seminars/08_GRAPH/08_GRAPH.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0y5O4CNrlG0u"
      },
      "source": [
        "# Семинар 8: бучение представлений на графах"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Tpnjuk9illhp"
      },
      "source": [
        "В этом ноутбуке мы посмотрим на разные методы обучения представлений для вершин графа на примере графа цитирований научных статей. Кроме того, воспользуемся графовыми эмбеддингами для визуализации графа Московского метро."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9mSTeQj9lHuP",
        "outputId": "451c927f-6503-4345-a3b6-e6e4d1bc5055"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "  Building wheel for node2vec (setup.py) ... \u001b[?25l\u001b[?25hdone\n"
          ]
        }
      ],
      "source": [
        "!pip -qq install node2vec"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "id": "X3VgHeRvli_F"
      },
      "outputs": [],
      "source": [
        "from node2vec import Node2Vec\n",
        "import networkx as nx\n",
        "from sklearn.manifold import TSNE\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns\n",
        "\n",
        "plt.rcParams.update({'font.size': 14})\n",
        "sns.set_style('whitegrid')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mhp_cFU_lRt7"
      },
      "source": [
        "## 1. Пример с графом Московского метро\n",
        "\n",
        "Один из самых частых примеров графов &mdash; транспортные сети. Возьмем в качестве примера граф, с которым каждый день сталкивается большое число москвичей.\n",
        "\n",
        "![](https://i.pinimg.com/originals/65/e1/03/65e1030f788ca888e7078f44a4a17c5e.png)\n",
        "\n",
        "Для простоты будем работать только с центром города. Каждая станция будет играть роль вершины графа. Соединим ребрами последовательные станции на каждой ветки. Строить граф будем с помощью библиотеки `networkx`."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "id": "vgcZkTimlSJB"
      },
      "outputs": [],
      "source": [
        "red = ['Park Kultury Red', 'Kropotkinskaya', 'Biblioteka Lenina', 'Okhotny Ryad',\n",
        "       'Lubyanka', 'Chistye Prudy', 'Krasnye Vorota', 'Komsomolskaya Red']\n",
        "orange = ['Oktyabrskaya Orange', 'Tretyakovskaya Orange', 'Kitay Gorod Orange',\n",
        "          'Turgenevskaya', 'Sukharevskaya', 'Prospekt Mira Orange']\n",
        "grey = ['Serpukhovskaya', 'Polyanka', 'Borovitskaya', 'Chekhovskaya',\n",
        "        'Tsvetnoy Bulvar', 'Mendeleevskaya']\n",
        "green = ['Paveletskaya Green', 'Novokuznetskaya', 'Teatralnaya',\n",
        "         'Tverskaya', 'Mayakovskaya', 'Belorusskaya Green']\n",
        "purple = ['Taganskaya Purple', 'Kitay Gorod Purple', 'Kuznetskiy Most',\n",
        "          'Pushkinskaya', 'Barrikadnaya']\n",
        "blue = ['Kurskaya Blue', 'Ploschad Revolutsii', 'Arbatskaya Blue',\n",
        "        'Smolenskaya', 'Kievskaya Blue']\n",
        "circle = ['Park Kultury Circle', 'Oktyabrskaya Circle', 'Dobryninskaya', 'Paveletskaya Circle',\n",
        "          'Taganskaya Circle', 'Kurskaya Circle', 'Komsomolskaya Circle', 'Prospekt Mira Circle',\n",
        "          'Novoslobodskaya', 'Belorusskaya Circle', 'Krasnopresnenskaya', 'Kievskaya Circle']"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "id": "ETLNFUx1l0qf"
      },
      "outputs": [],
      "source": [
        "lines = [red, orange, grey, green, purple, blue, circle]\n",
        "graph = nx.Graph()\n",
        "\n",
        "for line in lines:\n",
        "    graph.add_node(line[0])\n",
        "    for i in range(len(line) - 1):\n",
        "        graph.add_node(line[i + 1])\n",
        "        graph.add_edge(line[i], line[i + 1])\n",
        "\n",
        "graph.add_edge(circle[0], circle[-1])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0t3Y0N5dl4Qr"
      },
      "source": [
        "Также добавим в граф пересадки между станциями разных веток."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "id": "GQ3oJRDAl1Kf"
      },
      "outputs": [],
      "source": [
        "graph.add_edge('Park Kultury Red', 'Park Kultury Circle')\n",
        "graph.add_edge('Oktyabrskaya Orange', 'Oktyabrskaya Circle')\n",
        "graph.add_edge('Serpukhovskaya', 'Dobryninskaya')\n",
        "graph.add_edge('Paveletskaya Green', 'Paveletskaya Circle')\n",
        "graph.add_edge('Taganskaya Purple', 'Taganskaya Circle')\n",
        "graph.add_edge('Kurskaya Blue', 'Kurskaya Circle')\n",
        "graph.add_edge('Komsomolskaya Red', 'Komsomolskaya Circle')\n",
        "graph.add_edge('Prospekt Mira Orange', 'Prospekt Mira Circle')\n",
        "graph.add_edge('Mendeleevskaya', 'Novoslobodskaya')\n",
        "graph.add_edge('Belorusskaya Green', 'Belorusskaya Circle')\n",
        "graph.add_edge('Barrikadnaya', 'Krasnopresnenskaya')\n",
        "graph.add_edge('Kievskaya Blue', 'Kievskaya Circle')\n",
        "\n",
        "graph.add_edge('Chistye Prudy', 'Turgenevskaya')\n",
        "graph.add_edge('Lubyanka', 'Kuznetskiy Most')\n",
        "graph.add_edge('Okhotny Ryad', 'Teatralnaya')\n",
        "graph.add_edge('Ploschad Revolutsii', 'Teatralnaya')\n",
        "graph.add_edge('Chekhovskaya', 'Pushkinskaya')\n",
        "graph.add_edge('Chekhovskaya', 'Tverskaya')\n",
        "graph.add_edge('Pushkinskaya', 'Tverskaya')\n",
        "graph.add_edge('Kitay Gorod Orange', 'Kitay Gorod Purple')\n",
        "graph.add_edge('Tretyakovskaya Orange', 'Novokuznetskaya')\n",
        "graph.add_edge('Biblioteka Lenina', 'Borovitskaya')\n",
        "graph.add_edge('Biblioteka Lenina', 'Arbatskaya Blue')\n",
        "graph.add_edge('Borovitskaya', 'Arbatskaya Blue')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OAmCuiE_m4eq"
      },
      "source": [
        "Обучим **Node2Vec** на получившемся графе и визуализируем представления с помощью **TSNE**."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 67,
          "referenced_widgets": [
            "e6d163af1fb3473a9f2f43df48fe38b8",
            "f08722a81fc848d5a3b5a2d1b6c980af",
            "47bec3163bfd4a92b459cad09bec2821",
            "90464d0d25c64304bfa654c53ee01cbe",
            "fa7e890dd6604684983be6bd3d33b8d6",
            "2644943fed5e40979c485f0e22b19539",
            "2700987b40c242bf8bd3dd6397c334c8",
            "c538161459a84b92ae9b46f9c5d80370",
            "d4cdb3ab6a6d47c19f4c85932f0817ff",
            "52bd5d6e78724ac1b1e44f52fd630585",
            "47666499da8440138a09915be6a0ad8e"
          ]
        },
        "id": "ZXDg163Kl_Cr",
        "outputId": "7d11bdef-0ad7-4393-aaae-1f8001144480"
      },
      "outputs": [
        {
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "e6d163af1fb3473a9f2f43df48fe38b8",
              "version_major": 2,
              "version_minor": 0
            },
            "text/plain": [
              "Computing transition probabilities:   0%|          | 0/48 [00:00<?, ?it/s]"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "Generating walks (CPU: 1): 100%|██████████| 100/100 [00:04<00:00, 22.58it/s]\n"
          ]
        }
      ],
      "source": [
        "node2vec = Node2Vec(\n",
        "    graph, dimensions=8, num_walks=100,\n",
        "    walk_length=10, seed=103, p=2, q=1\n",
        ").fit()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "id": "rrQQolgVmChz"
      },
      "outputs": [],
      "source": [
        "embeddings = np.array([node2vec.wv[station] for station in sorted(graph.nodes)])\n",
        "embeddings = TSNE(\n",
        "    n_components=2, random_state=106,\n",
        "    learning_rate='auto', init='random'\n",
        ").fit_transform(embeddings)\n",
        "mapping = dict(zip(sorted(graph.nodes), embeddings))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IiExhAJOJxOj"
      },
      "source": [
        "Получаем следующую \"карту\" метро."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 575
