha_0: starting learning rate\n",
    "    :param num_samples: number of edge samples used for training\n",
    "    :param edges: edges in the graph\n",
    "    :param alias_table: alias table to sample edges\n",
    "    :param neg_samples: amount of negative samples\n",
    "    :param neg_table: table to use for negative samples \n",
    "    :return: trained embeddings\n",
    "    \"\"\"\n",
    "    trained_embeddings = embeddings.copy()\n",
    "    \n",
    "    start = time.time()\n",
    "    alpha = alpha_0\n",
    "    \n",
    "    for i in tqdm(range(int(num_samples))):\n",
    "        if i > 0:\n",
    "            alpha = alpha_0*(1-i/num_samples)\n",
    "        \n",
    "        edge = sample_alias(alias_table, num_edges)\n",
    "        u, v = edges[edge]\n",
    "        \n",
    "        acc_gradient = np.zeros(dim)\n",
    "        update(trained_embeddings[u], trained_embeddings[v], alpha, acc_gradient, local_label=1)\n",
    "        \n",
    "        for k in range(neg_samples):\n",
    "            v = random.choice(neg_table)\n",
    "            update(trained_embeddings[u], trained_embeddings[v], alpha, acc_gradient, local_label=0)\n",
    "        \n",
    "        trained_embeddings[u] += acc_gradient\n",
    "    print(f\"Training time: {time.time() - start}s\")\n",
    "    return trained_embeddings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "3950673e766cd6dd",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-12-31T10:32:15.027251Z",
     "start_time": "2023-12-31T10:31:50.800744Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1000000/1000000 [00:24<00:00, 41322.25it/s]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training time: 24.219100952148438s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[ 0.00823505,  0.13717892,  0.08407578, ..., -0.1156751 ,\n",
       "        -0.08785803, -0.04872237],\n",
       "       [ 0.02846845,  0.0141502 ,  0.11430858, ..., -0.05913688,\n",
       "        -0.19679494, -0.01355332],\n",
       "       [ 0.03013776,  0.0395401 ,  0.10177882, ...,  0.04407838,\n",
       "        -0.06701286,  0.04809669],\n",
       "       ...,\n",
       "       [ 0.03702577, -0.10309879, -0.05142961, ...,  0.19144263,\n",
       "        -0.00998952, -0.00372646],\n",
       "       [-0.0427767 , -0.08185791, -0.09965335, ..., -0.05694654,\n",
       "         0.16095217, -0.01283852],\n",
       "       [ 0.11431638, -0.03991154, -0.07062563, ...,  0.12532351,\n",
       "        -0.03888756,  0.08235593]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "embeddings = train_line(init_embeddings, alpha, T, edges, alias_table, neg_samples, neg_table)\n",
    "norm_embed = normalize(embeddings)\n",
    "norm_embed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "8686e04c6496fc5b",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-12-31T10:32:42.071253Z",
     "start_time": "2023-12-31T10:32:42.052809Z"
    }
   },
   "outputs": [],
   "source": [
    "def get_node_labels(G):\n",
    "    \"\"\"\n",
    "    Input:\n",
    "      G: Graph\n",
    "    Output:\n",
    "      labels: Array with labels. Each position of the array will correspond to the groups of id = index + 1\n",
    "    \"\"\"\n",
    "    labels = []\n",
    "    for n in G.nodes:\n",
    "        l = G.nodes[n].get('club')\n",
    "        labels.append(l)\n",
    "    return labels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "6b0f3c060d9366",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-12-31T10:32:42.590179Z",
     "start_time": "2023-12-31T10:32:42.574320Z"
    }
   },
   "outputs": [],
   "source": [
    "# Encode the labels for each node\n",
    "labels = get_node_labels(G)\n",
    "ls = np.zeros(num_nodes)\n",
    "for i, label in enumerate(labels):\n",
    "    if label == 'Mr. Hi':\n",
    "        ls[i] = 0\n",
    "    else:\n",
    "        ls[i] = 1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b772cb8bb2fe056d",
   "metadata": {},
   "source": [
