EDA/3_eda_dataset_valid_train.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exploratory Data Analysis - Train Validation Set Differences\n",
    "\n",
    "This notebook looks at the exploratory data analysis of the train and validation set of the arXiv CS dataset. In particular, the differences will be clarified."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Prerequisites\n",
    "\n",
    "In this section, all the basic requirements are met in order to keep the analyses as compact as possible.\n",
    "### Loading the packages and defining the visualisations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "current working directory: d:\\Github\\link-prediction-in-graphs\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "from dataset_split.dataset_splitter import Dataset_Splitter\n",
    "import networkx as nx\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import random\n",
    "import ogb\n",
    "import sys\n",
    "import os\n",
    "current_dir = os.getcwd()\n",
    "if os.path.basename(current_dir) != 'link-prediction-in-graphs':\n",
    "    parent_dir = os.path.dirname(current_dir)\n",
    "    os.chdir(parent_dir)\n",
    "print(f\"current working directory: {os.getcwd()}\")\n",
    "# ausführen\n",
    "sys.path.append('modelling/')\n",
    "\n",
    "\n",
    "# set default plt figsize to (12,6)\n",
    "plt.rcParams[\"figure.figsize\"] = (12, 6)\n",
    "pd.set_option('display.colheader_justify', 'center')\n",
    "# Set default font sizes\n",
    "plt.rcParams['axes.titlesize'] = 20\n",
    "plt.rcParams['xtick.labelsize'] = 16\n",
    "plt.rcParams['ytick.labelsize'] = 16\n",
    "plt.rcParams['axes.labelsize'] = 18\n",
    "plt.rcParams['legend.fontsize'] = 16\n",
    "plt.rcParams['legend.title_fontsize'] = 18\n",
    "\n",
    "\n",
    "def cosine_similarity(v1, v2):\n",
    "    dot_product = np.dot(v1, v2)\n",
    "    magnitude_v1 = np.linalg.norm(v1)\n",
    "    magnitude_v2 = np.linalg.norm(v2)\n",
    "    return dot_product / (magnitude_v1 * magnitude_v2)\n",
    "\n",
    "\n",
    "def calc_similarities(graph, nx_graph, edges, no_random=False):\n",
    "    # Calculate Similarities between all pairs of nodes\n",
    "    edges = edges.T\n",
    "    node_similarities = []\n",
    "    for i in range(len(edges[:, 0])):\n",
    "        node_similarities.append(\n",
    "            cosine_similarity(\n",
    "                graph.x[edges[i][0]],\n",
    "                graph.x[edges[i][1]]))\n",
    "\n",
    "    nodes = list(nx_graph.nodes())\n",
    "    n_links = len(edges[0])\n",
    "    random_links = np.array(random.choices(\n",
    "        nodes, k=n_links * 2)).reshape((2, n_links))\n",
    "    if no_random:\n",
    "        # Calculate similarities between all pairs of nodes\n",
    "        node_similarities_random = []\n",
    "        for i in range(len(random_links[0])):\n",
    "            node_similarities_random.append(\n",
    "                cosine_similarity(\n",
    "                    graph.x[random_links[0][i]],\n",