        },
        "id": "7RXsmdJJmH0a",
        "outputId": "b9473195-8b1e-406f-9494-da39b5afdbe8"
      },
      "outputs": [
        {
          "data": {
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",
            "text/plain": [
              "<Figure size 720x720 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "colors = ['red', 'orange', 'grey', 'green', 'purple', 'blue', 'brown']\n",
        "plt.figure(figsize=(10, 10))\n",
        "np.random.seed(100)\n",
        "\n",
        "for i, line in enumerate(lines):\n",
        "    vectors = np.zeros((len(line), 2))\n",
        "    for j, station in enumerate(line):\n",
        "        vectors[j] = mapping[station]\n",
        "    if colors[i] == 'brown':\n",
        "        vectors = np.concatenate((vectors, vectors[0].reshape(1, 2)))\n",
        "    plt.plot(vectors[:, 0], vectors[:, 1], color=colors[i], marker='o')\n",
        "\n",
        "plt.axis('off')\n",
        "plt.grid(False)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "r0UHRhqsmmR9"
      },
      "source": [
        "Зафиксируем одну станцию, например, Тверскую, и посмотрим на вероятности перехода в другие вершины, которые кодируются обученными эмбеддингами."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "2Ew8Sk6SmKni",
        "outputId": "cc5952cc-f778-44e4-d0eb-75b435232d3e"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "[('Mayakovskaya', 0.12168536),\n",
              " ('Belorusskaya Green', 0.090852804),\n",
              " ('Tverskaya', 0.076060995),\n",
              " ('Chekhovskaya', 0.059131026),\n",
              " ('Pushkinskaya', 0.055635113),\n",
              " ('Tsvetnoy Bulvar', 0.041126803),\n",
              " ('Barrikadnaya', 0.037645508),\n",
              " ('Belorusskaya Circle', 0.036519542),\n",
              " ('Teatralnaya', 0.026046349),\n",
              " ('Krasnopresnenskaya', 0.024490623)]"
            ]
          },
          "execution_count": 9,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "base = 'Tverskaya'\n",
        "dot_products = dict()\n",
        "for line in lines:\n",
        "    for station in line:\n",
        "        dot_products[station] = node2vec.wv[base] @ node2vec.wv[station]\n",
        "\n",
        "norm = np.exp(np.array(list(dot_products.values()))).sum()\n",
        "probabilities = dict(\n",
        "    zip(sorted(dot_products.keys()),\n",
        "    [np.exp(dot_products[station]) / norm \\\n",
        "    for station in sorted(dot_products.keys())])\n",
        ")\n",
        "\n",
        "probabilities = sorted(probabilities.items(), key=lambda item: -item[1])\n",
        "probabilities[:10]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "woD97M2LnMQC"
      },
      "source": [
        "## 2. Классификация научных публикаций (CORA)\n",
        "\n",
        "В качестве реальных данных возьмем граф цитирований научных статей. Он содержит 2708 уникальных статей, каждая относится к одной из семи тем. Всего в графе 5429 цитаты (ребра между статьями). Кроме того, каждая публикация описывается вектором из бинарных признаков &mdash; каждый обозначает наличие или отсутствие одного из 1433 слов словаря. [Ссылка на данные](https://relational.fit.cvut.cz/dataset/CORA)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "id": "42aXI1wsmiNa"
      },
      "outputs": [],
      "source": [
        "%%bash\n",
        "wget -q https://web.archive.org/web/20151007064508/http://www.cs.umd.edu/~sen/lbc-proj/data/cora.tgz -O cora.tgz\n",
        "tar -xf cora.tgz"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "id": "NoKU6YJOnQ2M"
      },
      "outputs": [],
      "source": [
        "import pandas as pd\n",
        "from sklearn.preprocessing import LabelEncoder\n",
        "from sklearn.model_selection import train_test_split"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "id": "wT4GuuZlnU4Q"
      },
      "outputs": [],
      "source": [
        "content = pd.read_csv('cora/cora.content', sep='\\t', header=None)\n",
        "content = content.rename(columns={0: 'Id', 1434: 'target'}, errors=\"raise\")\n",
        "content = content.set_index('Id')\n",
        "cites = pd.read_csv('cora/cora.cites', sep='\\t', header=None)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 519
        },
        "id": "dyJuNQipnYCm",
        "outputId": "8e98bb86-90c8-4e9d-b3cb-baf96c0327c6"
      },
      "outputs": [
        {
          "data": {
            "text/html": [
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              "      <th>1395</th>\n",
              "      <th>1396</th>\n",
              "      <th>1397</th>\n",
              "      <th>1398</th>\n",
              "      <th>1399</th>\n",
              "      <th>1400</th>\n",
              "      <th>1401</th>\n",
              "      <th>1402</th>\n",
              "      <th>1403</th>\n",
              "      <th>1404</th>\n",
              "      <th>1405</th>\n",
              "      <th>1406</th>\n",
              "      <th>1407</th>\n",
              "      <th>1408</th>\n",
              "      <th>1409</th>\n",
              "      <th>1410</th>\n",
              "      <th>1411</th>\n",
              "      <th>1412</th>\n",
              "      <th>1413</th>\n",
              "      <th>1414</th>\n",
              "      <th>1415</th>\n",
              "      <th>1416</th>\n",
              "      <th>1417</th>\n",
              "      <th>1418</th>\n",
              "      <th>1419</th>\n",
              "      <th>1420</th>\n",
              "      <th>1421</th>\n",
              "      <th>1422</th>\n",
              "      <th>1423</th>\n",
              "      <th>1424</th>\n",
              "      <th>1425</th>\n",
              "      <th>1426</th>\n",
              "      <th>1427</th>\n",
              "      <th>1428</th>\n",
              "      <th>1429</th>\n",
              "      <th>1430</th>\n",
              "      <th>1431</th>\n",
              "      <th>1432</th>\n",
              "      <th>1433</th>\n",
              "      <th>target</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Id</th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>31336</th>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>0</td>\n",
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              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>1</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>Neural_Networks</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1061127</th>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>0</td>\n",
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              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>...</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>Rule_Learning</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1106406</th>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>...</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>Reinforcement_Learning</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13195</th>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>0</td>\n",
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              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>...</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>Reinforcement_Learning</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>37879</th>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>Probabilistic_Methods</td>\n",
              "    </tr>\n",
              "    <tr>\n",
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              "      <td>...</td>\n",
              "      <td>...</td>\n",
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              "      <td>...</td>\n",
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              "  </tbody>\n",
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              "<p>2708 rows × 1434 columns</p>\n",
