ixxi-dante/nw2vec

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projects/correctness/gae-reproduction-cora-nw2vec-multitask_arch.ipynb

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Maintainability
Test Coverage
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Train nw2vec with the original VGAE architecture for Cora embeddings + a kernel for the scalar product decoding + an intermediate layer in decoding"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using TensorFlow backend.\n"
     ]
    }
   ],
   "source": [
    "import os\n",
    "\n",
    "# Train on CPU (hide GPU) due to memory constraints\n",
    "os.environ['CUDA_VISIBLE_DEVICES'] = \"\"\n",
    "\n",
    "import contextlib\n",
    "\n",
    "import numpy as np\n",
    "import keras\n",
    "from keras_tqdm import TQDMNotebookCallback as TQDMCallback\n",
    "\n",
    "from nw2vec import layers\n",
    "from nw2vec import ae\n",
    "from nw2vec import utils\n",
    "from nw2vec import batching\n",
    "import settings\n",
    "\n",
    "from gae.input_data import load_data\n",
    "from gae.preprocessing import sparse_to_tuple, mask_test_edges"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "@contextlib.contextmanager\n",
    "def gae_directory():\n",
    "    working_directory = os.path.abspath(os.curdir)\n",
    "    try:\n",
    "        # Move to the GAE directory\n",
    "        os.chdir('../../gae')\n",
    "        yield\n",
    "    finally:\n",
    "        # Move back\n",
    "        os.chdir(working_directory)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load data\n",
    "with gae_directory():\n",
    "    adj, features = load_data('cora')\n",
    "    features = features.toarray()\n",
    "\n",
    "#adj_train = mask_test_edges(adj)[0]\n",
    "adj_train, train_edges, val_edges, val_edges_false, test_edges, test_edges_false = mask_test_edges(adj)\n",
    "assert adj_train.diagonal().sum() == 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_ξ_samples = 1\n",
    "n_nodes = adj_train.shape[0]\n",
    "dim_data, dim_l1, dim_ξ_adj, dim_ξ_v = features.shape[1], 32, 16, 16\n",
    "overlap = 0\n",
    "dims = (dim_data, dim_l1, dim_ξ_adj, dim_ξ_v)\n",
    "loss_weights = {\n",
    "    'q_mulogS_flat': 1e-2 * 1.0 / (dim_ξ_adj - overlap + dim_ξ_v),\n",
    "    'p_adj': 1.0 / (n_nodes * np.log(2)),\n",
    "    'p_v': 1.0 / (features.shape[1] * np.log(2)),\n",
    "}\n",
    "\n",
    "# Actual VAE\n",
    "q_model, q_codecs = ae.build_q(dims, overlap=overlap,\n",
    "                               fullbatcher=batching.fullbatches, minibatcher=batching.pq_batches)\n",
    "p_builder = ae.build_p_builder(dims,\n",
    "                               feature_codec='SigmoidBernoulli',\n",
    "                               embedding_slices=[slice(dim_ξ_adj),\n",
    "                                                 slice(dim_ξ_adj - overlap, dim_ξ_adj - overlap + dim_ξ_v)],\n",
    "                               with_l1=True, share_l1=False)\n",
    "vae, vae_codecs = ae.build_vae(\n",
    "    (q_model, q_codecs), p_builder,\n",
    "    n_ξ_samples,\n",
    "    loss_weights=loss_weights\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def target_func(batch_adj, required_nodes, final_nodes):\n",
    "    return [\n",
    "        np.zeros(1), # ignored\n",
    "        utils.expand_dims_tile(utils.expand_dims_tile(batch_adj + np.eye(batch_adj.shape[0]), 0, n_ξ_samples), 0, 1),\n",
    "        utils.expand_dims_tile(features[final_nodes], 1, n_ξ_samples),\n",
    "    ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy\n",