    "**NODE PREDICTION**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "5b2e0831eb18e333",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-12-31T10:40:52.069124Z",
     "start_time": "2023-12-31T10:40:52.050329Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "F1 macro: 0.926984126984127 F1 micro: 0.9380952380952381\n"
     ]
    }
   ],
   "source": [
    "# my method\n",
    "acc, f1_macro, f1_micro = node_classification(norm_embed, ls)\n",
    "print('F1 macro:', f1_macro, 'F1 micro:', f1_micro)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ff92856e1c678a9e",
   "metadata": {},
   "source": [
    "# Creation of LINE-1 class based on the previous code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "87d75a17a4371902",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-01-02T07:57:39.412990Z",
     "start_time": "2024-01-02T07:57:39.380876Z"
    }
   },
   "outputs": [],
   "source": [
    "class Line:\n",
    "    def __init__(self, G, dim, alpha, neg_samples, num_edge_samples):\n",
    "        \"\"\"\n",
    "        Initializes a LINE-1 embedding algorithm\n",
    "        :param G: Graph as a networkx object\n",
    "        :param dim: dimension of embeddings\n",
    "        :param alpha: learning rate\n",
    "        :param neg_samples: number of negative samples in training\n",
    "        :param num_edge_samples: number of edge samples used in training\n",
    "        \"\"\"\n",
    "        self.neg_table_size = 1e8  # default, same as in the original source code\n",
    "        self.num_nodes = G.number_of_nodes()\n",
    "        self.num_edges = G.number_of_edges()\n",
    "        self.node2int = {node: i for i, node in enumerate(G.nodes())}  # dictionary for easy access in arrays\n",
    "        \n",
    "        # Compute the probability weights for each edge\n",
    "        self.edges = [[self.node2int[u], self.node2int[v]] for u, v in G.edges()]\n",
    "        edges_prob = np.array([G[u][v].get(\"weight\", 1) for u, v in G.edges()])\n",
    "        self.edges_prob = edges_prob/np.sum(edges_prob)\n",
    "        \n",
    "        # Create sampling tables for the algorithm\n",
    "        self.neg_table = init_neg_table(G, self.node2int, self.neg_table_size)\n",
    "        self.alias_table = generate_alias(self.edges_prob)\n",
    "        \n",
    "        # hyperparameters\n",
    "        self.dim = dim\n",
    "        self.alpha_0 = alpha\n",
    "        self.neg_samples = neg_samples\n",
    "        self.T = num_edge_samples\n",
    "        \n",
    "        self.embeddings = (np.random.random((self.num_nodes, self.dim)) - 0.5)/self.dim\n",
    "        \n",
    "    def update(self, u_i, u_j, alpha, acc_gradient, local_label):\n",
    "        \"\"\"\n",
    "        The update equation for the SGD in the LINE-1 algorithm\n",
    "        :param u_i: source representation for vertex i\n",
    "        :param u_j: source representation for vertex j\n",
    "        :param acc_gradient: accumulated gradient\n",
    "        :param local_label: label in the local graph (1=connected, 0=not connected)\n",
    "        :return: \n",
    "        \"\"\"\n",
    "        f_line = 1/(1 + np.exp(-(u_i @ u_j)))  # sigmoid\n",
    "        g = (local_label - f_line) * alpha\n",
    "        \n",
    "        acc_gradient += g * u_j\n",
    "        u_j += g * u_i\n",
    "        return \n",
    "\n",
    "    def train_line(self, file_name):\n",
    "        \"\"\"\n",
    "        Trains a LINE-1 algorithm embeddings via Edge Sampling with a minibatch size of 1\n",
    "        :return: trained embeddings\n",
    "        \"\"\"\n",
    "        \n",
    "        start = time.time()\n",
    "        alpha = self.alpha_0\n",
    "        for i in tqdm(range(int(self.T))):\n",
    "            if i > 0:\n",
    "                alpha = self.alpha_0*(1-i/self.T)\n",
    "            \n",
    "            edge = sample_alias(self.alias_table, self.num_edges)\n",
    "            u, v = self.edges[edge]\n",
    "            \n",
    "            acc_gradient = np.zeros(self.dim)\n",
    "            self.update(self.embeddings[u], self.embeddings[v], alpha, acc_gradient, local_label=1)\n",