    "                    graph.x[random_links[1][i]]))\n",
    "        return node_similarities, node_similarities_random\n",
    "    return node_similarities\n",
    "\n",
    "\n",
    "def replace_number(number):\n",
    "    return f\"{number:,}\".replace(\",\", \"'\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Creating Splits for dataset ogbn-arxiv\n",
      "Returning Splits for dataset ogbn-arxiv\n"
     ]
    }
   ],
   "source": [
    "# load dataset\n",
    "ds_split = Dataset_Splitter()\n",
    "dataset = ds_split.load_dataset(\"ogbn-arxiv\")\n",
    "data = dataset[0]\n",
    "\n",
    "split_edge, edge_index = ds_split.get_edges_split(dataset)\n",
    "train_nodes = np.unique(split_edge[\"train\"][\"source_node\"])\n",
    "valid_nodes = np.unique(split_edge[\"valid\"][\"source_node\"])\n",
    "\n",
    "train_edges = torch.cat((split_edge['train']['source_node'].unsqueeze(\n",
    "    0), split_edge['train']['target_node'].unsqueeze(0)), dim=0)\n",
    "valid_edges = torch.cat((split_edge['valid']['source_node'].unsqueeze(\n",
    "    0), split_edge['valid']['target_node'].unsqueeze(0)), dim=0)\n",
    "\n",
    "nx_graph_train = nx.DiGraph()\n",
    "\n",
    "# add training nodes and their edges to the graph\n",
    "nx_graph_train.add_nodes_from(train_nodes)\n",
    "nx_graph_train.add_edges_from([edge for edge in train_edges.T])\n",
    "\n",
    "nx_graph_valid = nx.DiGraph()\n",
    "# add training nodes and their edges to the graph\n",
    "nx_graph_valid.add_nodes_from(valid_nodes)\n",
    "nx_graph_valid.add_edges_from([edge for edge in valid_edges.T])\n",
    "\n",
    "train_target_nodes = split_edge['train']['target_node']\n",
    "valid_target_nodes = split_edge['valid']['target_node']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Node Similarities\n",
    "Node similarities between the validation and training set is calculated."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "node_similarities_train, node_similarities_random_train = calc_similarities(\n",
    "    data, nx_graph_train, train_edges, no_random=True)\n",
    "node_similarities2_valid, node_similarities_random_valid = calc_similarities(\n",
    "    data, nx_graph_valid, valid_edges, no_random=True)\n",
    "df1 = pd.DataFrame({'cosine similarity': node_similarities_train,\n",
    "                   'Typ': 'Positive Links', 'dataset': 'train'})\n",
    "df2 = pd.DataFrame({'cosine similarity': node_similarities2_valid,\n",
    "                   'Typ': 'Positive Links', 'dataset': 'valid'})\n",
    "\n",
    "train_min = np.round(df1['cosine similarity'].min(), 4)\n",
    "val_min = np.round(df2['cosine similarity'].min(), 4)\n",
    "train_max = np.round(df1['cosine similarity'].max(), 4)\n",