    "from sklearn.metrics import roc_auc_score\n",
    "from sklearn.metrics import average_precision_score\n",
    "\n",
    "val_scores = []\n",
    "test_scores = []\n",
    "\n",
    "def valtest_cb(epoch, logs):\n",
    "    _, adj_pred, _ = vae.predict_fullbatch(adj=adj_train, features=features)\n",
    "    adj_pred = scipy.special.expit(adj_pred[0, 0])\n",
    "    val_scores.append(get_roc_score(val_edges, val_edges_false, adj_pred))\n",
    "    test_scores.append(get_roc_score(test_edges, test_edges_false, adj_pred))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_roc_score(edges_pos, edges_neg, adj_pred):\n",
    "    # Predict on test set of edges\n",
    "    preds = []\n",
    "    pos = []\n",
    "    for e in edges_pos:\n",
    "        preds.append(adj_pred[e[0], e[1]])\n",
    "        pos.append(adj[e[0], e[1]])\n",
    "\n",
    "    preds_neg = []\n",
    "    neg = []\n",
    "    for e in edges_neg:\n",
    "        preds_neg.append(adj_pred[e[0], e[1]])\n",
    "        neg.append(adj[e[0], e[1]])\n",
    "\n",
    "    preds_all = np.hstack([preds, preds_neg])\n",
    "    labels_all = np.hstack([np.ones(len(preds)), np.zeros(len(preds))])\n",
    "    roc_score = roc_auc_score(labels_all, preds_all)\n",
    "    ap_score = average_precision_score(labels_all, preds_all)\n",
    "\n",
    "    return roc_score, ap_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/slerique/anaconda3/envs/base36/lib/python3.6/site-packages/tensorflow/python/ops/gradients_impl.py:100: UserWarning: Converting sparse IndexedSlices to a dense Tensor of unknown shape. This may consume a large amount of memory.\n",
      "  \"Converting sparse IndexedSlices to a dense Tensor of unknown shape. \"\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "c5fd2f6d9d3640c5abc51cc79b253efe",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(IntProgress(value=0, description='Training', max=200), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "n_epochs = 200\n",
    "\n",
    "history = vae.fit_fullbatches(batcher_kws={'adj': adj_train, 'features': features, 'target_func': target_func},\n",
    "                              epochs=n_epochs,\n",
    "                              verbose=0,\n",
    "                              callbacks=[TQDMCallback(show_inner=False),\n",
    "                                         keras.callbacks.LambdaCallback(on_epoch_end=valtest_cb)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "history = {'history': history.history}\n",
    "val_scores = np.array(val_scores)\n",
    "test_scores = np.array(test_scores)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, len(history['history']), figsize=(len(history['history']) * 5, 4))\n",
    "for i, (title, values) in enumerate(history['history'].items()):\n",
    "    axes[i].plot(np.array(values))\n",
    "    axes[i].set_title(title)\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f1f23c67630>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(val_scores[:, 0], label='Val AUC')\n",
    "plt.plot(val_scores[:, 1], label='Val AP')\n",
    "plt.plot(test_scores[:, 0], label='Test AUC')\n",