    "            \n",
    "            for k in range(self.neg_samples):\n",
    "                v = random.choice(self.neg_table)\n",
    "                self.update(self.embeddings[u], self.embeddings[v], alpha, acc_gradient, local_label=0)\n",
    "            \n",
    "            self.embeddings[u] += acc_gradient\n",
    "        \n",
    "        norm_trained_embeddings = normalize(self.embeddings)\n",
    "        np.save(f'./embeddings/{file_name}.npy', norm_trained_embeddings)\n",
    "        self.embeddings = norm_trained_embeddings\n",
    "        print(f\"Training time: {time.time() - start}s\")\n",
    "        return norm_trained_embeddings\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4b1e00e64b82159c",
   "metadata": {},
   "source": [
    "**LINK PREDICTION FOR KARATE CLUB:**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "fb1329a616271b6c",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-12-31T10:52:13.533878Z",
     "start_time": "2023-12-31T10:51:49.225690Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1000000/1000000 [00:24<00:00, 41367.23it/s]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training time: 24.176151037216187s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "# LINK PREDICTION\n",
    "train_data, test_data = train_test_split_graph(G)\n",
    "\n",
    "# Create graph from the train split in networkx format\n",
    "train_G = nx.Graph()\n",
    "train_G.add_nodes_from(train_data.x.squeeze().numpy())\n",
    "# Add edges to the graph\n",
    "train_G.add_edges_from(train_data.edge_label_index.numpy().T)\n",
    "\n",
    "model = Line(train_G, dim, alpha, neg_samples, T)\n",
    "embeddings = model.train_line('test')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "8ee30d2d8f5ea120",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-12-31T10:53:06.032942Z",
     "start_time": "2023-12-31T10:53:06.019707Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ROC-AUC: 0.48\n"
     ]
    }
   ],
   "source": [
    "# Set up test data\n",
    "test_edges = test_data.edge_label_index.numpy().T\n",
    "y_true = test_data.edge_label.numpy()\n",
    "\n",
    "print('ROC-AUC:', link_predictions(embeddings, test_edges, y_true))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "82c6384eec8ecd76",
   "metadata": {},
   "source": [
    "# BlogCatalog Experiments"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "4d95bea71df34b56",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-01-02T07:59:31.093730Z",
     "start_time": "2024-01-02T07:59:31.041056Z"
    }
   },
   "outputs": [],
   "source": [
    "# Load the data\n",
    "edges_path = './BlogCatalog-dataset/data/edges.csv'\n",
    "nodes_path = './BlogCatalog-dataset/data/nodes.csv'\n",
    "groups_path = './BlogCatalog-dataset/data/groups.csv'\n",
    "group_edges_path = './BlogCatalog-dataset/data/group-edges.csv'\n",
    "\n",
    "nodes_id = pd.read_csv(nodes_path, header=None, names=['id'])\n",
    "groups_id = pd.read_csv(groups_path, header=None, names=['group'])\n",
    "edges = pd.read_csv(edges_path, header=None, names=['id_1', 'id_2'])\n",
    "user_group_membership = pd.read_csv(group_edges_path, header=None, names=['id', 'group'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "546eae1f4ed03fd9",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-01-02T07:59:32.358876Z",
     "start_time": "2024-01-02T07:59:32.033973Z"
    }
   },
   "outputs": [],
   "source": [
    "# Create a graph\n",
    "G_BC = nx.Graph()\n",
    "\n",
    "# Add nodes to the graph\n",
    "G_BC.add_nodes_from(nodes_id['id'])\n",
    "\n",
    "# Add edges to the graph\n",
    "G_BC.add_edges_from(edges[['id_1', 'id_2']].values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "cdc0fee45e8beba6",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-01-02T07:59:35.409673Z",
     "start_time": "2024-01-02T07:59:35.290603Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of nodes: 10312  |  Number of edges: 333983\n"
     ]
    }
   ],
   "source": [