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            ],
            "text/plain": [
              "         1  2  3  4  5  6  ...  1429  1430  1431  1432  1433                  target\n",
              "Id                         ...                                                      \n",
              "31336    0  0  0  0  0  0  ...     0     0     0     0     0         Neural_Networks\n",
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              "1106406  0  0  0  0  0  0  ...     0     0     0     0     0  Reinforcement_Learning\n",
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              "...     .. .. .. .. .. ..  ...   ...   ...   ...   ...   ...                     ...\n",
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              "\n",
              "[2708 rows x 1434 columns]"
            ]
          },
          "execution_count": 13,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "content"
      ]
    },
    {
      "cell_type": "code",
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        },
        "id": "O8W8wY5OnZUs",
        "outputId": "2a628bc0-7188-45fc-c8cf-43db72fa8fbc"
      },
      "outputs": [
        {
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          "execution_count": 14,
          "metadata": {},
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      ],
      "source": [
        "cites"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "b4OXbYWGLYN0"
      },
      "source": [
        "Разобьем данные на трейн и тест."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {
        "id": "LPzhqtjwp4-8"
      },
      "outputs": [],
      "source": [
        "X = content.drop(columns=['target']).to_numpy()\n",
        "y = content['target'].to_numpy()\n",
        "index = content.index.to_numpy()\n",
        "y = LabelEncoder().fit_transform(y)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 16,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "w4lSbT7np_T0",
        "outputId": "35bc7bd4-e4cf-41cb-9cf6-1a65819cf233"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "((2031, 1433), (677, 1433))"
            ]
          },
          "execution_count": 16,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "X_train, X_test, y_train, y_test, train_index, test_index = \\\n",
        "    train_test_split(X, y, index, test_size=0.25, random_state=42)\n",
        "X_train.shape, X_test.shape"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xiWCEzA2Lasg"
      },
      "source": [
        "В качестве бейзлайна обучим логистическую регрессию на бинарных признаках публикаций."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "metadata": {
        "id": "XkmDv8aLqA3U"
      },
      "outputs": [],
      "source": [
        "from sklearn.linear_model import LogisticRegressionCV\n",
        "from sklearn.metrics import accuracy_score"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Gvn0OmOWqDQg",
        "outputId": "9314aba7-6158-47bf-f9f0-a0b1fe4424bb"
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "[Parallel(n_jobs=-1)]: Using backend LokyBackend with 2 concurrent workers.\n",
            "[Parallel(n_jobs=-1)]: Done   3 out of   3 | elapsed:   10.8s finished\n"
          ]
        }
      ],
      "source": [
        "log_regr = LogisticRegressionCV(\n",
        "    Cs=np.logspace(-2, 2, 8), cv=3, n_jobs=-1, verbose=1\n",
        ").fit(X_train, y_train)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "TCe4NPuSqF2p",
        "outputId": "476d470e-12f5-4739-9638-b70c8ed000f1"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Init features + Logistic Regression\n",
            "Train accuracy: 0.9798\n",
            "Test accuracy: 0.7563\n"
          ]
        }
      ],
      "source": [
        "print('Init features + Logistic Regression')\n",
        "print(f'Train accuracy: {accuracy_score(y_train, log_regr.predict(X_train)):.4f}')\n",
        "print(f'Test accuracy: {accuracy_score(y_test, log_regr.predict(X_test)):.4f}')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7CbL4IvaqWLa"
      },
      "source": [
        "## 3. Node2Vec\n",
        "\n",
        "Попробуем комбинацию **Node2Vec** + логистическая регрессия (считаем граф цитирований неориентированным). Во всех дальнейших экспериментах зафиксируем размерность эмбеддингов равной $d=256$.  "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 20,
      "metadata": {
        "id": "MqG7Gg3UqNoo"
      },
      "outputs": [],
      "source": [
        "graph = nx.Graph()\n",
        "for node in index:\n",
        "    graph.add_node(node)\n",
        "\n",
        "for i, row in cites.iterrows():\n",
        "    graph.add_edge(row[0], row[1])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 21,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 67,
          "referenced_widgets": [
            "efe21fc22e6047a5878593e124ea5748",
            "1342213cdfc4444b9a4e49bc6125f194",
            "eeda6ec1ebb442e5aa0f2524f53c0bee",
            "e9bb04b1467e45be8923d89ade476736",
            "163f2a49383446ad988ec2a2e4f1580e",
            "2b1b1f5649cf4a29b736701e4f677ae3",
            "c6b150482ce840e3be93f533dc914a04",
            "4d53a78800a24e80b5b91a313a3619ca",
            "1363149f40f145f4b68f5b1b034fb4a1",
            "ce18b7f70fa74dab9bccebf92b0c3c8d",
            "0634ef69ebbc4ed19f725d7ba8a2ecd4"
          ]
        },
        "id": "Oav-kYEhqfS-",
        "outputId": "7bebcb24-317c-44fa-ec27-1a24ffab4870"
      },
      "outputs": [
        {
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "efe21fc22e6047a5878593e124ea5748",
              "version_major": 2,
              "version_minor": 0
            },
            "text/plain": [
              "Computing transition probabilities:   0%|          | 0/2708 [00:00<?, ?it/s]"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "Generating walks (CPU: 1): 100%|██████████| 10/10 [01:33<00:00,  9.40s/it]\n"
          ]
        }
      ],
      "source": [
        "node2vec = Node2Vec(graph, dimensions=256).fit()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 22,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6MjKTRXhqhWB",
        "outputId": "a5e6a2fc-12f3-4bdc-b101-90d6c74d59db"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "((2031, 256), (677, 256))"
            ]
          },
          "execution_count": 22,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "train_embeds = np.array([node2vec.wv[str(node)] for node in train_index])\n",
        "test_embeds = np.array([node2vec.wv[str(node)] for node in test_index])\n",
        "train_embeds.shape, test_embeds.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 23,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "KaFM9rwGq9B1",
        "outputId": "4a76a680-35c7-423c-f677-91df9b960198"
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "[Parallel(n_jobs=-1)]: Using backend LokyBackend with 2 concurrent workers.\n",
            "[Parallel(n_jobs=-1)]: Done   3 out of   3 | elapsed:   10.2s finished\n"
          ]
        }
      ],
      "source": [
        "log_regr = LogisticRegressionCV(\n",
        "    Cs=np.logspace(-2, 2, 8), cv=3, n_jobs=-1, verbose=1, max_iter=10000\n",
        ").fit(train_embeds, y_train)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 24,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "FNcBRhOoq_U-",
        "outputId": "05f969fe-2e72-4e48-acff-99ec9f523d68"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Node2Vec + Logistic Regression\n",
            "Train accuracy: 0.8818\n",
            "Test accuracy: 0.8257\n"
          ]
        }
      ],
      "source": [
        "print('Node2Vec + Logistic Regression')\n",
        "print(f'Train accuracy: {accuracy_score(y_train, log_regr.predict(train_embeds)):.4f}')\n",