    "plt.plot(test_scores[:, 1], label='Test AP')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.88502075, 0.88627912])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "val_scores[val_scores[:, 0].argmax()]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.87328138, 0.87242801])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "val_scores[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.87378344, 0.87654362])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_scores[val_scores[:, 0].argmax()]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.88064624, 0.88442563])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_scores[test_scores[:, 0].argmax()]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.86689183, 0.87657118])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_scores[-1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Precision"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy\n",
    "from sklearn.metrics import roc_auc_score\n",
    "from sklearn.metrics import average_precision_score\n",
    "from keras import backend as K"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_roc_score(edges_pos, edges_neg, adj_pred):\n",
    "    # Predict on test set of edges\n",
    "    preds = []\n",
    "    pos = []\n",
    "    for e in edges_pos:\n",
    "        preds.append(adj_pred[e[0], e[1]])\n",
    "        pos.append(adj[e[0], e[1]])\n",
    "\n",
    "    preds_neg = []\n",
    "    neg = []\n",
    "    for e in edges_neg:\n",
    "        preds_neg.append(adj_pred[e[0], e[1]])\n",
    "        neg.append(adj[e[0], e[1]])\n",
    "\n",
    "    preds_all = np.hstack([preds, preds_neg])\n",
    "    labels_all = np.hstack([np.ones(len(preds)), np.zeros(len(preds))])\n",
    "    roc_score = roc_auc_score(labels_all, preds_all)\n",
    "    ap_score = average_precision_score(labels_all, preds_all)\n",
    "\n",
    "    return roc_score, ap_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "q_preds, adj_preds, v_preds = zip(*[vae.predict_fullbatch(adj=adj_train, features=features) for _ in range(10)])\n",
    "\n",
    "q_preds = np.array(q_preds)\n",
    "adj_preds = np.array(adj_preds)\n",
    "\n",
    "q_pred = q_preds.mean(0)\n",
    "adj_pred = scipy.special.expit(adj_preds[:, 0, :, :, :]).mean(1).mean(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.8688001613083257, 0.879954311859355)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_roc_score(test_edges, test_edges_false, adj_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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mz6YJ42l/FvwMpgBmAphCkpJCcgzraYwMwJAHSuo95P3jiqSKwnjax6/x0/Bug5dit8XYRIARPeH3ZNjYTDaaMJ72obzxXbCexoiW+nWaMEfzhPG0j19DsgBeDrzNSIFIe5qC4hp0HbUuLu94oVSVd7wqGLNveSXJdb1W2zjte+5Q8ke36myzPfuuD4RHu6my+44+Q8k1XfV4fuBybcSsPl3bFgOeDuyB8kt1u4beVqnfe28HJXd9T//MPrI4sBW6FOkvSttV23U7r0qK5Pyaltsm/AQmh0K3O3ODkisXdVfybv2I0LGXXvdaPzywn3brqAz07rheyc0l407jOk3c0x5eGuJz4SV3TGQWvJ0i5gE4B8DsVOwZwIZnRiZIk9I05mlP8nYAZSIyC8AjAB4nWQ6vhzk31fua0hjRk0Y3moY87UXkloTzKgDfSdsNYUpjZIDkbD+5RqRKU7urEOvnB3ZMuxr99DY80i+49lBdVviuds/f0V/bIUcM1tuuLJ0X2ES1p+prS1/VH3v9MVouv0Tfu+hT/cuYd2tgH3St0qmPYiXahqlepuUdfXRdNQkuX9dcoPe0nbjgdCUf9I4OM97TXbfzwnFBuPQzK3X4Q8H9epY1Nl6v0+zpquvmXL0GVLQjuFf3e/Ra1PIJDjO4QiDH3WispzGix3oaw3DElMYwHDGlCU/rDdUY8FAwi79igt4psOebweLC3vXaVyp/r37SfV7SodKVR+h1nZJYcH2HGe+rstMXa3+wZ2/WYcadrvlMyZtLdTqjPfcHmTBPuOU9VfbXCUcpecyXdJjxa4uHKPmJk6fGz2/8+BxV1u//9Ni/MmltvNNS/UyGjA/W9erkaFW29yq9npe/SC/M7Dpax+706qpjnVoXBP+bvPH62fedOUDJ2kMuCQtCMwx3bPbMMFwxpXEgFkPdlqDbH3WSdhNZ+mGQIWXbMD0lOnzQKiV/ikFKLpk6T8kf/2l4/HzDGToE+b5/ar/5Dn21K0zRTTo75YartOtL/8+CMIRZi3VYcL+kUN/Zp+t7t9qlhyb/veLb8fO9T2nXluI57yq5bqQen+3+js6w+YvnL4ifHzxcDzFr79Of6Xt3vqHktzfqvXE/3aCnnA8qDlyLNk3SQ7v+j4X3wASspzEMd8ymMQwHsj3nbAhMaYzoMaUJz97+rbD6nmBqeO1ftItJl+3BtGZ+kfZtX7NdhzvvOVWHBuT/S9s4qt6XtKvLzrO0LVVdosOKdn3RTslFb+vybXcE7v/5i7V7T207Pb6XTto2y+ulXXo2vZHgVlSnv015/XW4Q98XtA2z+gj972PfYCp4zXptkxT30dcm2zA7Huqt5B5V+nOsPS0Ijyjcqm3A4ya9peS5etb9P0je0S3XsJ7GiB7raQwjPJTcnz1rNtyZ5KMk15P8MOG1ziRfJbnC/9upqToMQ5G+cOeMEKanmQZgCoDHEl77BYDXRWSin6DtFwBubK6i1mvr0P/6wBZpPV2HBpePLImf5y/WobyxtdouqRmt3T6WTdB2SKvPg9+D5N2ZR/bSAbnvr9cJTA5apl3ftxym21Kc8FN50HJd984eSTsyJ23iik906HSHE4Nn8MP+Or3rU0cPVHLF1dpYaPeK/sneNDKwl7qXajeYCxJ2mQOA5386RsmTpz6g5PPe0Ilfus0J1rY2nabDweferVPvAs+hSfb3nkZE/on/TERwFoDp/vl0AN+EYYSkfojW3JGttNSm6S4i6wBARNaR7NbYhX6uqisAoKigfWOXGQcKkvuzZ/s8hVPi7s6t8to2/wZj/yfHN91saU9TSbLU72VKAaxv9h0ApLoatauDncCGddBrGDtvDFzuV1yq12k2d9G2wa+P1rsW3v6a3nGsLiGyoPMHel1mb53+2F0maWWuHJmUDrZc/zSecNan8fNnh3VVZSUL9e9Q/m7d7lZ6eQnnH1wWP3/syjNVWVF7HcJd8oFe41k/XIdPIC/4prXK13bZwu19ldz7jhVKfmKTtksGTtOfudWaIOygqou2Abfo3UOaJ4sVIgwt7Wnqc0nB/9tM8l7DCMh1mybMlPOT8BKtHUayguRlACYCOIXkCgCn+LJhHBA0OzwTkfMaKfp6mttiHChkcS8Shmh3d27fFrXHBmsNc+/Utz9kcrCtX/Udh6myUyfq+I8H7v62ks+YUKbk938ThPtWnqB3Ot76gJ7FGzX5HSW/8Ue9G3RyCu2Z7wexOsWr9brM+TdoW+uZtTrseP1m7W/3/M9OiZ+X3PqpKtt2nbYdDr9dh06v2K7tqW17A1usZpqOzXnnW3p7wBP7rlTyW9OHK/nCB15S8rQ/jY2fn/G9N1XZwqv0Z/wYTbAfzJ6ZG40RPdbTGEZ4iOw28sNgSmNEjylNeOoKiV2lwdrCyde9rcqfLAtsiS69dNOefEzPO+w6Sfs/fTxKTwSeUTY7fv7H+aNVWYcP9frGa2u1/VQ1Rqco6leivYhqngriXI76vrYzXqr8kpLH9Vqs5H9eru+17LeBXRK7W6dC2j1E20ufnql94Fbdp2NmqrcGqWUHrdK+eev36uf5zpM6t0HXJfp5vnT5iUqWUcH5k/NGqrIuSe2EdqHTZPl0chispzGixyYCDMMN62lcbrarBp3fCTxu/v6Y3hW4bYL3yrZB+snWlerhRrsPdKhA3gDtJvLIh4Pj5/lttUtOrEgPz2SBDgdqO1IPx3q3027237omyNj58KRxup1Jni2Pn6qHVN0HaReda4e/Ej9fMFBnCX3/ucOVvOpSPXwrKNDhz+eODIa7s1/Wz/ZXxzyv5PIj9JT0jI/0lPPYQcuUvHVKMK3cvkIPhSuPc9QCUxrDcCDLnTHDYEpjRI4NzwzDFVOa8NS1LsCeAcGuWW1P1eHO8778bPz80Gk/VmVtk2yYbmMrlMzn9Di7/32B7bDzVj32P+G7/1by/DuPVfLnXbUdsry1DmGorArccE6aMF+VffQNbSssH6DtlNV6czNMWTI6ft7mde3q0rpWf7uqksIj9qzV7kDdhgQhEN1/9okqm7RUhzdjnv6MB7+3V8mzj9c2Tsn5wa7cu2fqFLeu2zWbG41huLAf2DT7PHLTMBKhw5HSfUJkTCJ5FMl5JJeQXETyu2HqNqUxoieacOf6jEmDALzuy8nsBnCRiHwJwFgAfyDZsYHrFBTH8WgqkNwAYDWAEgAbI7txeKxdbjTWrr4i0rWB19G2ex8ZdN61oSpfdN+174rIiOav/E9ILgcwOiEkf66IHNbMez4AcI6IrGjqumjjafwHSbKspQ9jX2LtcqPF7Qr/O11CMjFQaqqITG30ak3ojEkAQPJYAK0AfNLUdYBNBBhR4xaEtrEppST5GoAeDRTd5NIkvyd6HMDFItJs60xpjOhJk0UgImMaKyMZKmMSyQ4A/g7gZhGZ39A1yWRqIiBsFxs11i43WtSuiLLRNJsxiWQrAM8DeExEnglbcUaUxmFcGinWLjda3K5oZs8azJhEcgTJh/1rxgP4KoBLSP7bP5rZXceGZ0YGiML3TEQ2oYGMSSJSBuAH/vkTAJ5wrduUxogWQc4HoUU6PCM5luRykuX+Fh0ZIxv33SHZh+Qckkv9VeqfZkm7iki+Q/IDv123+a/3J7nAb9dTvo3QdF04ADJspguS+QAeAHA6gKEAziM5NKr7N8A0eKvAiYRZRd6X1AL4uYgMATASwAT/GWW6XXsBnCwiXwZwFICxJEcCuBvAvX67tgC4LFRtOZ4APcqe5lgA5SKyUkSqAcyAt89NRsjGfXdEZJ2IvOef7wCwFECvLGiXiMhOXyz0DwFwMoCZru2iSKgjW4lSaXoBSEyDX+G/lk2oVWQATa4i70tI9gMwDMCCbGgXyXyS/4a33vEqvJXzrSJSH0se7v8ZtpfJXp2JVGkaclzN4keTOUgWA3gWwDUisr2566NARGIichSA3vBGDUMauixMXWbThKcCQJ8EuTeAzxu5NlNU+qvH9a4VofbdSSckC+EpzJ9FpH7zyoy3qx4R2QpgLjybqyPJ+hnY0P9P1oU7spUolWYhgEH+jEsrAOfCW7XNJjK67w5JAngEwFIRmZxF7epa7zJPsg2AMfDsrTkAznFuV44PzyJbpxGRWpJXAngZQD6AR0VkSVT3T8bfd2c0PE/aCgC/hrdq/LS/B88aAN+JuFmjAFwIYLFvPwDAL7OgXaUApvszoHkAnhaRv5H8CMAMkncCeB+ewjdNlg+9whB1aMCLAF5s9sIIyMZ9d0TkTTQetJjJdi2CNymR/PpKePaNY4VpaFQGMY8AI1Js1wDDaAGsy22tMaUxoiXLjfwwmNIYkZPN08lhMKUxosd6GsNwwyYCDMMFgXMa22zDlMaIHLNpDMMBW6cxDFdEbHhmGK5YT2MYrpjSGIYb1tMYhgsCIJbbWmNKY0SO9TSG4YrNnhmGG9bTGIYLFhpgGG4QAG0iwDDcyObsmWEwpTGixYZnhuGK+Z4ZhjM2e2YYrlhPYxgOiM2eGYY7ua0zGdsS3TiAiWJTJ5ctF0l2IPkZySlh6jalMaKnPnqzuSM1XLZcvAPAG2ErNqUxoqV+d+cwR2qE2nKR5HAA3QG8ErZiUxojUohwQzN/eFZCsizhuMLhVs1uuUgyD8AkANe7fAabCDCipy50N7JRREY0VkjyNQA9Gii6KWT9PwHwoois9fbTCocpjREt9cOzdFQlMqaxMpKVJEtFZF0TWy4eD+BEkj8BUAygFcmdItLklvOmNEbkROSwWb/l4kQ0srWhiFwQbxN5CYARzSkMYDaNkQmimT2bCOAUkisAnOLLIDmC5MOpVGw9jREx0ThsisgmNLDlooiUAfhBA69PAzAtTN2mNEa0WDYaw3DHgtAMwxVTGsNwQADYRrWG4YJFbhqGO6Y0huGAAIjl9lZopjRGxAggpjSG4YYNzwzDAZs9M4wWYD2NYThiSmMYDogAsVimW5ESpjRG9FhPYxiOmNIYhgtis2eG4YQAYoubhuGIudEYhgMiLimcshJTGiN6bCLAMNwQ62kMwwULQjMMN8xh0zDcEABibjSG4YBYEJphOCM5Pjyj5LhRZuQWJF8CUBLy8o0iMnZftqclmNIYhiO2a4BhOGJKYxiOmNIYhiOmNIbhiCmNYThiSmMYjpjSGIYjpjSG4YgpjWE48v/9AGdhKO2WjQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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IvUGbYck8IM9RtSmzAWAoOO7DwI1DwXElnQcg6eWS1gNvB74q6aFGP0K9Q6ClwPuAK9K/P8pTqbSzm6d/lJ3VZt5b/Kfdui3ZRiYb8PX3ZceucWUrt2V7TALse8pPov2n3x+ZWT441zd19m71ba6qkOj7jz9+sSsbmOLXG5iaLbPJvuFk/W1HuLJqNNMVIkdw3LtpQlqkcqoqgKT/Ipnwzkm172MkN/6Nki4isc2+vZmdCtoDq20SPCbJYwW6wBGd3eS+BG1InuHNWCZ8gYKGaKIVaFQIBQjqJpnghgIEBabdvUFDAYKGiDlADZQmG8+cmG0y3PPAPL/iXGdj+S6/+3+4/XhXNjCtgi9VBdPk4ML9meWdFX4FS1N8K0nnHl82cJLvztrf63/ujq7sz6Ydvjm2dHy2h241DDE43q1AQVCJNn8AhAIEDRCT4KDwtPkjIBQgaIh4AgSFxYDBwVCAoKgYEE+AGhBoQvam89K0CvV2dWeXd/sD0P4ef3O7+vx/WiVZaVd22iX1+qbAjtl+bNBSV4X0Quv9vRM21TfjlhyRBvzPNbB9kt+PKsQ6QFBsQgGC4qKYBAcFJ54AQWExsLACBcUmFCA3Eyf0c/ThWzNlm27296UeduXvM8v1Kz9u0hO3LnRlU16+zZW9ct4TruyuL700s3zvYf5N0LnOD98454E+V7bxNX6b3c/4/7ZJT2eXv/Bdf3LrLL/zWFdWlTYfArW3K18w+ljOIwc5guNOlPSdVH5XRsC2mgkFCOpnaCEsz1GFsuC45wInABdIOmHYaRcBO8zsBcBngSsb/QihAEFDNCsuEDmC46bvr0tf3wScLamhSUgoQNAYg8p3VCdPcNxnz0kDaT0DHNRI98MKFDSE8k+C50haXvb+ajO7urypjDrDW296AN1QgKB+apjgUj06dJ7guEPnrJfUBcwEtufuQQYtVQAJJnYOZMp6Z/nf5KPXZH9vHfdVMAf60QrZf+ccV/aL6f4TdeJbdmWW96/ywynOfs1mV9b3eldE6UE34DYDRx5wZQf2Zn8n9y87zr/WAt8cW5l8E9ycPBscF9hAEhz3XcPOGQrJeQfwNuBXZo2549WbIeZySRsk3Zceb2qkE0Eb0yQzaJ7guMB/AAdJWg18iCYkZsnzBPgG8AXgm8PKP2tmn2m0A0Gb07RkRbmC4x6gyXFo680QEwTjYkNMI2bQSyWtSIdIbpI8SRcP5YXq25kdVydoX2T5jrFKvQrwZeBoYDGwCbjKO7E8Q8yEHt8vJmhTmugKMRrUpQBmttnMSmY2CHyNZBUvCNqOusygkuYPJckD3go8WOn8PHRWsMQN9GfraWeF/btdvqWQQWeLMcCBCvttPazCz8i+Pv9i/SV/T3DpIN+OO2litikZ4EBfdpv90/3PNWm6v2+5GmN5eJOHejPEnClpMcnDbS3wgRHsYzBWMfK6OYxZ6s0Q8x8j0JegHRnvT4AgqMS4HwIFQUVCAYJCEwoQFJWxvsiVh5YqQP/2CWz4bnay6SV/9Qe33vKtCzLLN22d6db5u/N/5squvP8Nrsz2ZYc/BDiwJtvrc9DLYAM8s9pdJGdwhm/OnL7S78fAlArJtw9xQk9O8c2gU3873ZVVZbxbgYKgEvEECIpNKEBQWGIOEBSeUICgyKiJG2JGgwiLEhSalj4BbEaJvrOeyZQtveNlfr2JTvLnPl9/r/jRW2vrXEpnhUTZNi/bxbRji2+W7F7gJ6Huq5Dwev88vx8Ds3zzqZetpmuX73m663i/varEECgoLDEJDgpPmytAzAGCxmjBlkhJsyUtk7Qq/Zu5vC7p55J2SvpJ3rZDAYK6EYkVKM/RIB8GbjGzY4Bb8OMBfRp4Ty0NhwIE9ZMzIkQT5gnlUaGvA/4ssztmtwC7a2m4pXOA7s4Sh/dkW4HWrvTDC9oLsq0v3Q9Mdet0+caXill99izy/1snLVyfWX7vgUVunSN6ssMpAsyd4v+v1s3pcWXdHf5P6t6+bCe6Pcv9cJAHvcQPr/mkK0lpXnDcSswd2oNuZpsk+XEjayQmwUFjNCk4rqRfAvMyRP9cR69yEwoQNESzzKBm5oYKlrR5KBKJpPnAluZcNeYAQaO0JjDWUFRo0r8/arjFlFCAoH6sZVagK4BzJK0CzknfI+kUSdcMnSTpN8B3SVInrZf0xmoNxxAoaIwWLISZ2dPA2Rnly4H3l70/vda2QwGChhj3rhCSjiDJDTCPJBr81Wb2eUmzge8Ai0iiw73DzHZUamtCR4kF07JP2Xufn/S68w/Zzmbrz/afrUd/x49EveFM33x6/GI/UfZDv3lBtmB29j5cgI13HerKnhrw7bH/8Bc/dGVffvQMV7Z3f7YZdOHp6zLLAaZ3V4gjWY02V4A8c4AB4B/N7HjgNOCDaf7WvKtzwXgl7wR4DCtJVQUws01mdk/6ejdJ+prDyLk6F4xfRPvnB6hpDpBmijkZuIsRXJ0L2oexfHPnIbcZVNI04HvA35uZv77//HrPZog5sLOBsWYwNhnvQyAASd0kN/+3zOz7afHmdFWOSqtz5RliJvVMakafg7HEeFcASSIJh/6wmf17mWjEVueCNqF13qAjRp45wKtJfKwfkHRfWvYRktW4GyVdROI0WDV95e7eifzq0WMzZYPn1PEtmW8GXfUef59uR59fb+UD2WEYAeyQ7L2zHXv9/bYDi/xhnw34vz9X/vw8VzY4xTe7ymnzsaem+O1NaGCpdgzf3HnIkyDjt/gOxM9bnQuKRbuHRYmV4KAhxvLwJg+hAEH9jPEJbh5CAYLGCAUIisrQSnA7EwoQNIQG21sDWqoAUyf2cepRazNl9y473q+3LvtLfvpUP6Tf1DV+guoB3yLI4AT/HzrYm20Mm7rON2funu17fGqH38eZj/r1dh7vX2/KhmyT7N4j/e+q40Cd+6JiDhAUnRgCBcUmFCAoMvEECIpNmytARIUI6qdFUSHyBMeVtFjSHZIekrRC0l/kaTsUIKibFu4Iy7P9dh/wXjN7EbAE+JwkP75kSmsTZW+ayIYrjsmU9S7xPRwPejC7/EXHZsfqBHh4SlaUvYSrTv2uK/vXR891ZYPfz46v+fRr/ETZhyzzvVIn7vY/85Z3+Zv6ux6b5sr2vSjb+/TlR/mb/Zff52z2z4O1ZAx0PnBm+vo64Fbgsud2wx4te71R0hbgYGBnpYZjDhA0RA2/7i0LjivpFcAEYE21hkMBgvqpbSGsJcFx092J/wm8z6zChpGUUICgIZq1H6AZwXElzQD+H/BRM7szz3VjEhw0RItig1bdfitpAvAD4Jtm5k/yhhEKENSPkUyC8xyNkSc47juAM4ALJd2XHourNdxaK9A0semVzv7ZqX1uvWl/81Rm+Z/uXuTWGZzuW1g+dPO7XVnnbv83oXRGtrXn5CP9sIMrJhzuyiZN9j/zcQdtc2UPm+8od8j0fZnly1cvcutMPaymrELPoRUrwXmC45rZ9cD1tbYdc4CgMdp8JTgUIKib2BATFBuz2BATFJz2vv9DAYLGiCFQUFwMGO9DoAoZYi4H/hrYmp76ETP7aaW2rNPo78k2T1bIXc3qTdmuH6UZ/j5XKoT7s/4Kps7pfpPWl23CvXfVQr9ShSwwe3v9kIorNi3y+9Hp33Sbd2U736nP/8x79vnOdVVp7/s/1xNgKEPMPZKmA3+UtCyVfdbMPjNy3QvGOuN+CJR64Q154u2WNJQhJgja3gpUkyvEsAwxAJemu2+uzdqlE4xzipAjbIiMDDFfBo4GFpM8Ia5y6j2bIaa0Z28TuhyMFZKFMMt1jFXqzhBjZpvNrJT6XH8NeEVW3fIMMZ3T/PSkQZsymPMYo9SdIWYoPVLKWwFn42Iwnmn3J0AjGWIuSN1NjSRR9geqNdTRPciMQ7M9D3ft8OMVaoOTW2ya7/FJBRNj1y5fVppS4efKEc18IDs5NcC+V/rDvv4d/n7h+bf55tNtJ/m/W117suvtn+9/V5O31rkcNMbH93loJENMRZt/UATCFygoOmN4eJOHUICgfixyhAVFJ54AQaFp7/s/FCBoDA229xiopQowc+IBlix8OFN2882vcusNOolU9s/1zZnz7/DNfrsWVPDQfI2f2Lrj0eyFvI5+/2ewf5+fBWbKXN9EuvEsf9Gwc4a/md7WTs4WVPCc7Vqwy5VVxGjJIpek2cB3gEUkJvd3mNmOYecsBL4PdALdwP81s69UazvCogR1I/ItgjVhISxPcNxNwKvMbDFwKvBhSYdWazgUIGiM1sQFOp8kKC7p3z97fjesz8yG4tZMJOe9HQoQNEZrFOA5wXGBzB1Sko6QtAJYB1xpZhurNRyT4KB+apsDVIwO3YzguGa2DjgxHfr8UNJNZra5Up1QgKAharACVYwO3YzguGVtbZT0EHA6cFOlc2MIFDRAzuFP40OgPMFxD5c0OX09i8SJ85FqDbf0CbBj91S++9tTM2V2Ur9b75UvXp1Zfu/NfnLtTa+u4PE5qcKv1ibHjAic/sYVmeW3rsrOegMwa2Z2rE6AE+b4T+f7O3wDxoQu36Q5+aXZJs2n7/Az5uw9pk5b5lBw3JHnCuBGSRcBTwJvhyQ4LnCJmb0fOB64SpKROG9+xsweqNZwDIGCxmjBOkDO4LjLgBNrbTsUIGiIsbzZJQ+hAEFjhAIEhcUMSuELFBSZeAIEhSYUoAYGoXNf9tLDy1/6aGY5wCkzs5M83zn7hW6ds0/zLWC3rvHNlqXt/kb1h7ZnmxKPmLsjsxzgidV+Stv7Bvyvv/eA70W65xk/lmfPodlm0APzfNOpdvib+itShOC4QeBjUD0V75gmFCCoHyMmwUHBiTlAUGhCAYLi0hRHt1ElT4aYScDtJLtsuoCbzOxjko4EbgBmA/cA7zEzf7MqQKcxMDN7r+4djx7lVruj/wXZgin+vt9bHj7OlVlvBSfYStlX1s7OLFeFxNV0+WPkvVv9cJCde3xnPk30+/jMkzOdflS4UQcr5eepgAFtvik+jzt0L3CWmZ1EEgp9iaTTgCtJMsQcA+wALhq5bgZjlta4Q48YVRXAEvakb7vTw4Cz+O/NBpn7NIPxTuoKkecYo+TND9CZRobeAiwD1gA7zWxodWU9kTapeBiYDeY6xiq5JsFmVgIWS+oBfkCy+eB5p2XVlXQxcDFA5+yeOrsZjFnafCW4pi2RZrYTuBU4DeiRNKRAhwOZO/AjQ8w4Z7zPASQdnP7yk+65fD3wMPBr4G3paZn7NINxjlliBcpzjFHyDIHmA9dJ6iRRmBvN7CeSVgI3SPokcC9JGqX6qWBK7JyWvV9Y6/z9u6Wp/pc+Yaev91bhJ2H24q2Z5U/v9J3TSgN+g90TfQe1qfN7XdmevU7GHKCjM/tz927zv6vuef6+5aqM4V/3POTJELOCJDXq8PLHcBLjBUXBsFKFNFVtQKwEB/UzDtyhIy5Q0Bg2mO9oAEmzJS2TtCr96yZllzRD0gZJX8jTdihAUDcG2KDlOhokT3ToIT4B3Ja34VCAoH7MWvIEIEd0aABJLwPmAjfnbTjmAEFD1DAJrhgctwrPiQ4t6Xn7TCV1AFeR5LR+XhAtD1kLzViStgJDG3znANtadvGxz1j9Phaa2cFZAkk/J+l3HraZ2RJPWCU69HVm1lN27g4ze848QNKlwBQz+zdJFwKnmNml1TrVUgV4zoWl5ZWiBReN+D58JD0CnFkWHfpWM3vhsHO+RRINehCYBkwAvmRmleYLMQQK2oKh6NBX4HgdmNm7h16XPQEq3vwQk+CgPbgCOEfSKuCc9D2STpF0TSMNj+YQ6OIaJkHjnvg+RodRU4AgGAvEECgoNKEAQaEZFQWQtETSI5JWS6o6Ux9vSLpW0hZJD5aV5fZ3CZpHyxUg3VfwReBc4ATgAkkntLofo8w3gOGLQrX4uwRNYjSeAK8AVpvZY2kcoRtIfD0Kg5ndDmwfVpzL3yVoLqOhAIeRZPIeIiJKJOTKhh40l9FQgKy9j2GLDUaF0VCA9cARZe/diBIFY3Pq50KebOhBcxgNBbgbOEbSkZImAO8k8fUoOlWzoQfNZ1RWgiW9Cfgc0Alca2afanknRhFJ/wWcSeJKvBn4GPBD4EZgAWk2dDMbPlEOmky4QgSFJlaVKB+CAAAAJElEQVSCg0ITChAUmlCAoNCEAgSFJhQgKDShAEGhCQUICs3/B2yCcZMDhuWvAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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lO/S8sDPoD0RhZniYcMnW9wRlTSnLUrd1hx2L9O6DE9P3Hhr+Vy/a9r6gDNalyHwewMk7bgBOfpF3gp2c4zWAk1sMzEeBnHzjBpCZKU09nDH5+UTZEx1vDebb0zU9Mb2/EL7W8ZN/F5S9umVOUNa0J7xd4bumbkxM7+zpCObZvTdZd4Cjp2wNyppT9n9tSZHt2pK880b/5KnBPMdPKS9gN+BNICfnuAE4ucUnwpy84xNhTr7xUSAnz6RtJNYIuAE45WN4J3gk9Fgra/rekih7rXdiMN9AYNFbISX48yu94eHH/mnha7W0hBevbexJLnNvX1iRgbZwE2Frb3hoMo3dfeFNhgcC99bfPvL7Gh41fCe43Agx10n6naRn4uO80VXTqVss41GnlBshBuCbZjYvPu5LkDt5oJjxqFOy7A36iKS3jr4qTsMxDuYBKtnU5WpJK+MmUnB/bUkLJK2QtGLvrv4KLufUI7JsR71SrgF8D3g7MA/YAnw99MXSCDGTDwyH93QalCr2ASTNl/SCpHWS3hR4UVKbpB/H8ieq0TIpywDMbKuZFcysCPyAKMq345SNpGbgFuBc4FjgEklDt9W7HNhlZkcB3wRuqvS6ZQ2DSpo1GCQPuBB4Nu37