    "# Create a dictionary to store groups for each ID\n",
    "group_dict = {}\n",
    "\n",
    "# Populate the group_dict\n",
    "for _, row in user_group_membership.iterrows():\n",
    "    user_id = row['id']\n",
    "    group_id = row['group']\n",
    "\n",
    "    # Check if the user_id is already in the dictionary\n",
    "    if user_id in group_dict:\n",
    "        group_dict[user_id].append(group_id)\n",
    "    else:\n",
    "        group_dict[user_id] = [group_id]\n",
    "\n",
    "# Add group labels to the nodes\n",
    "for user_id, groups in group_dict.items():\n",
    "    nx.set_node_attributes(G_BC, {user_id: groups}, 'group_belonging')\n",
    "\n",
    "# Print basic graph information\n",
    "print(\"Number of nodes:\", G_BC.number_of_nodes(), ' | ', \"Number of edges:\", G_BC.number_of_edges())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "291a38c7c5403646",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-01-02T07:59:43.585249Z",
     "start_time": "2024-01-02T07:59:43.574107Z"
    }
   },
   "outputs": [],
   "source": [
    "# Find and preprocess labels for the graph\n",
    "labels = []\n",
    "for n in G_BC.nodes:\n",
    "    l = G_BC.nodes[n].get('group_belonging')\n",
    "    labels.append(l)\n",
    "\n",
    "mlb = MultiLabelBinarizer()\n",
    "preprocessed_labels = mlb.fit_transform(labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "e3c34ea3eecc88fb",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-01-01T16:51:49.728577Z",
     "start_time": "2024-01-01T16:51:49.216331Z"
    }
   },
   "outputs": [],
   "source": [
    "# hyperparameters from the paper\n",
    "dim = 128\n",
    "alpha = 0.025\n",
    "neg_samples = 5\n",
    "T = 1e9\n",
    "\n",
    "model = Line(G_BC, dim, alpha, neg_samples, T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "7c88795d61e93b6a",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-01-02T00:05:22.587398Z",
     "start_time": "2024-01-01T16:52:24.885477Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1000000000/1000000000 [6:51:10<00:00, 40534.59it/s] "
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training time: 24670.298993110657s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "# Train embeddings\n",
    "embeddings_model = model.train_line('blog_catalog')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "43766d0b6e1c1028",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-01-02T08:00:02.047833Z",
     "start_time": "2024-01-02T08:00:02.021887Z"
    }
   },
   "outputs": [],
   "source": [
    "# Load embeddings\n",
    "embeddings_model = np.load('./embeddings/blog_catalog.npy')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b2a91deb",
   "metadata": {},
   "source": [
    "**Node Classification:**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "12b648de1b3c24c7",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-01-02T07:32:48.299327Z",
     "start_time": "2024-01-02T07:32:13.226848Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shuffle 1 -- F1 macro: 0.13017053259341307 F1 micro: 0.2820697044531669\n",
      "Shuffle 2 -- F1 macro: 0.13326918522823067 F1 micro: 0.28435586594060624\n",
      "Shuffle 3 -- F1 macro: 0.13090842578101675 F1 micro: 0.28251294671104815\n",
      "Shuffle 4 -- F1 macro: 0.13240513704466383 F1 micro: 0.2822681394728502\n",
      "Shuffle 5 -- F1 macro: 0.13221650178836997 F1 micro: 0.2826689728522681\n"
     ]
    }
   ],
   "source": [
    "N = 5\n",
    "f1_macros, f1_micros = np.zeros(N), np.zeros(N)\n",
    "for i in range(N):\n",
    "    _, f1_macro, f1_micro = node_classification(embeddings_model, preprocessed_labels)\n",
    "    f1_macros[i] = f1_macro\n",
    "    f1_micros[i] = f1_micro\n",
    "    print(f'Shuffle {i+1} --', 'F1 macro:', f1_macro, 'F1 micro:', f1_micro)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "871f07b9",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-01-02T07:32:52.911225Z",
     "start_time": "2024-01-02T07:32:52.891384Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-----  Final results: -----\n",