        "print(f'Test accuracy: {accuracy_score(y_test, log_regr.predict(test_embeds)):.4f}')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3uQYDIFBL9Ll"
      },
      "source": [
        "Итак, мы уже смогли превзойти бейзлайн. Попробуем добавить исходные бинарные признаки к эмбеддингам вершин."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 25,
      "metadata": {
        "id": "UAb1nU0zrYzK"
      },
      "outputs": [],
      "source": [
        "n2v_train = np.concatenate([X_train, train_embeds], axis=1)\n",
        "n2v_test = np.concatenate([X_test, test_embeds], axis=1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 26,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "rRV2lkm4rknJ",
        "outputId": "b62c000a-c8cc-4e82-ea11-4fd99241e5ee"
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "[Parallel(n_jobs=-1)]: Using backend LokyBackend with 2 concurrent workers.\n",
            "[Parallel(n_jobs=-1)]: Done   3 out of   3 | elapsed:   24.4s finished\n"
          ]
        }
      ],
      "source": [
        "log_regr = LogisticRegressionCV(\n",
        "    Cs=np.logspace(-2, 2, 8), cv=3, n_jobs=-1, verbose=1, max_iter=10000\n",
        ").fit(n2v_train, y_train)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 27,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "60E3hPJarmqI",
        "outputId": "7796a332-fdbd-4169-8d7e-0e62624df4f4"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Node2Vec + Init features + Logistic Regression\n",
            "Train accuracy: 0.9710\n",
            "Test accuracy: 0.8789\n"
          ]
        }
      ],
      "source": [
        "print('Node2Vec + Init features + Logistic Regression')\n",
        "print(f'Train accuracy: {accuracy_score(y_train, log_regr.predict(n2v_train)):.4f}')\n",
        "print(f'Test accuracy: {accuracy_score(y_test, log_regr.predict(n2v_test)):.4f}')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sKRomP6vMat0"
      },
      "source": [
        "Получили еще большее качество."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "g5dL6Er6r35y"
      },
      "source": [
        "## 4. Neighborhood autoencoder\n",
        "\n",
        "Теперь попробуем обучить **Neighborhood autoencoder**. Возьмем следующую функцию похожести:\n",
        "\n",
        "$$\n",
        "s_{\\mathcal{G}}(v_i, v_j) = \\exp\\left(-\\frac{d_{\\mathcal{G}}(v_i, v_j)}{\\tau}\\right),\n",
        "$$\n",
        "\n",
        "где $d_{\\mathcal{G}}(v_i, v_j)$ &mdash; расстояние между вершинами в графе, а $\\tau$ &mdash; фиксированный гиперпараметр. Для препроцессинга посчитаем попарные расстояния между вершинами графа."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 28,
      "metadata": {
        "id": "3PgrAPLrrxOi"
      },
      "outputs": [],
      "source": [
        "import torch\n",
        "from torch.utils.data import TensorDataset, DataLoader\n",
        "from tqdm.notebook import tqdm\n",
        "from IPython.display import clear_output"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 29,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 49,
          "referenced_widgets": [
            "92fa4005bbc64066903ec3d0a700f15b",
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            "dd53ec529adc400ca568bafc25e424cf"
          ]
        },
        "id": "coCTrKewsA5L",
        "outputId": "d96aff36-548d-406f-faa8-e7aab1f16506"
      },
      "outputs": [
        {
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "92fa4005bbc64066903ec3d0a700f15b",
              "version_major": 2,
              "version_minor": 0
            },
            "text/plain": [
              "  0%|          | 0/2708 [00:00<?, ?it/s]"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "distances = nx.all_pairs_shortest_path_length(graph)\n",
        "id_to_index = {id: i for i, id in enumerate(index)}\n",
        "\n",
        "sim_matrix = torch.zeros((X.shape[0], X.shape[0]))\n",
        "tau = 5.\n",
        "for node_id, dists in tqdm(distances, total=X.shape[0]):\n",
        "    i = id_to_index[node_id]\n",
        "    for neighbor_id, dist in dists.items():\n",
        "        j = id_to_index[neighbor_id]\n",
        "        sim_matrix[i, j] = np.exp(-dist / tau)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 30,
      "metadata": {
        "id": "Bcu8kbnlsKIf"
      },
      "outputs": [],
      "source": [
        "dataset = TensorDataset(sim_matrix)\n",
        "dataloader = DataLoader(dataset, batch_size=64, shuffle=True)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 31,
      "metadata": {
        "id": "CaWQ3C4UsQAB"
      },
      "outputs": [],
      "source": [
        "from torch import nn\n",
        "\n",
        "class Autoencoder(nn.Module):\n",
        "    def __init__(self, dims):\n",
        "        super().__init__()\n",
        "        assert len(dims) >= 2\n",
        "        self.encoder = []\n",
        "        self.decoder = []\n",
        "\n",
        "        for i in range(len(dims) - 1):\n",
        "            self.encoder.append(nn.Linear(dims[i], dims[i + 1]))\n",
        "\n",
        "            if i != len(dims) - 2:\n",
        "                self.encoder.append(nn.LeakyReLU(0.2))\n",
        "\n",
        "        for i in range(len(dims) - 1, 0, -1):\n",
        "            self.decoder.append(nn.Linear(dims[i], dims[i - 1]))\n",
        "\n",
        "            if i != 1:\n",
        "                self.decoder.append(nn.LeakyReLU(0.2))\n",
        "        self.decoder.append(nn.Sigmoid())\n",
        "\n",
        "        self.encoder = nn.Sequential(*self.encoder)\n",
        "        self.decoder = nn.Sequential(*self.decoder)\n",
        "  \n",
        "    def encode(self, x):\n",
        "        return self.encoder(x)\n",
        "    \n",
        "    def decode(self, x):\n",
        "        return self.decoder(x)\n",
        "\n",
        "    def forward(self, x):\n",
        "        return self.decode(self.encode(x))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 32,
      "metadata": {
        "id": "-1Da1T_UsSoE"
      },
      "outputs": [],
      "source": [
        "autoencoder = Autoencoder([sim_matrix.shape[0], 512, 256])\n",
        "optimizer = torch.optim.Adam(autoencoder.parameters(), lr=1e-3)\n",
        "criterion = nn.MSELoss()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MCCOlOjVNayD"
      },
      "source": [
        "Обучим автоэнкодер."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 33,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 342,
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        "id": "FCPwz-visohv",
        "outputId": "69ffdd4a-bab4-4be8-cf78-2334ac86f798"
      },
      "outputs": [
        {
          "data": {
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",
            "text/plain": [
              "<Figure size 504x360 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "num_epochs = 10\n",
        "losses = []\n",
        "plt.rcParams.update({'font.size': 14})\n",
        "\n",
        "for epoch in range(1, num_epochs + 1):\n",
        "    autoencoder.train()\n",
        "    running_loss = 0.0\n",
        "    for sim_vecs, in tqdm(dataloader):\n",
        "        optimizer.zero_grad()\n",
        "        outputs = autoencoder(sim_vecs)\n",
        "        loss = criterion(outputs, sim_vecs)\n",
        "        loss.backward()\n",
        "        optimizer.step()\n",
        "        running_loss += loss.item() * sim_vecs.shape[0]\n",
        "        \n",
        "    losses += [running_loss / len(dataset)]\n",
        "    clear_output()\n",
        "    plt.figure(figsize=(7, 5))\n",
        "    plt.plot(range(1, epoch + 1), losses)\n",
        "    plt.xlabel('epoch')\n",
        "    plt.ylabel('MSE loss')\n",
        "    plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 34,
      "metadata": {
        "id": "HNl0XJ5xs0Ma"
      },