g7zaNY0bl300WZgSZaX5uOT0tObn0sfeHS5vftjuRXhIc83jJyULUmZDm98RFLHsicCNDUfKjTefG5ClvOrufSzsmwxLUlWpYvPmFGCdma0HkLSYKBrpcyXfuQC4Lv58D/AdSTIrf0FGuRFizpQ0j6hy2wD813IVcBoYYyRLIWZIWlFyfquZ3VpyfhhQut58E3DqkDJe/46ZDUjaAxwEdI5E7VLKjRDz9+Ve0BlnZH/3dprZySnyJEsaWnqW74yIxt7a16k5VRwF2gSUeirNBjaHviOpBTiANwdxHxFuAE5lVG8UaDkwV9KRkiYAFxNFIy1lMDopwCeA/1dJ+x98MZxTKVXqBMdt+quB+4Fm4HYzWyXpy8AKM1tK1PT+kaR1RG/+iyu9rhuAUzbVnuSKl9TcNyTtSyWfe6hySN4xNYCOST2cduKaRNkzW8JbEk74l+RVk8UJ4WvNPG9o8/E/2Htb+FotPeH/6ISrtiSmb9kdXtXZ+uuw7IBztwVlaXT1hIdq2+9KDua9/6Bwa/eQj4c3EHh5OGXcIcbJM/W8zCELbgBOZbgBOLmlzhe6ZcENwKkMNwAnz6RsUtcQ+ESYk2vGtAbY193G47+ZmyjTQHg4rX92oJ5NGYF78flwxJmWE1Iypqy0HHh+VrIg5S3YPyvcRuhaG44sk0pKs2Pfu5L1t6Zwpj3Ph4eFK9GlEfAmkFM+3gl2co8bgJNr3ACcvCIafxTIDcApH+8DlEFo4DVtTVUZD9nS/jMpotRsgZEUlbs3zmisIwvpn3ZflfyK3QCcXOMG4OQZbwI5+cYNwMkt5qNATt7xGsDJM43eB8gSIGOOpF9JWi1plaTPxunTJT0oaW38N7hDtDOOyUGAjAHgGjM7BjgNuCretHQhsMzM5gLL4nMnT2T98TeyAZjZFjN7Kv7cBawm2qPxAmBR/LVFwMdGS0mnPhGNHx9gRH2AeD/2E4EngJmDO0Sb2RZJZS5udxqZev5xZyGzAUiaDPwT8Odm9pqUbR5f0gJgAUDz9OQ9a5wGpsENIJNLpKRWoh//P5rZT+LkrZJmxfJZQOIuT6URYpond1RDZ6eeGO99AEWv+r8HVpvZN0pEpRuVXgb8rPrqOXVNxvZ/PTeTsjSB3gtcCvxW0jNx2heAG4Elki4HXiHDno1HTO3klnOSQwvc/HJSJNaIrr+bk5je1xFuhl1yzUNB2QOX/n5Q1rxnX1D2/p+tSkz/1fbfC+bZfXuy7gBnf+6xoCyN9ftmBGW7rkr2W35t7pRgnouueyAou2Y4Zer4x52FLAEyfk144e5Z1VXHaTR8KYSTa+q5eZMFNwCnfOq8g5sFNwCnMtwAnLwyOBPcyPjWiE5FqGiZjoqukXHhpaRfStot6RdZyx7TGmBqE5zVXkiULe7YHcy3bk9gS0JrDuY5ddK6oOyhjUcGZQOdO1LKfDExfc2kmcE83V3hbQdP7ngpKEujOWXoZfnG5AG7iQe1B/Oc1p58X8Mydn2AwYWXN0paGJ9/PuF7NwOTGEHcaq8BnIoYo4mwTAsvzWwZ0DWSgr0P4FRG9h/3cJHi0xi1hZduAE5FjODtnhopXtJDwFsSRF8sQ63MuAE4lVG9OMFnh2SStkqaFb/9gwsvy8H7AE75xLtCZDkqZNQWXroBOGUzhh5hNwLnSFoLnBOfI+lkSbe9ro/0r8DdwFmSNkn68HAFj2kTqMeKrOlPXm25qy88TFdoT7bTQlt4NeiG/oPDihx4QFAUHliFDf3JqzDTdB+YGH7HbOgLr+psTmlbbO8Lr+wM3dvApPCdhe4rYpihWhv9cVAz20HCwkszWwFcUXL+n0ZatvcBnIpo9JlgNwCnfHwxnJN33B/AyTVuAE5+McakEzyayMbwBtqOmG1v+YvPJiuSEie4eX9gJCVlZ5bCpPCrqaWrvNHfgSmBMlPegs094Wul6ZhKyr+sZW/y9SzllgsdYT1evup/PhmawZ184Byb98Hk/+dQHv1JuJxa4jWAUxmNXQG4ATjlMx4cYtwAnPKxyp1dao0bgFMZjf37dwNwKsObQE5+MWC8N4EkzQHuIHJWKBJ58nxL0nXAnwLb469+wczuSyvrndO288j530mUXbUpvMncS391dGJ639TwAq+//sptQdk33ndOUFbo3BmU/fnq3ySm37n91GCel756TFB25Y33BGXNKWOrT3cfEZT9dn6ys9T+eYcH81z73duDsmG3/mvs33+mGmAwQsxTkqYAT0p6MJZ908y+NnrqOfXOuG8Cxb6Yg/6YXZIGI8Q4TsOPAo1oSnRIhBiAqyWtlHS7B8nLIXmIETbI0AgxwPeAtwPziGqIrwfyLZC0QtKKzh3JewI5jUk0EWaZjnql7AgxZrbVzApmVgR+AJySlLc0QsyMg9L8rZyGpJjxqFPKjhAzGB4p5kLg2eqr59Q7jV4DVBIh5hJJ84haeBvIsB1dEaPXBhJl/cWU2iFkpimrQXusNSxsDl9LreFHEipzIEX3tFWY/SlbO/aneCcPFMOFqiVZf2sKP6zUZ5VGnbfvs1BJhJjUMX8nD/haICfv1HHzJgtuAE75mLtEOnnHawAn1zT2798NwKkMFRu7DTSmBjBgsD0watBTCKtSbE0ewiumaL9jYHJQZu1tQZk6OoKy3YVJiempureEhx9D5Q3H/uKEoCx0bzYKekTLocvLWi94DeCUjajvSa4suAE4leEG4OQaNwAnt3gfwMk7Pgrk5BjzJtBIeLV/Kje/+qFE2Qud4ciXLYcmq1kMj2ay5NX3BGV75oWjx7TsD0dLWbIledXkK7vCznAtM8MrN3++5YSgrCnF2XZndzgiTfu8ZF26Dw7rceerYad+WB4WjYPNcT1GmFMZY+AQI2m6pAclrY3/vsnKJc2T9LikVbGb7iezlO0G4FTEGDnELASWmdlcYFl8PpRu4FNm9k5gPvC3kqYNV7AbgFMZZtmOyrgAWBR/XgR87M1q2BozWxt/3kwUSzglUmKEd4Kd8jGDQub2zQxJK0rObzWzWzPmnRlvz0McLDvcYQQknQJMAF4crmA3AKcysr/dO9MCZEh6iGj3waF8cSTqxL7qPwIuizdsSMUNwKmMKo0CmdnZIZmkrZJmxW//WUTNm6TvTQX+GfhLM/u3LNcdUwPoaO7lPVOTAy+v3jUzmK9/b/JDHkjZZugdU7YGZSu3Jb1oIpr39gVlR03Znpj+Wu/EYJ6efVODsrdN2RGUpdHaFA703b81eTXrwMTwmHHas/rnNEXGbnPcpcBlRBHiLwN+NvQLkiYA9wJ3mNndWQv2TrBTAQZWzHZUxo3AOZLWAufE50g6WdLgLsh/BLwf+LSkZ+Jj3nAFexPIKR9jJJ3g8i9jtoOEjarNbAVwRfz5H4B/GGnZbgBOZTT4TLAbgFMZbgBOfmn8xXDDBsqWNBF4BGgjMph7zOxaSUcCi4HpwFPApWYWHkIB2g6fY7M+HwisXEwJlN2bLLOUrRGLbeG2aTDwNqTuchAMbJ2iSFNfWJamYyop12vuCcjSgopPTAmU/WfhANcHtB5ip8+4KFxwCb989bt1GSg7yyhQL/BBM3sX0Vbo8yWdBtxEFCFmLrALuHz01HTqlrFZCjFqDGsAFrE3Pm2NDwM+CAwGuUpcn+GMd+KlEFmOOiVrfIDmeGfobcCDRGssdpu9vtXzJjxsUv4wMCtmOuqVTJ1gMysA8+LlpfcCSaEPE+s5SQuABQDNBw67OtVpNBp8d+gRzQSb2W7gYeA0YJqkQQOaDWwO5Hk9Qkzz5PBmVU6DMt77AJIOHnQskNQOnA2sBn4FfCL+WuL6DGecYwbFYrajTsnSBJoFLJLUTGQwS8zsF5KeAxZLuh54miiMUiozpnRxxRkPJ8p+ujHsH2v/lOynO9AeHts76dJVQdn668LBq1v29gdls7+WvLx81Y7w4rrC0rCP8dxPrQ3K0tjaPSUs/FqyD8jeQ8NRYOZdGY5uFQ6hHVPHb/csZIkQs5IoNOrQ9PUEAuM5ecGwQmNH/vSZYKd8xm459KjhBuBURh0PcWbBDcApGwPMawAnt5h5DeDkm0bvBA+7GrSqF5O2Ay/HpzOAzjG7eP1Tr8/jCDNLHFuV9EsivbPQaWbzq6dWdRhTA3jDhaUV9bg8tlb486gN7hTv5Bo3ACfX1NIAsm6Llxf8edSAmvUBHKce8CaQk2vcAJxcUxMDkDRf0guS1klKCnYwrpF0u6Rtkp4tSRs2CopTfcbcAGK/gluAc4FjgUskHTvWetSYHxJFMSklSxQUp8rUogY4BVhnZuvjfYQWE0UAyQ1m9giwc0jysFFQnOpTCwM4DNhYcu47SkS8IQoKkBoFxakOtTCAJD9GH4t1akItDGATMKfkPLijRM7YGkc/GQzzkxgFxakutTCA5cBcSUfGUT0uJooAkncGo6CA77IxZtRkJljSecDfAs3A7WZ2w5grUUMk3QWcSbSUeCtwLfBTYAlwOPAKcJGZDe0oO1XGl0I4ucZngp1c4wbg5Bo3ACfXuAE4ucYNwMk1bgBOrnEDcHLN/wexVXowEF89TAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for layer in vae.layers:\n",
    "    if hasattr(layer, 'kernel'):\n",
    "        fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(6, 4))#, sharey=True)\n",
    "        im1 = ax1.imshow(K.eval(layer.kernel).T)\n",
    "        ax1.set_title('{} kernel'.format(layer.name))\n",
    "        plt.colorbar(im1, ax=ax1)\n",
    "        if hasattr(layer, 'bias') and layer.bias is not None:\n",
    "            im2 = ax2.imshow(K.eval(K.expand_dims(layer.bias, -1)))\n",
    "            ax2.set_title('{} bias'.format(layer.name))\n",
    "            plt.colorbar(im2, ax=ax2)\n",
    "        else:\n",
    "            ax2.set_visible(False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot the embeddings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pickle\n",
    "\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy\n",
    "import scipy.sparse as sp\n",
    "import seaborn as sb\n",
    "\n",
    "from sklearn.manifold import MDS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Downscale the embeddings\n",
    "mds = MDS(n_jobs=-2, )\n",
    "mds.fit(q_pred[:, :dims[-1]].astype(np.float64))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load the ground truth labels\n",
    "\n",
    "def parse_index_file(filename):\n",
    "    index = []\n",
    "    for line in open(filename):\n",
    "        index.append(int(line.strip()))\n",
    "    return index\n",
    "\n",
    "with gae_directory():\n",
    "    ty = pickle.load(open(\"data/ind.cora.ty\", 'rb'), encoding='latin1')\n",
    "    ally = pickle.load(open(\"data/ind.cora.ally\", 'rb'), encoding='latin1')\n",
    "    test_idx_reorder = parse_index_file(\"data/ind.cora.test.index\")\n",
    "test_idx_range = np.sort(test_idx_reorder)\n",
    "\n",
    "labels = sp.vstack((ally, ty)).toarray()\n",
    "labels[test_idx_reorder, :] = labels[test_idx_range, :]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Turn labels into colors\n",
    "palette = sb.color_palette(n_colors=labels.shape[1])\n",
    "colors = np.array(palette)[np.argmax(labels, axis=1)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Plot the downscaled embeddings and the links\n",
    "fig, ax = plt.subplots(figsize=(15, 15))\n",
    "edges = np.array([[mds.embedding_[i], mds.embedding_[j]] for (i, j) in sparse_to_tuple(sp.triu(adj))[0]])\n",
    "edges = edges.transpose([2, 1, 0])\n",
    "ax.plot(edges[0], edges[1], color='lightgrey', zorder=1)\n",
    "ax.scatter(mds.embedding_[:, 0], mds.embedding_[:, 1], c=colors, zorder=2)"
   ]
  }
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