      "F1 macro: 0.13179395648713885 F1 micro: 0.28277512588598797\n"
     ]
    }
   ],
   "source": [
    "print('-----  Final results: -----')\n",
    "print('F1 macro:', np.mean(f1_macros), 'F1 micro:', np.mean(f1_micros))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e59560b0",
   "metadata": {},
   "source": [
    "**Link Prediction:**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "684a2b79",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-01-02T08:05:41.901477Z",
     "start_time": "2024-01-02T08:05:15.219668Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shuffle 1 -- ROC-AUC: 0.8322549740413538\n",
      "Shuffle 2 -- ROC-AUC: 0.8312477973232344\n",
      "Shuffle 3 -- ROC-AUC: 0.8317219786259195\n",
      "Shuffle 4 -- ROC-AUC: 0.8322335444664115\n",
      "Shuffle 5 -- ROC-AUC: 0.8315037324345762\n"
     ]
    }
   ],
   "source": [
    "N = 5\n",
    "roc_auc_scores = np.zeros(N)\n",
    "for i in range(N):\n",
    "    train_data, test_data = train_test_split_graph(G_BC)\n",
    "\n",
    "    # Prepare edges\n",
    "    test_edges = test_data.edge_label_index.numpy().T\n",
    "    y_true = test_data.edge_label.numpy()\n",
    "    \n",
    "    score = link_predictions(embeddings_model, test_edges, y_true)\n",
    "    roc_auc_scores[i] = score\n",
    "    print(f'Shuffle {i+1} --', 'ROC-AUC:', roc_auc_score)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "606e03c6b2817b0c",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-01-02T08:06:09.246235Z",
     "start_time": "2024-01-02T08:06:09.214288Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-----  Final results: -----\n",
      "ROC-AUC: 0.8317924053782992\n"
     ]
    }
   ],
   "source": [
    "print('-----  Final results: -----')\n",
    "print('ROC-AUC:', np.mean(roc_auc_scores))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "dcb8904a",
   "metadata": {},
   "outputs": [],
   "source": [
    "print('-----  Final results: -----')\n",
    "print('ROC-AUC:', np.mean(roc_auc_scores))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "596e891f",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-01-02T08:06:21.685804Z",
     "start_time": "2024-01-02T08:06:21.662988Z"
    }
   },
   "source": [
    "# PubMed Experiments"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "5afc1486",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-01-02T08:06:46.800323Z",
     "start_time": "2024-01-02T08:06:46.790853Z"
    }
   },
   "outputs": [],
   "source": [
    "from torch_geometric.datasets import Planetoid\n",
    "dataset = Planetoid(root='/tmp/PubMed', name='PubMed')\n",
    "data = dataset[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "baabdb6f",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-01-02T08:06:30.119316Z",
     "start_time": "2024-01-02T08:06:29.133726Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of nodes: 19717  |  Number of edges: 44324\n"
     ]
    }
   ],
   "source": [
    "# convert to networkx\n",
    "G_pubmed = to_networkx(data)\n",
    "G_pubmed = G_pubmed.to_undirected()\n",
    "\n",
    "# Create a dictionary to store groups for each ID\n",
    "group_dict = {}\n",
    "\n",
    "# Populate the group_dict\n",
    "for i in range(len(data.y)):\n",
    "    user_id = i\n",
    "    group_id = int(data.y[i].numpy())\n",
    "\n",
    "    # Check if the user_id is already in the dictionary\n",
    "    if user_id in group_dict:\n",
    "        if type(group_id) == int:\n",
    "            group_dict[user_id].append(group_id)\n",
    "        else:\n",
    "            group_dict[user_id].extend(group_id)\n",
    "    else:\n",
    "        if type(group_id) == int:\n",
    "            group_dict[user_id] = [group_id]\n",
    "        else:\n",
    "             group_dict[user_id] = list(group_id)\n",
    "\n",
    "# Add group labels to the nodes\n",
    "for user_id, groups in group_dict.items():\n",
    "    nx.set_node_attributes(G_pubmed, {user_id: groups}, 'group_belonging')\n",
    "\n",
    "# Print basic graph information\n",