      "outputs": [],
      "source": [
        "autoencoder.eval()\n",
        "with torch.no_grad():\n",
        "    ae_embeds = autoencoder.encode(sim_matrix)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 35,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Fhb2_NEStRLB",
        "outputId": "be0c8223-8e3b-4e13-e722-203ddfb99831"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "((2031, 256), (677, 256))"
            ]
          },
          "execution_count": 35,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "train_ae_embeds = np.stack([ae_embeds[id_to_index[node]].numpy() for node in train_index])\n",
        "test_ae_embeds = np.stack([ae_embeds[id_to_index[node]].numpy() for node in test_index])\n",
        "train_ae_embeds.shape, test_ae_embeds.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 36,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "kf_MscfFtTfk",
        "outputId": "fce53751-39d7-4acd-e465-a04721267b42"
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "[Parallel(n_jobs=-1)]: Using backend LokyBackend with 2 concurrent workers.\n",
            "[Parallel(n_jobs=-1)]: Done   3 out of   3 | elapsed:   22.6s finished\n"
          ]
        }
      ],
      "source": [
        "log_regr = LogisticRegressionCV(\n",
        "    Cs=np.logspace(-2, 2, 8), cv=3, n_jobs=-1, verbose=1, max_iter=10000\n",
        ").fit(train_ae_embeds, y_train)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 37,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3iWmfTIbtVUv",
        "outputId": "ba7ccaab-c42c-4805-b74b-c862a17bec1a"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Neighborhood Autoencoder + Logistic Regression\n",
            "Train accuracy: 0.8552\n",
            "Test accuracy: 0.8124\n"
          ]
        }
      ],
      "source": [
        "print('Neighborhood Autoencoder + Logistic Regression')\n",
        "print(f'Train accuracy: {accuracy_score(y_train, log_regr.predict(train_ae_embeds)):.4f}')\n",
        "print(f'Test accuracy: {accuracy_score(y_test, log_regr.predict(test_ae_embeds)):.4f}')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ByGH-QVBNeKq"
      },
      "source": [
        "Получили качество чуть хуже, чем у Node2Vec, но все еще выше бейзлайна. Снова попробуем комбинацию с метаданными публикаций."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 38,
      "metadata": {
        "id": "LF8da10qtWIS"
      },
      "outputs": [],
      "source": [
        "ae_train = np.concatenate([X_train, train_ae_embeds], axis=1)\n",
        "ae_test = np.concatenate([X_test, test_ae_embeds], axis=1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 39,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "sBRndi3ztbgK",
        "outputId": "75b0a7b1-a871-4e9b-eaf6-75d89393e4cb"
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "[Parallel(n_jobs=-1)]: Using backend LokyBackend with 2 concurrent workers.\n",
            "[Parallel(n_jobs=-1)]: Done   3 out of   3 | elapsed:   44.8s finished\n"
          ]
        }
      ],
      "source": [
        "log_regr = LogisticRegressionCV(\n",
        "    Cs=np.logspace(-2, 2, 8), cv=3, n_jobs=-1, verbose=1, max_iter=10000\n",
        ").fit(ae_train, y_train)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 40,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ZN0iGRO1tdWC",
        "outputId": "42386d99-47ad-41da-d8fd-03d9febd7cf9"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Neighborhood Autoencoder + Init features + Logistic Regression\n",
            "Train accuracy: 0.9975\n",
            "Test accuracy: 0.8346\n"
          ]
        }
      ],
      "source": [
        "print('Neighborhood Autoencoder + Init features + Logistic Regression')\n",
        "print(f'Train accuracy: {accuracy_score(y_train, log_regr.predict(ae_train)):.4f}')\n",
        "print(f'Test accuracy: {accuracy_score(y_test, log_regr.predict(ae_test)):.4f}')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZxTS46zJNn3f"
      },
      "source": [
        "Качество вышло хуже, чем у аналогичной комбинации Node2Vec, но небольшой прирост есть."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WDqecB8ZwtF4"
      },
      "source": [
        "## 5. Neighborhood aggregation\n",
        "\n",
        "Ну, и на десерт &mdash; метод **Neighborhood aggregation**. Для него нам понадобится матрица смежности, которая будет определять связи между нейронами в полносвязной нейронной сети. Пусть метод и умеет генерировать эмбеддинги для новых вершин (а потому его можно обучить только на тренировочной выборке), мы обучим его на всех доступных данных для честного сравнения с предыдущими методами."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 41,
      "metadata": {
        "id": "nnlROh_zukJh"
      },
      "outputs": [],
      "source": [
        "adj_matrix = nx.convert_matrix.to_numpy_matrix(graph)\n",
        "adj_matrix /= adj_matrix.sum(axis=1)\n",
        "adj_matrix = torch.tensor(adj_matrix, dtype=torch.float)\n",
        "features = torch.tensor(X, dtype=torch.float)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 42,
      "metadata": {
        "id": "nqzwuD00zNoi"
      },
      "outputs": [],
      "source": [
        "class NeighborhoodAggregation(nn.Module):\n",
        "    def __init__(self, adj_matrix, input_dim, embed_dim=256, num_layers=3):\n",
        "        super().__init__()\n",
        "        self.adj_matrix = nn.Parameter(adj_matrix, requires_grad=False)\n",
        "        self.embed_layer = nn.Linear(input_dim, embed_dim)\n",
        "        self.layers = nn.ModuleList([nn.Linear(2 * embed_dim, embed_dim) \\\n",
        "                                     for _ in range(num_layers)])\n",
        "        self.act = nn.Tanh()\n",
        "    \n",
        "    def forward(self, features):\n",
        "        embeds = self.act(self.embed_layer(features))\n",
        "\n",
        "        for layer in self.layers:\n",
        "            neighborhood_embeds = self.adj_matrix @ embeds\n",
        "            embeds = torch.cat([embeds, neighborhood_embeds], dim=1)\n",
        "            embeds = self.act(layer(embeds))\n",
        "\n",
        "        return embeds\n",
        "\n",
        "class SimilarityLoss(nn.Module):\n",
        "    def __init__(self):\n",
        "        super().__init__()\n",
        "        self.mse = nn.MSELoss()\n",
        "\n",
        "    def forward(self, embeds, sim_matrix):\n",
        "        outputs = torch.sigmoid(embeds @ embeds.T)\n",
        "        return self.mse(outputs, sim_matrix)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 59,
      "metadata": {
        "id": "p8GZxau71X5B"
      },
      "outputs": [],
      "source": [
        "model = NeighborhoodAggregation(adj_matrix, features.shape[1])\n",
        "optimizer = torch.optim.Adam(model.parameters(), lr=1e-4)\n",
        "criterion = SimilarityLoss()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "smnC1nZsOMJp"
      },
      "source": [
        "Обучим метод (по сути полным градиентным спуском)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 60,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 342
        },
        "id": "0R9AkRUX3dZo",