    "val_max = np.round(df2['cosine similarity'].max(), 4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot Similarity Distribution\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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0zDPP6D//+Y8aNWqkUaNGqXr16goPD9e8efO0adMmHTx4UO+8847efffde44lK8b/X6ncpk0bPfXUU6pdu7ZKliyp6OhonTt3TkuWLNG+ffu0ZcsWvfrqq6bby7Pz5ptv6siRI+rWrZsGDRqkChUq6Nq1a4qKiso1lqVLl+r27dvq2LGjrl69qqefflrvvPNOhjZ5rY5MM2rUKC1cuFCS1KJFCw0aNEiVKlWSk5OT/v77b3388cf6559/NHz4cJUuXTpTReW9fN+YI+31V6JECVWqVCnbdpZ+nnr27KkePXpo7dq1WrZsmVxcXEzz2w4ZMkRt27a9h7OXqlSpooYNG+rPP//UypUrNXXq1Gzbfv/996bq2n79+pl1nLS7bKTUaSjyKyAgQLt27VJ4eLjGjBmjDz/8MF/z81erVk0eHh6KjIzUrl279NJLL+U7RgBAEWXhpDEA4CFyr5W2W7duNfUbMmRIpv3ZjXn27Nk8VTalpKQYb9y4kWl7+orX3Chd9VHbtm2Nd+7cybZtXittJRnd3d2Nx44dy9QmODjYVDlZrlw5Y0JCQob9+a20zWus6eVUTZiQkGCqQHNxcTEeOnQoU5uQkBBjmTJljFJqpWxYWFi2ser/V03Gx8dnavPOO++Y2qxZsybHmLMzbtw40xiTJk3KtD8lJcXYr18/U5uFCxdmanP+/HnT/qVLl95THEaj0RgXF2e6dk5OTjk+nxcvXsy0rUGDBkYptYr5t99+y7T/xo0bxlq1ahml1Ort4ODgDPsHDBhgqnrLqUr17opjozHvlbZpr/W7j200plbXOTg4GCUZu3Xrlml/QkKCqUL3ySefNN6+fTvL+BYvXmw61ubNm7M9j+z4+fkZJRl79eqVY7usrkNeK20lGZs0aZLlOfTq1cv0PHp5eRl79uxpTEpKytAmKSnJ2KhRI6OUWvmcVVVffiptU1JSjKdPn86yX5opU6YYJRkNBoPx1KlTmfbfXcWf1furoOK9W06fdZs3bzbt//zzz7PsHxcXZ2zTpo0pnvTXN7/fN3lRs2ZN03dMTizxPN3t6tWrRnd39wxjlC5dOk/nntNzPm/ePNN4+/fvz3aMhg0bGqXU6nRzDR061HSMLVu2mN3/bukrjyUZfXx8jMOGDTMuX77cePz4cWNKSorZY7Zu3dooyVijRo18xwcAKLqY0xYAUOSVKFHC9Hva/Hh58e+//5p+b9GiRbbtDAaDPD097y24u1hZWenzzz+Xvb19gYw3efJk1axZM9P2Rx55RG+99ZYk6cqVK6aFToqqtWvXmlbPnjRpkh5//PFMbSpUqKAPPvhAUmrl5d3Vzek5ODho6dKlWVYrjR492rQ9rTLNHPHx8fr8888lpV7nrOa/NBgMWrhwoem1OX/+fLOPk1crVqwwXbv0FddZ8fPzy/D4r7/+0v79+yWlrtreoUOHTH08PT21ePFiSVJKSoqp0jBN2vsoICBALi4u2R7by8sr95PJwYwZM/TII49k2l6lShVTJXlWc+9+9913CgkJkYODg1asWCEnJ6csx3/ppZf0xBNPSEqdV9pcadehefPmObbLz3UwGAz6/PPPszyHESNGSEqdV/fOnTtavHhxphXmra2tNWzYMElSRERElvPr5ofBYFCVKlVybDNlyhR5e3vLaDRq/fr1ObatVq3aPc/vXNDSqpJ79uxpWkzrbg4ODqb3+oULF0yLakn35/vm8uXLknKv1C8Kz1OZMmUyVT7Pnz8/39+1ffr0Mb3us5vr+uzZs6a5f82tspVS3ztpzL0rIis9e/bU1KlTTVX4165d0+LFizVw4EDVrFlTXl5eevrpp7Vy5cos5+3PSlpc58+fz/dc3QCAooukLQCgyEufKMppgZ27pS2GIt1bkuZeNG3a9J4X+LmbwWDQwIEDs92ftriVJG3durVAjllY0uIzGAwaMmRItu2effZZubu7Z+iTlfbt22f7j2lXV1dVrVpVkkzTG5jjwIEDioyMlJS6IM7dibE0bm5u6t27tyTp2LFjCg0NNftYefHzzz9LSr3V29zbYNNfw+wSUVLq6zbtjwN3X/e099Hvv/+us2fPmnX8vDIYDHr++eez3V+vXj1J0o0bN0zPTZq0hFPLli1VsmTJHI+Tlkzbt2+f2TGmXYfvv/9esbGxZvfPi8ceeyzLP9JIUp06dUy/t2/fPtvkcPp29/L6N0dKSoquXr2qkydPKjg4WMHBwTp+/Lh8fX0lpU73kJP0CThLioqKMi2U16tXrxzb1qxZU97e3pIyvo4K+/smPj7e9P1nbuLTUs/T3X9kuXt6nXtRqlQptW/fXpKyXUxt5cqVpt9z+lzJTvr/zzB3io3sTJs2TX/++ad69eolBweHDPsiIyO1fv169evXT4888oiCgoJyHS/t/R8fH5/pMxEA8OAgaQsAKPLS/wPKzc0tz/0qVqxoqor76KOP9Mgjj2jKlCnavn17oSZdCkrFihVNyYGslCxZ0pQgPnr0aIEdtzAEBwdLSj2nnBJrdnZ2qlu3boY+WalRo0aOx0v7B605Sf406Y/bsGHDHNum359TvPlx6NAhSamJy+yqSLOTFpOdnV2W1c3ppZ3L6dOnlZCQYNr+wgsvSEqtPnv00UfVt29fLV26VGfOnDErlpx4e3tnqKi/W/oE5d3PaVqC47fffjOtLJ/dz5w5cyRlrIrMq7Q/oAQGBqpixYoaOXKk1q5dq7CwMLPHyk61atWy3efh4WF2u3t5/efGaDTq66+/VuvWreXi4qJy5cqpRo0aql27tuknbQ7v8PDwHMcqyM/L/Dh06JAp+ffcc8/l+jpKO6/0r6PC/r65ceOG6fe8JG0t/Txt2LBB33//fYZtL730Up4rSXOSVj0bGhqq7du3Z9qflrRt2LBhrhXHWXF1dTX9fvv27XuMMrMGDRpo9erVunHjhrZv367Zs2erV69eGb4TT58+rVatWuX6fZL+NVCQMQIAihaStgCAIi/9PyjNvfX422+/VePGjSWlVkPOmDFDbdu2lYeHh1q0aKHPPvtMd+7cKbBYC2qaBSlvt2X6+PhIyvgP+qIoLb68nFPp0qUz9MlKbslLK6vU/8VJW4jGHOmPm1u8abHe3a8gpb3+01fy5VVaTF5eXrKxyXn92bRzMRqNGaYhadu2rebPny9HR0fduXNH33//vYYMGaKqVavK19dXL7/8cq6VernJ6/MpZX5Or1+/bvbx4uLizO4zefJkDRkyRAaDQdevX9eCBQv0zDPPqFSpUnr00Uc1depUXbt2zexx08vpOqS/Bnltdy+v/5zcuXNHnTt31oABA7Rz585cr2Nu+wvy8zI/7uU1JClTMrYwv2/SV2fmdl0t/TxFRUWZFpIsVaqUxo8fL0n6559/CmRxvO7du5veA3dPkXDw4EGdOHFC0r1NjSBlnJIpv+/prDg6Oqp169YaP368Vq9erdDQUK1du9Y0vc3t27c1ZsyYHMdI/5zZ2toWeIwAgKKBpC0AoMhLqzSUpOrVq5vVt1y5cgoMDNTWrVs1YsQIPfLIIzIYDEpMTNTu3bv1yiuv6NFHH9WpU6cKJNaCvNU3P6vQF1XF7ZyKW7zZye95vPrqqwoJCdFHH32kTp06maawuHLlihYtWqS6detq0qRJBRGq2dISk0899ZSOHj2a5x9z2dra6osvvlBwcLAmTZqkJk2amOZO/ueff/T222+rSpUqRX5+6fyYOXOmfvnlF0mp01GsWrVKZ86cUUxMjJKTk2U0GmU0Gk0Vp7nNtVkUpkaQMia3Fy1alOfX0MyZMzOMU5jfNx4eHqY/vOT2ByJLP09vvvmmrly5IkmaN2+eZsyYYbqDYubMmTp58qRZ493NxcVFTz/9tCRpzZo1GRLhaVW21tbW6tOnzz2Nn36KkYMHD+Yj0ryxtrZW9+7dtXHjRtNnyvbt23N8ntPvS/s8BgA8eHIuuQAAoAjYsmWL6fdmzZrd0xht27ZV27ZtJaXe5r1161YtXrxY27dv19mzZ9WnT58MyeGiIC8VPmlt7q5ATl9tl9Wcf2nu122VafHl5ZzSbjnO78JW9yr9ca9du5bjrejpb48urHi9vb11+fLle5ozNy2miIgIJSUl5Vhtm3Yu2S2UVKpUKY0ZM0ZjxoxRSkqKDh8+rLVr12r+/PmKjIzUzJkz1aBBA1My5X4pUaKErl69qoSEBD366KOFfrxatWppxowZmjFjhu7cuaM9e/Zo5cqVWrFihWJiYvTcc8/p7Nmz91QZXZQZjUbTAn3NmzfX9u3bM3zOpFfUK//vlr6y0snJKd+vo8L4vjEYDPL29ta///6b44Kcln6edu/erUWLFkmSunbtakqcLlmyRA0bNlR8fLyGDRumnTt35uuPSf369dO3336rqKgo/fzzz+rVq5dSUlL03XffScp53vPctGzZ0vT7xo0b9eabb95znOaoXbu2GjZsqN27d8toNOrs2bPZfq+kvQZKlSqVaY5cAMCDg0pbAECRFhwcrG3btkmS/Pz8VL9+/XyPWaJECfXp00fbtm1Tt27dJEmHDx/W6dOnM7SzdJXl+fPnM6xifbewsDCFhIRIUqYkQ/o5+XL6B35uFV8FdQ3S4jt//nyOc4AmJiaakhn3IwGXlfTHTVuBPDt//fVXlv0KUkBAgKTUuVvNnRszLaaEhATT/JXZSTuXqlWrmqq9smNlZaWAgADNmDHD9P6UpFWrVpkVX0FIq+ALCgrKMBfv/eDg4KB27drpyy+/1AcffCAp9bbltMXjHiQ3btwwJfafffbZbBOBMTEx+a6kNEdBfEY9/vjjpnH27t2b7/HSy+v3TV7Url1bUs6f25Z8nu7cuaOhQ4fKaDTK1dVVCxcuNO2rV6+e6Zb/33//3ZRYvlcdO3Y0zfmeVl27a9cuU4XvvU6NIKVe57T/19i9e/d9qbZNk36xtpxe22mvgUceeaTQYwIAWA5JWwBAkRUXF6cXXnjBdOvmuHHjcp2X01xp1VBS5sVY0qpX4uP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      "text/plain": [
       "<Figure size 1400x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Concatenate all dataframes into a single one\n",
    "df_cosine = pd.concat([df1, df2])\n",
    "plt.figure(figsize=(14, 7))\n",
    "plt.title(\"Distribution of cosine similarities (arXiv CS)\")\n",
    "# Plot for the first graph\n",
    "sns.histplot(data=df_cosine[df_cosine['dataset'] == 'train'], x='cosine similarity',\n",
    "             kde=False,  element='step', stat='density', color=\"green\", alpha=0.5, label=f\"Train, n = {replace_number(len(df_cosine[df_cosine['dataset'] == 'train']))}\\n min = {str(train_min)}\",)\n",
    "\n",
    "# Plot for the second graph\n",
    "sns.histplot(data=df_cosine[df_cosine['dataset'] == 'valid'],\n",
    "             x='cosine similarity', kde=False, element='step', stat='density', color=\"blue\", alpha=0.5, label=f\"Validation, n = {replace_number(len(df_cosine[df_cosine['dataset'] == 'valid']))}\\n min = {str(val_min)}\",)\n",
    "plt.xlim(0, 1)\n",
    "plt.tight_layout()\n",
    "plt.legend(loc=\"upper left\")\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "link-prediction-in-graphs-5axuDq5Y",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}