    "print(\"Number of nodes:\", G_pubmed.number_of_nodes(), ' | ', \"Number of edges:\", G_pubmed.number_of_edges())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "9336fe9b",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-01-02T08:08:28.855728Z",
     "start_time": "2024-01-02T08:08:28.709205Z"
    }
   },
   "outputs": [],
   "source": [
    "# Find and preprocess labels for the graph\n",
    "labels = []\n",
    "for n in G_pubmed.nodes:\n",
    "    l = G_pubmed.nodes[n].get('group_belonging')\n",
    "    labels.append(l)\n",
    "\n",
    "mlb = MultiLabelBinarizer()\n",
    "preprocessed_labels = mlb.fit_transform(labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7352fa65",
   "metadata": {
    "is_executing": true
   },
   "outputs": [],
   "source": [
    "# hyperparameters from the paper\n",
    "dim = 128\n",
    "alpha = 0.025\n",
    "neg_samples = 5\n",
    "T = 1e9\n",
    "\n",
    "model_pm = Line(G_pubmed, dim, alpha, neg_samples, T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3d64f463",
   "metadata": {
    "is_executing": true
   },
   "outputs": [],
   "source": [
    "# Train embeddings\n",
    "embeddings_model_pm = model_pm.train_line('pubmed')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8f09393b",
   "metadata": {},
   "source": [
    "For some reason the training process did not produce output here. However, the model was trained for 1 billion edge samples and approx. 7 hours like the others. The trained embeddings of the model have been stored in the embeddings folder with the rest."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "7bb05aa75659fc7a",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-01-02T08:09:23.233927Z",
     "start_time": "2024-01-02T08:09:23.185166Z"
    }
   },
   "outputs": [],
   "source": [
    "# Load embeddings\n",
    "embeddings_model_pm = np.load('./embeddings/pubmed.npy')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "566dac26",
   "metadata": {},
   "source": [
    "**Node Classification:**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "ca6e1e9b",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-01-02T08:09:44.636373Z",
     "start_time": "2024-01-02T08:09:36.974091Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shuffle 1 -- F1 macro: 0.584720816700087 F1 micro: 0.6090905586327772\n",
      "Shuffle 2 -- F1 macro: 0.5834123957665296 F1 micro: 0.6075628553713592\n",
      "Shuffle 3 -- F1 macro: 0.5858065457451254 F1 micro: 0.6095841873443479\n",
      "Shuffle 4 -- F1 macro: 0.5852300553174254 F1 micro: 0.6089855115098677\n",
      "Shuffle 5 -- F1 macro: 0.5866945366373131 F1 micro: 0.6105517506204459\n"
     ]
    }
   ],
   "source": [
    "N = 5\n",
    "f1_macros, f1_micros = np.zeros(N), np.zeros(N)\n",
    "for i in range(N):\n",
    "    _, f1_macro, f1_micro = node_classification(embeddings_model_pm, preprocessed_labels)\n",
    "    f1_macros[i] = f1_macro\n",
    "    f1_micros[i] = f1_micro\n",
    "    print(f'Shuffle {i+1} --', 'F1 macro:', f1_macro, 'F1 micro:', f1_micro)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "398b09a4",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-01-02T08:09:50.866926Z",
     "start_time": "2024-01-02T08:09:50.836522Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-----  Final results: -----\n",
      "F1 macro: 0.5851728700332961 F1 micro: 0.6091549726957595\n"
     ]
    }
   ],
   "source": [
    "print('-----  Final results: -----')\n",
    "print('F1 macro:', np.mean(f1_macros), 'F1 micro:', np.mean(f1_micros))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "599aa2ae",
   "metadata": {},
   "source": [
    "**Link Prediction:**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "939df5d2",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-01-02T08:10:37.119136Z",
     "start_time": "2024-01-02T08:10:32.582897Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shuffle 1 -- ROC-AUC: 0.865288980379858\n",
      "Shuffle 2 -- ROC-AUC: 0.8635653650180004\n",
      "Shuffle 3 -- ROC-AUC: 0.8626191021979644\n",
      "Shuffle 4 -- ROC-AUC: 0.865102403553699\n",