        "outputId": "b67f79dc-88a6-4b3d-ebd5-ef42eab4b049"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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NysvL4ePjg+joaKxevRrBwcHw8vLC1q1bkZWVZQj2zjQ0NCAnJ8ek+jtSX1/f5hhOkkZkldSJPnZP117bUAu2T8fYNh0T0zZFJSXIyem915Bb4ntjUmjqdDoAMARkSUkJ9uzZg6CgIMTExHRfdSZYtWoV/v3vf2PChAmQyWQICwvDzJkzkZ2dfc3XqlQqhIaGinr/nJycNscIy5di95nTGBocAoWs714K217bUAu2T8fYNh27vrY5AwDw9PRCaGiw+YuyEeb63nQWvCaF5sKFC3HzzTfjT3/6E2pqanDXXXehrq4OtbW1WL58OWbPnn3NY7i7u0Mmk0GtVhttLy0t7fC8qJeXF0pLS422qdVqyOVyuLu7AwAGDhyITz/9FLW1taiuroaPjw8ee+wxBAQEmPLRuoWfuz10AlB4uR4BHg5Wq4OIqDWOzopnUjfo6NGjGDt2LABgx44dcHJyQlpaGl588UV89NFHJr2RUqlEeHh4m6HYtLQ0REdHt/uaqKiodvePiIiAQqEw2u7g4AAfHx9cvnwZ+/fvx5QpU0yqqzv4utkDAC7yvCYR2RBOBBLPpNCsra2Fi4sLAGD//v2YOnUqFAoFxo4di/z8fJPfbP78+di8eTM2btyI3NxcLFu2DMXFxUhISAAALFmyBEuWLDHsn5CQgKKiIixfvhy5ubnYuHEjNm/ejAcffNCwz759+/DTTz8hPz8fBw4cwP33348hQ4YgPj7e5LrMza85NMsZmkRkXa2DkpkpnknDswMGDMDhw4cxadIk7N+/H2+++SYA4PLly7CzszP5zeLi4lBeXo7Vq1ejuLgYwcHBSE5Ohp+fHwDg0qVLRvsHBAQgOTkZK1euREpKCnx8fLB06VJMnz7dsE9VVRVee+01FBYWws3NDdOmTcPjjz/epidqSX7u9pBKgHNltVargYgIMA5KLm4gnkmhOX/+fCxZsgQODg7w9fXFqFGjAAC//vorgoO7dlI5MTERiYmJ7T63bt26NttGjx6NzZs3d3i8uLg4xMXFdamG7qaSy+DrZo88NdflJSLrah2TvDWYeCaFZkJCAsLDw1FYWIibbrrJMIt24MCBePTRR7u1wJ5qsJcj8koZmkRkXUbDs5wKJJpJoQnoVwWKjIw02nbLLbeYu55eY5CnI1KzLkIQBEgkEmuXQ0R9VOuY5OiseCaH5p49e/DBBx/g9OnTkEgkGDp0KBYsWICJEyd2Z3091mAvR1TVa1Ba0wgvJ9W1X0BE1A1aByVnz4pn0uzZjRs34u9//zsGDhyI//u//8PixYvh7++Pv/3tb9i0aVN319gjBfdzBgCcLKyyciVE1Je1HpLlOU3xTOppfvDBB3jqqadw3333GbbdfffdCA8PxwcffIC5c+d2W4E9VUh/fWgeL6zCTUO9rrE3EVH3MO5pWq+O3sKknmZBQYHhdmCtTZgwARcvXjR7Ub2Bt7MKXk5KHC+stHYpREQAeMmJOZgUmr6+vjhw4ECb7fv37zdcY0ltDevvgpxLHJ4lItvAc5rimTQ8++CDD2LZsmU4duyYYcm7w4cP4+uvv0ZSUlK3FtiTRfq74oO9Z1DfpIWdQmbtcoioD2qdk1qGpmgmX6fp6emJNWvWYMeOHQCAIUOG4I033sCtt97arQX2ZNEBbtDoBPx+8TJGDfKwdjlE1Ae1ngik0TI0xTL5kpOpU6di6tSp3VlLrxMTqL8Ty+Fz5QxNIrKK1p3LRq3OeoX0En33Zo8W4OWkQpC3Iw7kll57ZyKibtC6b9nEnqZoHfY0o6OjTV7J5vDhw2YrqLeZGOyD9QfP8bwmEVlF68k/TRr2NMXqMDSfeeYZS9bRa90S4o01B85i3yk1pob1s3Y5RNTHGPc0GZpidRiac+bMsWQdvda4IE94OiqRmnmRoUlEFtf6nGYTlwQSjec0u5lCJsWsEb7YcawIRZX11i6HiPqa1qHJ4VnRGJoWMD92EDQ6HZL3nrF2KUTUh3F4VjyGpgUEejpi7kh/fJKWh2MFXFaPiCyn9XWaDE3xGJoW8uSMYfBwVGLB/zJQXMVhWiKyDOPrNHlOUyyGpoV4Oqnw0Z9GoaymEX/8MB0XymutXRIR9QGcPWtenYZmQkICKitbhhNfffVVVFRUGB6XlZXhlltu6bbieptIf1d8cP+NKLhchzvfOYDvfr/EBZSJqFu1/h2jYWiK1mloZmVloampyfB4/fr1qKpquWuHTqdDUVFR91XXC42/wQub/xqLfi52eHj9YSQk/4ItRwqgrm6wdmlE1AtxRSDzMnntWYC3lTGXoT5O+ObvsVj3yzl8uO8s/pGSCQCwV8jg5qCAs50cTio5nOwU8HRUwttZBW8nlf7P5h8nFdwcFCav2kREfRPXnjWvLoUmmY9cJsX82MH449hAZOVXIPN8BYqr6lFR24Sqeg2qGzS4XNeEs+pqFFc2oKGd66sUMglc7ZVQyaWQyySQSyVQyKRXfiSQX/lTJpVCLpVAJpVc9eeV7bIOtjc/lrW/3U4hg6NKDkfllT9VcjjbyeHhqIRCxtPlRLagefasTCrhOU0z6DQ0JRIJezLdTC6T4sZBHrixk7ugCIKA6gYNSqoa9D/VDYa/l9c2oUmrg0arQ5NWQJNWp3+sE9Co0aG+SQetTgutToBGJ0Cr0135U4BGK7S//cqf2utcPUQiATwdVXBVChiaUYPQAS4IG+CCmEB3eDmprrepiOh6XPlnrJRJubiBGXQamoIg4IknnoBCoQAANDY2IikpCXZ2dgBgdL6Tuo9EIoGznQLOdgoM8Xay2PsKgnGItvypg0YroL5Ji5oGLaobNKht1PeOq+r14V5cVY/cglKcKqrGD8eKIAj6MI0OcENc5ADMGxUAFzuFxT4LUV+nkElQz9AUrdPQvHr92TvuuKPNPrNnzzZvRWQzJBKJftj3Om/OkpOTg9DQUNQ2apBzqQoHTqux41gRln2bg9d3nMRfJw3Fn8cP5t1fiLpR83iRUi5FVYMGgiBwBFGETkNz5cqVlqqDejEHpRwjA90xMtAdj0y5AUcvXsZbu07hle0n8HXWRbybGIOhPs7WLpOoVxJaDc8KAqDVCZDLGJrX67pmaxQUFOD06dOcTUvXJcLPFcn334iP549CaXUj7njnAL7Oumjtsoh6peaJQEq5/tc9LzsRp9PQ3LZtGzZs2GC07dlnn8WUKVMwa9YszJo1i9dp0nW7JcQH2x69GRG+rnj0syw890026pu01i6LqFcx9DSvhCYvOxGn09Bct24dpNKWXdLS0vD555/jkUcewZtvvgmtVov//ve/XXrD9evXY/LkyYiMjER8fDwyMjI63T89PR3x8fGIjIzElClTkJKSYvS8VqvFG2+8YTjm5MmT8frrr0Oj0XSpLrKOfi52WL9gDP48fjA+TsvDxFd+xKJ1hzB3dRrmvHsAb+w8ict1nHBGdL2a+5XNl4HxshNxOg3Ns2fPIioqyvB4165diI2NxcMPP4xp06bhqaeewoEDB0x+s23btmHFihVYtGgRUlNTER0djQULFqCgoKDd/fPz87Fw4UJER0cjNTUVDz30EJYtW4bt27cb9vnggw+wYcMGPP300/juu++wdOlSbNiwAe+//77JdZF1KWRSJN0ehg1/GYNIP1fkllRDLpNAJpHgjZ2nMOk/e7Dul3NcAozoOjSfRmvuaWo4PCtKpxOBamtr4eLiYnicmZmJ2267zfB46NChUKvVJr/Z2rVrMWfOHMybNw8AkJSUhH379iElJQWLFy9us/9nn30GHx8fJCUlAQCCgoJw5MgRrFmzBtOnTzfUNGnSJEyePBkA4O/vj8mTJ+O3334zuS6yDTcN9cJNQ72Mth29eBkvbj2GpNSjWLP/LGZE9MfNQ70QE+jOWbdEJmg9EQhgT1OsTnua/fv3x6lTpwAA1dXVOHnyJGJiYgzPV1RUwMHBwaQ3amxsRHZ2NmJjY422x8bGIjMzs93XZGVltdl//PjxOHr0qOEa0ZEjR+LgwYPIzc0FAJw+fRq//PILJkyYYFJdZNsi/Fzx2cKxeO++GPg4q/DB3jP4w4cHMfz5H5D44S/4JC0PxZW81RrRtfCcpnl02tOcMWMGli9fjpKSEuzbtw/e3t5Gw7VHjx7FkCFDTHqj8vJyaLVaeHkZ9yQ8PT2RlpbW7mvUajXGjRtntM3LywsajQbl5eXw8fHBggULUFNTg5kzZ0Imk0Gj0WDRokVITEw0qS6yfRKJBDMiBmBGxABU1Tch/WwZ0nJLsfdkCZ79JhvPbcnG6EEemDl8AGZE9IePs521SyayGc09TZWcPU1z6DQ0//rXv6KwsBAvv/wyvLy88Morr0AmaxkS27p1KyZOnNjtRXZm27ZtSE1NxauvvoqhQ4ciJycHK1asgL+/P+6+++5OX9vQ0ICcnBxR719fXy/6GL1Vd7WNL4C5QRLMDfLBuQo37M+rwd68KjzzdRme/TobQz2ViBpgj+gB9gjvZw+ljV6Txu9Ox9g2Hetq21yq0o/K1dXWAABOnj4Dobx3Lmdpie9Np6FpZ2eHVatWdfj8unXrTH4jd3d3yGSyNudAS0tL4e3t3e5rvLy8UFpaarRNrVZDLpfD3d0dALBq1So8+OCDmDlzJgAgJCQEBQUFSE5OvmZoqlQqhIaGmvwZ2tO86g21ZYm2CQUw48pgxMmiKnx/tBD7T6mx+Vg5Nh69DEelDBOCvTEltB8mhXjD04bWvuV3p2Nsm451tW0cSmsA5MPTzRU4VwO/gECEBrp3X4FWZK7vTWfBa7G7nCiVSoSHhyMtLc1oMlFaWhqmTZvW7muioqKwc+dOo21paWmIiIgwrIdbX19v1PsFAJlMBp2OQxB9TXA/ZwT3c8YjU25ATYMGP+eWYtfxYuw+XoTvjhZCIgGiAtwwKcQHk0J8EO7rAqnUNnuhROZy9XWanIUuTqehuWjRIpMO8t5775m03/z587FkyRIMHz4cMTExSElJQXFxMRISEgAAS5YsAQBD7zYhIQHr16/H8uXLkZCQgMOHD2Pz5s149dVXDcecNGkSkpOT4e/vbxieXbt2LdfE7eMcVXLcGtYPt4b1gyBEILugEjtzivDjiRK8vvMkXttxEl5OKkwZ5oO44QNwU5Anb2dGvVLrtWcBrggkVqehuWfPHvj6+mLMmDFmebO4uDiUl5dj9erVKC4uRnBwMJKTk+Hn5wcAuHTpktH+AQEBSE5OxsqVK5GSkgIfHx8sXbrUcLkJADz99NN488038fzzzxuGeufNm4e//e1vZqmZej6JRIIIP1dE+LnisVuDoa5uwN6TJdh9vBjf/n4Jn2fkw81BgWlh/XDv6IGIHtg7h66obzJcp8lLTsyi09D885//jK+//hq//vor4uPjER8fj/79+4t6w8TExA5ntrZ3jnT06NHYvHlzh8dzcnLC0qVLsXTpUlF1Ud/h5aRCfIw/4mP8Ud+kxb5Tamz7/RK2/V6ILzIuYIS/Kx6ZcgMmD/Ph3SCox2vuV8qunIrQcc1wUTodj3riiSfw008/4V//+heOHj2KadOm4S9/+Qu+//573kuTegU7hQxTw/rh9Xui8Mu/p+CFO8Nxua4Jf/4kA4kfHsSpoiprl0gkSnNGtoSmFYvpBa55Ekcmk2HKlCl49913sWvXLowZMwZvvPEGJkyYgJqaGkvUSGQRTio57h83CDv+ORHP3xGOnEuVuP3t/UhJP2/t0ohE0KekVMKepjl0aeZDXV0dqqqqUFtbCwcHBw5dUa+kkEnxp5sGYfvjEzB6sAf+9dXvePWHE7wVHvVILT3N5sf8HotxzdCsr6/H5s2bkZiYiFmzZuHixYt4+eWXsWvXLpOX0CPqiXyc7fDx/NG458YAvL37NN7addraJRF1meGcpoTDs+bQ6USg5juHBAYGYu7cuVi9erXRAu5EvZ1MKsFLd0WiSafD6ztP4oZ+ToiLHGDtsoi6rPmaZC1TU5ROQ3PTpk3w9fWFj48P9u7di71797a7n6nXaRL1RBKJBCvmROKsugZPbvoNMQPd0d+V69tSz2AYnuU5TbPoNDRnz57N85ZE0M+yfX1eFGa8uRdPpx7FB/eP5L8N6hGE5olAV3qazExxOg3Nl156yVJ1ENm8QWEGRnsAACAASURBVF6O+OfUYKzYdhy7jxdjSmg/a5dEdE1tLzlhaorBdcOIumB+7GAM8nTAK9tPQMdzQ9QDtB2etWIxvQBDk6gLFDIpHp8ajOOFVdjyWwEEQcB7P+XiRCEXQSDbdPXwLHua4jA0ibpo1nBfDOvvjLd2nUJmfgVe+u44lm7+3dplEbWrpafZ/JihKQZDk6iLpFIJ/jZpKHJLavCnNekA9HeQKK6st3JlRB2TGS45sXIhPRxDk+g6xEUOgJ1Ciqp6DQAgLbcUo1fssnJVRG21TATS/7rn8Kw4DE2i6yCTSvDK3BEY4GqH0YM9DNtrGzVWrIqoY1xGzzwYmkTXadYIX/z8rymI8HU1bFu57Tgq63kHILIdzROBJJw9axYMTSKRnOxaLnde98s5vPL9CStWQ2SMKwKZF0OTSKTaBuMh2bKaRjRotFaqhshY25tQW6+W3oChSSTSvWMGwsNRaXj87e+XMHHVHusVRNRK8znMlmX0mJpiMDSJRArydsLhpKlG2wp5+QnZiLa3BmNoisHQJDKTZ2eFGT1+7YcTaOJFcWRlV689y6+kOAxNIjOZHzsYIwPdDY/f2n0au3KKrVgREdDc1+SC7ebB0CQyo1Vzh+OmIE/D45IqDtOSdbX0NJsfMzTFYGgSmVGQtxP++4cYw+Okr7Ox7pdzVqyI+rrmiJTyOk2zYGgSmZm7oxJPzww1PE5KPWrFaoj0ODxrHgxNom7wl5uHYKiPk+ExF3Mna2nOSAnY0zQHhiZRN/l4/ijMu9EfADB6xS5cruPyemR5zecwJRJAKuE5TbEYmkTdxN/dAQ9NDDI8Tj9bZsVqqK9qjkgJ9Oc1texqisLQJOpGQd5O2L14IhQyCRb8LwPnS2utXRL1MUKr1JRKJRyeFYmhSdTNhng7YfIwHwDAf388beVqqK8x3OUEEg7PmgFDk8gCVieORFxkf2z5rQBlNY3WLof6kuaJQBL98Cxnz4pj8dBcv349Jk+ejMjISMTHxyMjI6PT/dPT0xEfH4/IyEhMmTIFKSkpRs9PnjwZISEhbX4WLlzYnR+DqEukUgkSRg1EbaMWc99Lg45jZGQhV5/T5FdPHIuG5rZt27BixQosWrQIqampiI6OxoIFC1BQUNDu/vn5+Vi4cCGio6ORmpqKhx56CMuWLcP27dsN+2zatAn79+83/GzevBkSiQS33XabpT4WkUkmBHsj6fYwnCmpwS9nS61dDvURhktOJBJIJLxOUyyLhubatWsxZ84czJs3D0FBQUhKSoK3t3eb3mOzzz77DD4+PkhKSkJQUBDmzZuH2bNnY82aNYZ9PDw84O3tbfj56aef4OTkxNAkm/SH0QPhrJJj4f8OIf8yh2mp+xnOaV4ZnmVmimOx0GxsbER2djZiY2ONtsfGxiIzM7Pd12RlZbXZf/z48Th69Ciamtpe8yYIAjZt2oQ77rgDdnZ25iueyEzslTKsmT8KNY0afHui0trlUB+iH54FLzkRSW6pNyovL4dWq4WXl5fRdk9PT6SlpbX7GrVajXHjxhlt8/LygkajQXl5OXx8fIyeO3DgAC5cuIB58+aZVFNDQwNycnK68Cnaqq+vF32M3opt0z4nADcFOODrnEoM/Pog4oJdrF2SzeF3p2NdbZtzF/WXOeWdOwedTovSsrJe27aW+N5YLDQt4YsvvkBkZCSGDRtm0v4qlQqhoaHX3rETOTk5oo/RW7FtOvak8wDMXZ2GlN8r8fis0ZBeWReU9Pjd6VhX26ZYVgKgEIMHBUKpKIWrm3uvbVtzfW86C16LDc+6u7tDJpNBrVYbbS8tLYW3t3e7r/Hy8kJpqfGECbVaDblcDnd3d6PtpaWl2L17t8m9TCJrGu7vhsdv8oa6uhGPfZ7FITPqNkKr1Q14naZ4FgtNpVKJ8PDwNkOxaWlpiI6Obvc1UVFR7e4fEREBhUJhtP2rr76CQqHAzJkzzVs4UTe50d8eAPDNkQLsO1Vi5WqotzJEJq/TNAuLzp6dP38+Nm/ejI0bNyI3NxfLli1DcXExEhISAABLlizBkiVLDPsnJCSgqKgIy5cvR25uLjZu3IjNmzfjwQcfNDpu8wSgmTNnwtHR0ZIfiei6OSllOPLMNKjkUmw6dIE9AOoehruc8DpNc7DoOc24uDiUl5dj9erVKC4uRnBwMJKTk+Hn5wcAuHTpktH+AQEBSE5OxsqVK5GSkgIfHx8sXboU06dPN9rv4MGDyMvLwyuvvGKxz0JkDq4OCkwN64etv13CQA8HLJlh2vl4IlO1XHLC6zTNweITgRITE5GYmNjuc+vWrWuzbfTo0di8eXOnxxw7dixOnDhhlvqILO2lu4ajvLYRH+4/iwdiB8HHmZdLkfkIV/U0mZnicO1ZIitzUsmxYk4kNFodPth7xtrlUC8jGK09y+s0xWJoEtmAQE9H3Bnlhw/2ncW7e3gnFDKflrmzkiu3BmNoisHQJLIRz90RjpGB7lj9Yy7qm7TWLod6IQ7PisfQJLIRrvYKPH5rMKoaNNj626Vrv4DIBM2zspuHZ9nTFIehSWRDxgV5YkSAG577Jht7T/LaTRKvdURKJRJcrmtCdYPGavX0dAxNIhsik0rw3n0x8HOzx983HEZdI4dpSZzWE4EkEgnScksR8+IO6xbVgzE0iWzMAFd7PHdHOCrrNdj6W/v3miUy3ZXh2SvL6AFAo0ZnxXp6NoYmkQ0aO8QDIf2c8e6eXP6CI1GMLznhjQHEYmgS2SCJRIInbwvBWXUN7n4vDTU8B0XXyWjtWd5NRzSGJpGNmjysH966Nxq/X7yMld/1zvsfUvdrWRGoZXiWrh9Dk8iG3THCF/NuDMCXhy6iqr7J2uVQD9Sy9qzx8OyMN/ZyBOM6MDSJbFzC6IGoa9Liq8MXrV0K9WD6tWdbHh8vrELm+Qqr1dNTMTSJbNwIf1eMDHTH+z/loraRPQPqmtZrGUiumggk43htlzE0iWycRCLB/00LQWFlPe7/KB07jxVx0W0ymfFNqI2fY2h2HUOTqAcYF+SJ1++JwonCKvzlfxl48svfGJxkkpZl9CRtLjmRMQG6zOL30ySi63NnlB+mhvXDO7tP4909ufBxVvGm1XRNGq0+NBVSaTs9S/Y0u4r/zyDqQRyUciyZMQy3RfRHSvp5NGm58AF1rnlEQiZrG5BcvL3rGJpEPdCcaD+U1zbhwGm1tUshG6e5EppyadvbgvE/XV3H0CTqgSaGeMPZTm50C7H/23gEyXtzrVgV2SKtTh+MMqmkzXlwnhfvOoYmUQ+kksswLaw/th8tRF2jFvlltdh06AJWbDtu7dLIxjRpW3qa2qu6ms3nO8l0nAhE1EPdOzoAXx6+gBe2ZqO6oeUWYrWNGjgo+U+b9AznNKUS6K7qWWrY0+wy9jSJeqgbB3kgPsYPKen52HKkAGEDXAAA2QWVVq6MbElzMCpk0jYTfzQ8p9ll/O8oUQ/2n7kjMDNyAHzd7OHlpMKo5TtxJL8CowZ5WLs0shGtz2le3bFkT7Pr2NMk6sGkUgmmhPZD6AAXeDur4Odmj6z8ChRX1eOpL3/jIu9kCEaZRNK2p6ljT7OrGJpEvchwf1f8duEynvsmG5/9mo8fsousXRJZmVYnQHrlXppXz5blRKCu4/AsUS8SFeCG744W4nxZLQDgZFGVlSsia2vSCpBL9f2jNqHJ4dkuY0+TqBeZHe1n9Dgrn7d+6uu0Oh3kV1YD4kQg8djTJOpF+rnY4aX4SJTWNKKkqgGf/5qP+iYtDp4tgyAIuCXEx9olkoVpdIJhzVn2NMVjaBL1MgmjBwIAfjxejI/T8rDq+xP438956OdihwNPTbZucWRxWp0AubS5p2n8HM9pdp3Fh2fXr1+PyZMnIzIyEvHx8cjIyOh0//T0dMTHxyMyMhJTpkxBSkpKm32Ki4vx5JNPYuzYsYiMjERcXBzS09O76yMQ9Qjjgjyhkkux5sBZyKQSXKyoQ/6Vc511jdprvJp6C31PU/+rvu3sWYZmV1k0NLdt24YVK1Zg0aJFSE1NRXR0NBYsWICCgoJ298/Pz8fChQsRHR2N1NRUPPTQQ1i2bBm2b99u2KeyshL33nsvBEFAcnIytm3bhqSkJHh6elrqYxHZJDuFDP+5ewT+Pmko1j4wCgDwc24psvIrEPrM99hxjDNr+wKNVmfoabadPctzml1l0eHZtWvXYs6cOZg3bx4AICkpCfv27UNKSgoWL17cZv/PPvsMPj4+SEpKAgAEBQXhyJEjWLNmDaZPnw4A+PDDD+Ht7Y1Vq1YZXhcQEGCBT0Nk+2aN8MWsEfobEfu72+PD/Wdgr5ABAD7YewZTw/oBACpqG/HoZ1l4emYobujnbM2Sycw0OqFlIhDPaYpmsZ5mY2MjsrOzERsba7Q9NjYWmZmZ7b4mKyurzf7jx4/H0aNH0dSkv2h7586dGDFiBB577DGMGzcOd955Jz799FPD3cqJCJBIJLh/XCBOFlXjyIXLCPR0wKHz5Ybh2h3HivDTyRJMfX0vXtx6zMrVkjl1ek6Tixt0mcV6muXl5dBqtfDy8jLa7unpibS0tHZfo1arMW7cOKNtXl5e0Gg0KC8vh4+PD/Lz87FhwwY88MADWLhwIXJycrBs2TIAwH333ddpTQ0NDcjJyRHxqYD6+nrRx+it2Dads3T7jPHQ4e9jvRDopkB/JwXmf3UeK1Mz8I9x3tieWWzY76P9ZzE3SILqRi3e+VmNv9zoCS9Hy84Z5HenY11tm/KKy9BqmpCTk4OGJuMVoopK1L2qnS3xvenxs2cFQUBERIRheDcsLAznzp3D+vXrrxmaKpUKoaGhot4/JydH9DF6K7ZN56zRPiMiWv5+Tz6wMeMC/nBzGH4tyMdtEf2vDOGexeChwfho/1n8lFeDYYH98K8bLVsnvzsd62rbOGTUwqGuBqGhoZBKLwBomQTm6ubRq9rZXN+bzoLXYsOz7u7ukMlkUKuN7zRfWloKb2/vdl/j5eWF0tJSo21qtRpyuRzu7u4AAG9vbwQFBRntM2TIEFy6dAlE1LGHb9H/u7nvo4OQSyVYPC0YIwLcIAjAmZIa5FzS3y2ltoEzbXuqldty8H12Yct1mldOW619YBQclDLehPo6WCw0lUolwsPD2wzFpqWlITo6ut3XREVFtbt/REQEFAoFACAmJgZnz5412icvLw++vr5mrJ6o9/F3d8AXi8bhL+MHY8s/xmOojzOCvJ0AAIfOleGnkyUAWpbi+/F4MT5Jy7NWuXQd3t97BgDaTAQK7u8Me4UMTZw922UWveRk/vz52Lx5MzZu3Ijc3FwsW7YMxcXFSEhIAAAsWbIES5YsMeyfkJCAoqIiLF++HLm5udi4cSM2b96MBx980LDPn/70Jxw5cgSrV6/GuXPn8N1332HdunVITEy05Ecj6pGiAtzw9O1h8HWzBwAM8XaEk0qOpK+zUdOgwchAd5woqoIgCJj/8a949ptsqKsbrnncmgYN/rP9BK8HtRFXTwRSSCWQy9ou4E7XZtFzmnFxcSgvL8fq1atRXFyM4OBgJCcnw89Pv17m1UOqAQEBSE5OxsqVK5GSkgIfHx8sXbrUcLkJAAwfPhz//e9/8dprr+Hdd9+Fr68vHn30UfzhD3+w5Ecj6hVUchnmjvTHx2l5+MvNQ3CDjxOe2PQbtmcXGvbZmHHBMLS7bOsxHLtUiQ0Lxhod5+O0PLzz42m4OSjwl5uHWPQzUFtXL9gul0khl0rRxBWBusziE4ESExM77AWuW7euzbbRo0dj8+bNnR7zlltuwS233GKO8oj6vP+bHoJwXxfMjvZDbYMW/5b9jkWfHgYADPRwwBs7T+K2iP7wddNPGgL0Q7jBra7vLK1uBACor/xJ1nX1OU25rLmnqR+eLa9phEwmgYudwmo19hS8ywkRGXFSyXH3jQFQyKRwdVAgcUwgAOCPYwOxcdE4aHUCUtLPY8uRlpW8/vjRQRRV1hsen1VXAwBOF1cbHfvqi+vJMq4+p6mQSiGTStCkE5B+tgzRL+7A0s1HrVlij8HQJKJOPXdHOHYvnojn7ghHPxc7TBrmg/f3nsHijUcQPdANr98zAkWVDdh06AIAoKSqAb9fvAwAOHKhApX1+msDD50rw5B/b8ORdm5XptMJ7S5Icr60FmsPnG2znTr37W+XDLOfgfZ7mgqpFFqtgPUHzwEA0s+Wtj0QtcHQJKJrGuLtZPjFu3haMAZ5OmDMYA/878HRmBPtj5iBbthypACCIODhTw+hql6Dv4wfjPKaRjz3dTYAYMsR/ZyFj/afbTNrM2bZDjz55W9t3vf+NQfx/JZjKK6qb/MctaWuboBGq8PfNhzGbW/uM2xvPqc5bojnlccSyKQSaHQ6HDpXDoB3PDFVj1/cgIgsa1h/F/z4f7cA0C/PBwDzbgzAU1/9jrtWp+Hw+Qosmx2B+8YGory2CbuPF0GnEww9n2+OFMBRJcPK+OEAgLPqGlTUNuGLjAtYNXeE0XvlleqX+ctT18LH2c7oOUEQDO9P+jvX3LhsJ+4fF9jmuebZsx/cfyMuVtRBIpFAIZNgZ45+JSgXOzlKaxrRoNFCJZdZtO6ehj1NIuoyiURiFFj3jApAwqgAZBdU4vbhAzDvRv1NE8bf4Iny2iZ8c6QAmecrMDFYv5DJD9lFEAQBeeoaTPrPHsNxWl+i0nq4Nk9dY/T+FbWNGPyvbfgiI99o+5H8CjRo2r/MRRAEHDit7rXrUlfU6SddbT58scN9HFVyw4St1qeX7xurD9riymtfTtTXMTSJSDSJRIKX7hqO4y/OwDt/iIFSrv/VMn6oN5RyKR77PAvOdnK8Mnc4Vs0djtKaRhwvrMKaq85XHi24bPj73e/9bPj7mVah+eWhC4h6YQcA4OMDeYbtFyvqcOd/D+C5b7LbrfHzX/OR+OFBfPu78aVtl+ua2t0fABo0WsPiDqaqbtCYdC2ruVXWaQAAdU1t/9Ogbec/Cs0huzI+EmOuDNvevOpH/G39YcS9uQ8HTqtRUsUQvRpDk4jM5urhUm9nFd67LwY33+CF9QvGwMfFDhODvaGUSfGPlEx8eegC7ozyRWbSVDgoZXj3x9MQBAHnyhuRceVcm1ImRW5Jyyzc13eeNPzdSdVyhin7yuSjXTkti883O1NSjU9+1k94Kbzccn70p5MlGPH8D/g1r6zdz/OvL3/HtNf34nJtx8F6tVlv78eNy3aavL8YP2QX4qXvjgNoCf/2bvfV3n0zy2v0+/s4q9DfpWXo+9vfL+HYpUokfngQs/97oDvK7tEYmkTUrSYP64d1fx6DYf1dAAD9XOzw77hhyC2phrezCounhsDdUYl/Tg3GjydK8HVWAb48VgGpBEhfOgV33+iPn06U4EJ5LXQ6AVX1GsOxz6hbwjS7QH/OtLiqAV9nGQ9R3v72fsM51ZJWvcADp/VrYe+7smTg1Zp7pfnltYZtFyvqsOHg+Q4/79krvWJThoEFQcD+U9c/ZLxw3SG891MuAKCykx5ze0Fa3aBvRx9nOwR6OiBmoJvhOTuFPhouVtQZzcIlhiYRWcEDsYNx5Nlp2PnPiRjo6aDfdtMghA1wwWOfZ2HH6Wo8cNNg+Djb4e+ThwIS4M2dp/DDsUJcrmvCq3ePwNMzQ6GubkRJVQMEQcDh8+WG4z/6WRYaNfrelVYnoLbVudLme4gCQNWVy2F+OVOGshrjhRhOFlWh4coxLpTXGbb/bf1h/Hvz77jQKkjbU35V77Sosh7z3vsZBRUtx9p06ALu++ggUrM6Pg9pivombafDzJ0tl+fjooKdQoav/hqLP48fjInB3tj6j5uRdHsYVHIp/nelh056nD1LRFZx9eozcpkUKQvG4qvMC5DWluH+W/W3eBrgao/7xwbiw/1nsfHQBQz3d0Vc5ACcL6sFkIOP087CzV6JfafU+PukodDoBLz3Uy4yz5djzBBPwwILIf2cUVrTgHOlLWF3qkj/XHpeGf6+4bBhOUBBEDDt9b2G/VoH5KXL+tD705p0vHffSNzQaiWk+lbnEy9droOHoxKAPoCf2PQbjuRX4LP08/jntBAALedq89RtA7i+SQuZVAKF7Np9m4rapk5Ds72eZjPPKzUCQNLtYYa/D/VxwonCSnz263mMHeKBkYHu+PLQRYwe7IFxQZ7XrKm3YmgSkc1wdVBgfuxg5OTUG50ffWxqMHQCoNXp8M+pIbBXyhDS3xl3Rvnivz/qhyenh/fDP6cGo6pBgw/2ncFXhy8iJtAdb+8+BQBIvn8k1h7IwxcZ+aht1A9NniiqglIuRaNGh7TcUuh0AqRSidHEI8C4p9l8zWNuSQ2Wb8vBx/NHG5672KoXWVRZj3BfVwAwCmCZtCUEm3vDje2ccxz+/A+QSoBbgn3w9h+i24Rn69WVymoar7unKe8klB+7NRiZ5yuw+Isj6OdiZ/h8byZE4c4ovw5f15sxNInI5jmp5HhmVlib7SvjI+GokkOj1eFft4VCKpXA1V6BB24ahI/2n8Wu48VQVzfgiekhCPR0xKwRA/BxWh4+TsvDycIqVDdokLJgLC6W12HxxiM4UVSF0AEuyLgyMeil+Egk7ztjCM36Jq2hpwkYz7zVaHVY8EmG4XHh5fZnnl6saOlVNg/Vth6yBfRh2hyo32cX4nRxNUIHuBieFwQBiz49ZHhcXtt5aLY3Eeil+Mhrnq/0dbPHGwlRmPnWflysqMObCVH438/n8Ow32Ygd6oXaBv3s4jFDPODcR9atZWgSUY/loJRjxZzINtufum0Y3B0USM8rx50jfHHXSH8AwMhAD9wa2g+rvj8BAPjn1GCMHeKJgoo6yKQSvPrDSdw/LhCv7TiJAa52uGdUANLzyrD9aCEqahuxM6cYOgF44c5w/JpXjh3HCqHR6iCXSZGeV4Yz6ho4KGWobdSi8Eq4Xn2uNL+sJSDPXzm/2ronCwB5pcY93dwS49C8UF6HH44VGR6X1TR2eSJQwuiBHe7fWrivK16+KxIDXO0xIdgb4b4uiHtzP2597SdU1jVBJ+gX8l/zwCgM9XEy6Zg9GUOTiHodhUyKv0++od3n3kyIwrt7TsPTUYUHbhoEQN+jWhoXihe2HsPOnCL4udnjowduhEQiwUMTgvDV4YtISP4FZ9Q1GD3YA/eOHgh3ByW2HCnAt79fwp1Rfthy5BLsFFJkPH0r7nznAHafKMbjU4MNvbk3E6KwPbsQv13QXxpTXFlvmGl7rrQWWp1gWKqw+Vxrs9xi4xA9Xmh87Wh5baNhjd/2iL1v5j2jWgJ2qI8zXrl7ONYfPI/oADdE+rviuW+ycec7+zF2iCckEgl8XPRt2/rON70FQ5OI+hRHlRxPTB/WZvuD4wdjRIAbThVVYWpYP3g6qQAAIf2d8dRtw/DSd8cx2MsRqxNjoJBJMSOiP0YGumPxF0ewZv9ZHLlwGXeP9IeDUo4FE4Zgyabf8OauU9iVUwwnlRy3BPvgfGktvjtaiNySajx7ZU3eh28Jwuo9uXjvp1z8bdJQAEDm+XJIJMAb90Thxa05OF1iHKLHrwTxB/ffiAX/y0BZTaOh19qeziYCXY87o/yMzmlGBbjh1R9O4nhhFSQA0nLV+OLXfEwM9oaLvQLOdnLEDvXChBu8Ya/s2cv0MTSJiK4YGeiOkYHubbYvmhiEe0cNhINKZpiQo5BJseZPo7B82zGcKKzCE9NDsHCC/obb8dF++PLQBbyx8xSUMilW3xcDVwcF7h0zEKt/ysUdb+9HTaMWSbeH4cHYQThXWoO3d5/ChBu8kV1wGR8dOIvbIvrjzig/bPv9EvaeLMHFijr4udlDEASk55VhoIcDpob1g4udHL9duIyTRdUI8nZEbklNm/rF9jSvxd/dAa/fE2V4XFbTiLd3n8K+U2o0aLQoq27E/34+B6VcisGejhjo6YCBHg4I9HRAgIcDAj0c4O/uYFhJypYxNImITODq0Haii6uDos0i84B+RuqaB0ZhZ04Rwga4GC5L8XJS4fV7ovDSd8cx3N8V940dCIlEgn/dFop9p9SY9c5+AMCYwR54bZ4+hJ66LRR3vL0fCck/497RA7E3uwi/5Ndi8dRgAPoF9Hcf16+CdMcIP7y+U38+9tLletwY6I6Mc+Vt7irT3TwclXh2VrjhcZNWh/SzZfjpZAnOlNTgfGkt9p0qQX1TS10SCeDrao+BHvpAHeipD9X+Lnbo52IHb2f99aTWxtAkIuoGjip5u5dlTA/vj+nh/Y22BXg4YNfiidhxrAjOdgpMC+tnCIjBXo74+MHReGLjEaz6/gRUcgmWzAjBwxODAACJYwciPa8MY4d4YMGEwfB1s7tyjrUAY4Z4YPzLPyLA3aH7P3AnFDIpYod6IXaol2GbIAgoqWrA+bJanCutxfmy2it/rzHMer6ak0oOTyclPByV8HRUwdNRCU8nJTyd9H/30mnavMbcGJpERDbAx9kOiWPa3tYL0A8b71o8ETWNWuSdPomI8KGG524f7gutTsCtYf3goJTj7it3mGmeMfz+H0di9CCP7v8AXaSfMGQHHxc73NhOfTUNGuSX16Lwcj2KqxpQXFkPdXUjymr0PxfKa/HbhQqU1TQaztneHOiI8SO7t26GJhFRDyCRSOCkkhtm2DaTSSWIj/Hv8HVX92p7CkeVHMP6uxjWLO6IIAiorNNAXdOAysLuX/LP9s+6EhERdUAikcDVQYEgbyfYWWAiEUOTiIjIRAxNIiIiEzE0iYiITMTQJCIiMhFDk4iIyEQMTSIiIhMxNImIiEzE0CQiIjIRQ5OIiMhEDE0iIiITSQRB6N4brdmwrKwsqFQqa5dBREQ2pKGhAVFRUe0+16dDk4iIqCs4PEtERGQihiYREZGJGJpEREQmYmgSERGZiKFJRERkIoYmERGRiRiaIqxfvx6TJ09GZGQk4uPjkZGRYe2Sut2vv/6KRYsW4eabb0ZISAi++uoro+cFQcDbznYKYAAACvtJREFUb7+N8ePHY/jw4fjjH/+IU6dOGe1z+fJlPPHEExg5ciRGjhyJJ554ApWVlZb8GGb3/vvv46677kJMTAzGjh2LRYsW4eTJk0b79NW2AfT/VmbNmoWYmBjExMTgnnvuwZ49ewzP9+W2ae39999HSEgIXnjhBcO2vtw2b7/9NkJCQox+YmNjDc9bpW0Eui7ffvutEBYWJnz++efC6dOnhRdeeEGIiooSLl68aO3SutWePXuEV199Vfjuu++E4cOHC19++aXR8++//74QFRUlfP/998KJEyeERx55RIiNjRWqqqoM+/z5z38W4uLihMOHDwuHDx8W4uLihIceesjSH8WsHnzwQWHTpk3CiRMnhOPHjwt//etfhZtuukkoLy837NNX20YQBGHHjh3Cnj17hLy8POHMmTPCa6+9JoSFhQk5OTmCIPTttmmWmZkpTJo0SZg1a5bw/PPPG7b35bZ56623hOnTpwvFxcWGn9LSUsPz1mgbhuZ1mjt3rrB06VKjbVOnThX+85//WKkiy4uKijIKTZ1OJ8TGxgrvvvuuYVtdXZ0QFRUlpKSkCIIgCKdPnxaCg4OFjIwMwz6//vqrEBwcLOTm5lqu+G5WXV0tDBs2TNi1a5cgCGyb9owaNUpISUlh2wiCUFlZKUyZMkX4+eefhfvuu88Qmn29bd566y1h5syZ7T5nrbbh8Ox1aGxsRHZ2ttEwAQDExsYiMzPTSlVZ34ULF1BSUmLULnZ2dhg1apShXTIzM+Hg4ICYmBjDPiNHjoSDg0OvaruamhrodDq4uLgAYNu0ptVq8e2336K2thbR0dFsGwBJSUmYPn06xo4da7SdbQPk5+dj/PjxmDx5Mh5//HHk5+cDsF7byEV8lj6rvLwcWq0WXl5eRts9PT2RlpZmpaqsr6SkBADabZfi4mIAgFqthoeHByQSieF5iUQCDw8PqNVqyxXbzZYvX47Q0FBER0cDYNsAwIkTJ5CQkICGhgY4ODjgnXfeQUhICA4fPgyg77bNF198gfPnz+OVV15p81xf/94MHz4cK1euxJAhQ1BWVobVq1cjISEBW7dutVrbMDSJzGzlypU4dOgQUlJSIJPJrF2OzRg8eDBSU1NRVVWF7du348knn8S6deusXZZVnTlzBq+99ho2bNgAhUJh7XJszsSJE40ejxgxArfeeitSU1MxYsQIq9TE4dnr4O7uDplM1uZ/KqWlpfD29rZSVdbX/Nnba5fm/w16eXmhrKwMQqv7BAiCgLKysjb/Y+yJVqxYgW+//RaffPIJAgICDNvZNoBSqURgYCAiIiKwePFihIaG4uOPP+7TbZOVlYXy8nLcfvvtCAsLQ1hYGNLT07FhwwaEhYXBzc0NQN9sm/Y4Ojpi6NChyMvLs9r3hqF5HZRKJcLDw9sMxaalpRmG4/oif39/eHt7G7VLQ0MDMjIyDO0SHR2N2tpao/MJmZmZhvNbPdmyZcsMgRkUFGT0XF9vm/bodDo0Njb26ba59dZbsWXLFqSmphp+IiIiMHPmTKSmpmLw4MF9tm3a09DQgLNnz8Lb29tq3xvZc88995yoT9FHOTk54e2334a3tzfs7Ozw7rvvIiMjAytWrDBM/uiNampqkJubC7VajY0bNyI4OBjOzs5oamqCi4sLNBoNkpOTMXjwYGi1Wrz00ksoKSnBCy+8AKVSCQ8PDxw5cgRbt25FaGgoCgsL8eyzzxquseqpnn/+eaSmpuLNN9/EgAEDUFtbi9raWgD6/2RJJJI+2zYA8J///AdKpRI6nQ6XLl3CJ598gi1btmDx4sUYNGhQn20blUoFT09Po5+tW7fC19cX8fHxff578/LLLxu+N3l5eXjhhRdw7tw5vPDCC9b7fXNdc25JEARB+PTTT4VJkyYJ4eHhwpw5c4T09HRrl9TtfvnlFyE4OLjNz5NPPikIgn4a+FtvvSXExsYKERERQmJionDixIn/b+/uQqJY4ziOf612KcHCDVq19CbWioVoK0ItSOgqDaLoppUKeiGQ3rbNXFkKw6jcXujFGylIIrGL6A1EiAKLJXuBKErISi9UpIJcY2svWtw5F9Ic99iJ4RyPrcff52p2nplnnn1ufjvz7PBP6mNgYMDw+/2Gx+MxPB6P4ff7jS9fvvyOrzNqfjYn+fn5xvnz581jJurcGIZhVFZWGsXFxYbb7TYKCgqMLVu2GA8fPjTbJ/Lc/NXwV04MY2LPzb59+4zly5cbbrfbWLFihbFr1y7j3bt3ZvvvmBsVoRYREbFIa5oiIiIWKTRFREQsUmiKiIhYpNAUERGxSKEpIiJikUJTRETEIoWmSAoKBALs3Lnzdw8jSSqOSWSs6T1NkRQUjUYxDIPp06ezadMmXC4Xhw8fHpNrP3nyhM2bN9PW1obD4fjpmEQmKlU5EUlBGRkZo97n9+/fsdvt//j8/2JMIuON7jRFUlAgECASiZCZmcnNmzeT2u7fv8+cOXN4//49oVCIZ8+eMXXqVAoLC6mqqjKrP/zoY8mSJVy9epV4PE5bWxu3b9/mypUrdHV1mUV7g8EgTqeT3t5eVq1alXS9devWceLECbO/+vp6YCiET548SXNzM9FolAULFnDw4EGWLl0K/HnH2tDQwJkzZ3j79i1z586lpqYGt9s9BrMoMvq0pimSwoLBIB6Ph/Xr1xMOhwmHw2RnZ/Pp0yfKyspwuVxcv36dy5cvE4vFKC8vJ5FImOc/ffqUjo4OLl26RENDAwDxeJw9e/Zw584d6uvriUQi7N+/H4Ds7GwuXLgAQHNzM+FwmGAw+NOxhUIhWlpaOHbsGLdu3SI/P58dO3aYBYB/OH36NH6/nxs3bpCZmcmBAwfQb3UZr/R4ViSFZWRkYLPZmDZtWlKt1qamJubPn09FRYW5r7a2lmXLlvH69WsWLlwIDFXROH78eNJj2Q0bNpjbubm5VFdXU1JSwocPH8jKymLGjBkAOByOpDXN4WKxGNeuXePo0aMUFxcDQ5VeHj9+TGNjIz6fzzx27969FBQUAFBeXo7X6+Xjx49kZWX9y9kRGXsKTZFxqL29Palu4HDd3d1maLpcrhHrmO3t7dTV1fHmzRsGBgbM/X19fZaDrLu7m3g8zuLFi819kydPZtGiRXR2diYdO2/ePHN71qxZwFChYIWmjEcKTZFxKJFIsHLlSiorK0e0zZw509xOT09PaovFYmzbto2ioiJCoRAOh4NIJEJZWRnxeHxUxpaWlpb0ecqUKSPahj9CFhlPFJoiKc5mszE4OJi0z+1209LSQk5ODjabzXJfXV1dRCIRfD4fubm5ANy9e3fE9eDXwZaXl4fNZuP58+fk5eUBMDg4yIsXL1izZo3l8YiMN/ojkEiKmz17Nq9evaK3t5f+/n4SiQRer5doNIrP5+Ply5f09PTw6NEjDh06xNevX/+2r5ycHOx2O42NjfT09NDa2sq5c+dGXC8tLY3W1lb6+/v59u3biH7S09PZuHEjp06d4sGDB3R2dlJdXc3nz5/xer2jPgciqUKhKZLitm7dis1mo7S0lMLCQvr6+nA6nTQ1NTFp0iS2b99OaWkpR44cwW63//JdTIfDQW1tLffu3aOkpIS6ujoCgUDSMU6nk927d3P27FmKioqoqan5aV8VFRWsXr2aqqoq1q5dS0dHBxcvXjTXLUX+j/SepoiIiEW60xQREbFIoSkiImKRQlNERMQihaaIiIhFCk0RERGLFJoiIiIWKTRFREQsUmiKiIhYpNAUERGx6A83RbTmg9c4HQAAAABJRU5ErkJggg==",
            "text/plain": [
              "<Figure size 504x360 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "num_epochs = 500\n",
        "losses = []\n",
        "plt.rcParams.update({'font.size': 14})\n",
        "\n",
        "for epoch in range(1, num_epochs + 1):\n",
        "    model.train()\n",
        "    optimizer.zero_grad()\n",
        "    embeds = model(features)\n",
        "    loss = criterion(embeds, sim_matrix)\n",
        "    loss.backward()\n",
        "    optimizer.step()\n",
        "    losses += [loss.item()]\n",
        "\n",
        "    if epoch % 10 == 0:\n",
        "        clear_output()\n",
        "        plt.figure(figsize=(7, 5))\n",
        "        plt.plot(range(1, epoch + 1), losses)\n",
        "        plt.xlabel('iteration')\n",
        "        plt.ylabel('MSE loss')\n",
        "        plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 61,
      "metadata": {
        "id": "08dQiWj038KR"
      },
      "outputs": [],
      "source": [
        "model.eval()\n",
        "with torch.no_grad():\n",
        "    agg_embeds = model(features)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 62,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "YXGWMlNb4PLd",
        "outputId": "4820f7e8-c6d4-47a4-e16c-c9f8e035b7e9"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "((2031, 256), (677, 256))"
            ]
          },
          "execution_count": 62,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "train_agg_embeds = np.stack([agg_embeds[id_to_index[node]].numpy() for node in train_index])\n",
        "test_agg_embeds = np.stack([agg_embeds[id_to_index[node]].numpy() for node in test_index])\n",
        "train_agg_embeds.shape, test_agg_embeds.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 63,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "h1HqSwre4Wzj",
        "outputId": "7731f1a6-5259-4c41-b313-91ee98ca1cf7"
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "[Parallel(n_jobs=-1)]: Using backend LokyBackend with 2 concurrent workers.\n",
            "[Parallel(n_jobs=-1)]: Done   3 out of   3 | elapsed:   15.3s finished\n"
          ]
        }
      ],
      "source": [
        "log_regr = LogisticRegressionCV(\n",
        "    Cs=np.logspace(-2, 2, 8), cv=3, n_jobs=-1, verbose=1, max_iter=10000\n",
        ").fit(train_agg_embeds, y_train)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 64,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "oVOWcL7e4ZyJ",
        "outputId": "afd92d34-51b5-4464-d466-fb974e21dfb9"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Neighborhood Aggregation + Logistic Regression\n",
            "Train accuracy: 0.8892\n",
            "Test accuracy: 0.8287\n"
          ]
        }
      ],
      "source": [
        "print('Neighborhood Aggregation + Logistic Regression')\n",
        "print(f'Train accuracy: {accuracy_score(y_train, log_regr.predict(train_agg_embeds)):.4f}')\n",
        "print(f'Test accuracy: {accuracy_score(y_test, log_regr.predict(test_agg_embeds)):.4f}')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BFXpaNh5O3z9"
      },
      "source": [
        "Получилось качество, сопоставимое с Node2Vec. Гипотетически, мы могли бы и превзойти этот метод, если использовали бы ту же функцию потерь (основанную на случайном блуждании по графу и кросс-энтропии)."
      ]
    }
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