      "Shuffle 5 -- ROC-AUC: 0.8669947337358243\n"
     ]
    }
   ],
   "source": [
    "N = 5\n",
    "roc_auc_scores = np.zeros(N)\n",
    "for i in range(N):\n",
    "    train_data, test_data = train_test_split_graph(G_pubmed)\n",
    "\n",
    "    # Prepare edges\n",
    "    test_edges = test_data.edge_label_index.numpy().T\n",
    "    y_true = test_data.edge_label.numpy()\n",
    "    \n",
    "    score = link_predictions(embeddings_model_pm, test_edges, y_true)\n",
    "    roc_auc_scores[i] = score\n",
    "    print(f'Shuffle {i+1} --', 'ROC-AUC:', roc_auc_score)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "35ba65eb",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-01-02T08:10:42.244403Z",
     "start_time": "2024-01-02T08:10:42.219765Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-----  Final results: -----\n",
      "ROC-AUC: 0.8647141169770693\n"
     ]
    }
   ],
   "source": [
    "print('-----  Final results: -----')\n",
    "print('ROC-AUC:', np.mean(roc_auc_scores))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ddd63586",
   "metadata": {},
   "source": [
    "# Cora Experiments"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "283a9443",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-01-02T08:12:19.005883Z",
     "start_time": "2024-01-02T08:12:14.163245Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Downloading https://github.com/abojchevski/graph2gauss/raw/master/data/cora.npz\n",
      "Processing...\n",
      "Done!\n"
     ]
    }
   ],
   "source": [
    "from torch_geometric.datasets import CitationFull\n",
    "dataset = CitationFull(root='/tmp/Cora', name='Cora')\n",
    "data = dataset[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "ec100b5d7eb8f028",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-01-02T08:16:59.140074Z",
     "start_time": "2024-01-02T08:16:58.370256Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of nodes: 19793  |  Number of edges: 63421\n"
     ]
    }
   ],
   "source": [
    "# convert to networkx\n",
    "G_cora = to_networkx(data)\n",
    "G_cora = G_cora.to_undirected()\n",
    "\n",
    "# Create a dictionary to store groups for each ID\n",
    "group_dict = {}\n",
    "\n",
    "# Populate the group_dict\n",
    "for i in range(len(data.y)):\n",
    "    user_id = i\n",
    "    group_id = int(data.y[i].numpy())\n",
    "\n",
    "    # Check if the user_id is already in the dictionary\n",
    "    if user_id in group_dict:\n",
    "        if type(group_id) == int:\n",
    "            group_dict[user_id].append(group_id)\n",
    "        else:\n",
    "            group_dict[user_id].extend(group_id)\n",
    "    else:\n",
    "        if type(group_id) == int:\n",
    "            group_dict[user_id] = [group_id]\n",
    "        else:\n",
    "             group_dict[user_id] = list(group_id)\n",
    "\n",
    "# Add group labels to the nodes\n",
    "for user_id, groups in group_dict.items():\n",
    "    nx.set_node_attributes(G_cora, {user_id: groups}, 'group_belonging')\n",
    "\n",
    "# Print basic graph information\n",
    "print(\"Number of nodes:\", G_cora.number_of_nodes(), ' | ', \"Number of edges:\", G_cora.number_of_edges())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "f655a9d8",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-01-02T15:37:18.317917Z",
     "start_time": "2024-01-02T15:37:18.273374Z"
    }
   },
   "outputs": [],
   "source": [
    "# Find and preprocess labels for the graph\n",
    "labels = []\n",
    "for n in G_BC.nodes:\n",
    "    l = G_BC.nodes[n].get('group_belonging')\n",
    "    labels.append(l)\n",
    "\n",
    "mlb = MultiLabelBinarizer()\n",
    "preprocessed_labels = mlb.fit_transform(labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "307507bdc5823595",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-01-02T08:25:08.889170Z",
     "start_time": "2024-01-02T08:25:08.711394Z"
    }
   },
   "outputs": [],
   "source": [
    "# hyperparameters from the paper\n",
    "dim = 128\n",
    "alpha = 0.025\n",
    "neg_samples = 5\n",
    "T = 1e9\n",
    "\n",
    "model = Line(G_cora, dim, alpha, neg_samples, T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "d9c07c54",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-01-02T15:32:19.600449Z",
     "start_time": "2024-01-02T08:28:20.588228Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1000000000/1000000000 [7:02:43<00:00, 39427.18it/s]  "
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training time: 25363.266119003296s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "embeddings_model = model.train_line('cora')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4803eddc",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load embeddings\n",
    "embeddings_model_cora = np.load('./embeddings/cora.npy')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46f231ce",
   "metadata": {},
   "source": [
    "**Node Classification:**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "2422862ffc4eb2b9",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-01-02T15:40:18.458026Z",
     "start_time": "2024-01-02T15:37:35.018608Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shuffle 1 -- F1 macro: 0.32989731612247497 F1 micro: 0.43609715291880846\n",
      "Shuffle 2 -- F1 macro: 0.33266220261992957 F1 micro: 0.43743492506223836\n",
      "Shuffle 3 -- F1 macro: 0.33242125821771956 F1 micro: 0.4367266778821719\n",
      "Shuffle 4 -- F1 macro: 0.3324039384675669 F1 micro: 0.43625996777262205\n",
      "Shuffle 5 -- F1 macro: 0.3358879504993825 F1 micro: 0.4384843277704064\n"
     ]
    }
   ],
   "source": [
    "N = 5\n",
    "f1_macros, f1_micros = np.zeros(N), np.zeros(N)\n",
    "for i in range(N):\n",
    "    _, f1_macro, f1_micro = node_classification(embeddings_model_cora, preprocessed_labels)\n",
    "    f1_macros[i] = f1_macro\n",
    "    f1_micros[i] = f1_micro\n",
    "    print(f'Shuffle {i+1} --', 'F1 macro:', f1_macro, 'F1 micro:', f1_micro)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "fd0e8ad916b1577b",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-01-02T15:57:52.492267Z",
     "start_time": "2024-01-02T15:57:52.406803Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-----  Final results: -----\n",
      "F1 macro: 0.33265453318541466 F1 micro: 0.4370006102812495\n"
     ]
    }
   ],
   "source": [
    "print('-----  Final results: -----')\n",
    "print('F1 macro:', np.mean(f1_macros), 'F1 micro:', np.mean(f1_micros))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "65143cae",
   "metadata": {},
   "source": [
    "**Link Prediction:**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "93bcd02853d86fef",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-01-02T15:58:59.403853Z",
     "start_time": "2024-01-02T15:58:53.445382Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shuffle 1 -- ROC-AUC: 0.9252773225425427\n",
      "Shuffle 2 -- ROC-AUC: 0.9247955608423507\n",
      "Shuffle 3 -- ROC-AUC: 0.9256148629356571\n",
      "Shuffle 4 -- ROC-AUC: 0.9247566080216278\n",
      "Shuffle 5 -- ROC-AUC: 0.927311955029223\n"
     ]
    }
   ],
   "source": [
    "N = 5\n",
    "roc_auc_scores = np.zeros(N)\n",
    "for i in range(N):\n",
    "    train_data, test_data = train_test_split_graph(G_pubmed)\n",
    "\n",
    "    # Prepare edges\n",
    "    test_edges = test_data.edge_label_index.numpy().T\n",
    "    y_true = test_data.edge_label.numpy()\n",
    "    \n",
    "    score = link_predictions(embeddings_model_pm, test_edges, y_true)\n",
    "    roc_auc_scores[i] = score\n",
    "    print(f'Shuffle {i+1} --', 'ROC-AUC:', score)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "6b6b988fab70750d",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-01-02T16:06:09.533552Z",
     "start_time": "2024-01-02T16:06:09.501097Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-----  Final results: -----\n",
      "ROC-AUC: 0.9255512618742804\n"
     ]
    }
   ],
   "source": [
    "print('-----  Final results: -----')\n",
    "print('ROC-AUC:', np.mean(roc_auc_scores))"
   ]
  }
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