{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "altJYU0bAd8s"
   },
   "source": [
    "# LOAD DATASET"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 208
    },
    "colab_type": "code",
    "id": "X6afS_dOwNhd",
    "outputId": "62c030a3-cfcb-41d8-c20b-5354e40c4bb1"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "--2018-12-30 15:11:50--  https://raw.githubusercontent.com/first20hours/google-10000-english/master/20k.txt\n",
      "Resolving raw.githubusercontent.com (raw.githubusercontent.com)... 151.101.112.133\n",
      "Connecting to raw.githubusercontent.com (raw.githubusercontent.com)|151.101.112.133|:443... connected.\n",
      "HTTP request sent, awaiting response... 200 OK\n",
      "Length: 155418 (152K) [text/plain]\n",
      "Saving to: ‘20k.txt’\n",
      "\n",
      "20k.txt             100%[===================>] 151,78K   804KB/s    in 0,2s    \n",
      "\n",
      "2018-12-30 15:11:51 (804 KB/s) - ‘20k.txt’ saved [155418/155418]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "!wget https://raw.githubusercontent.com/first20hours/google-10000-english/master/20k.txt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 208
    },
    "colab_type": "code",
    "id": "hf7hkVZ_uCFk",
    "outputId": "021efafa-ecf4-411e-f6fb-56e1fcf24840"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "--2018-12-31 04:31:37--  https://s3-us-west-1.amazonaws.com/fasttext-vectors/wiki.en.vec\n",
      "Resolving s3-us-west-1.amazonaws.com (s3-us-west-1.amazonaws.com)... 52.219.20.45\n",
      "Connecting to s3-us-west-1.amazonaws.com (s3-us-west-1.amazonaws.com)|52.219.20.45|:443... connected.\n",
      "HTTP request sent, awaiting response... 200 OK\n",
      "Length: 6597238061 (6,1G) [binary/octet-stream]\n",
      "Saving to: ‘wiki.en.vec.1’\n",
      "\n",
      "wiki.en.vec.1       100%[===================>]   6,14G  5,61MB/s    in 14m 42s \n",
      "\n",
      "2018-12-31 04:46:21 (7,13 MB/s) - ‘wiki.en.vec.1’ saved [6597238061/6597238061]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "!wget https://s3-us-west-1.amazonaws.com/fasttext-vectors/wiki.en.vec"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "bgKPX0gSAlSx"
   },
   "source": [
    "# PREPARE DATASET"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "ADbG0MIluWWp"
   },
   "outputs": [],
   "source": [
    "# UTILS #\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "from tqdm import tqdm\n",
    "import matplotlib.cm as cm\n",
    "#from yellowbrick.cluster import SilhouetteVisualizer\n",
    "\n",
    "# TEXT LIBS #\n",
    "import gensim\n",
    "\n",
    "# ML LIBS #\n",
    "from sklearn.cluster import KMeans\n",
    "from sklearn.metrics import silhouette_samples, silhouette_score\n",
    "from sklearn.metrics.pairwise import cosine_similarity, euclidean_distances"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "TptxwDMC18Ca"
   },
   "outputs": [],
   "source": [
    "google_words = []\n",
    "with open('20k.txt', 'r') as f:\n",
    "    google_words = [w[:-1] for w in f]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "-dJRPZtm2d_M"
   },
   "outputs": [],
   "source": [
    "model = gensim.models.KeyedVectors.load_word2vec_format('wiki.en.vec.1', binary=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "NtKqVGDVG-zo"
   },
   "source": [
    "fasttext с mipt-telecom качалась неприлично долго, поэтому я использовала google colab, на котором ограничена память. Что бы уложиться пришлось качать только .vec без ngram и выкинуть из выборки некоторые слова. Благо их не много..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 1337
    },
    "colab_type": "code",
    "id": "nAec07UyFAFd",
    "outputId": "fb11c903-d79f-4203-e606-ea3ad1ec2026"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Unknown word sexcam\n",
      "Unknown word milfhunter\n",
      "Unknown word postposted\n",
      "Unknown word starsmerchant\n",
      "Unknown word ampland\n",
      "Unknown word thumbzilla\n",
      "Unknown word livesex\n",
      "Unknown word worldsex\n",
      "Unknown word msgstr\n",
      "Unknown word sublimedirectory\n",
      "Unknown word viewpicture\n",
      "Unknown word acdbentity\n",
      "Unknown word zshops\n",
      "Unknown word listprice\n",
      "Unknown word knowledgestorm\n",
      "Unknown word vsnet\n",
      "Unknown word feof\n",
      "Unknown word bufing\n",
      "Unknown word voyuer\n",
      "Unknown word beastality\n",
      "Unknown word tittens\n",
      "Unknown word storesshop\n",
      "Unknown word blogthis\n",
      "Unknown word libdevel\n",
      "Unknown word spermshack\n",
      "Unknown word xlibs\n",
      "Unknown word milfseeker\n",
      "Unknown word pricetool\n",
      "Unknown word acdbline\n",
      "Unknown word trustpass\n",
      "Unknown word debuginfo\n",
      "Unknown word telefonsex\n",
      "Unknown word madthumbs\n",
      "Unknown word kudoz\n",
      "Unknown word phonephone\n",
      "Unknown word zoofilia\n",
      "Unknown word zerodegrees\n",
      "Unknown word secsg\n",
      "Unknown word condosaver\n",
      "Unknown word classicvacations\n",
      "Unknown word tiava\n",
      "Unknown word insest\n",
      "Unknown word searchsearch\n",
      "Unknown word ripencc\n",
      "Unknown word docume\n",
      "Unknown word pinkworld\n",
      "Unknown word conftest\n",
      "Unknown word registerregister\n",
      "Unknown word printprinter\n",
      "Unknown word savesave\n",
      "Unknown word animalsex\n",
      "Unknown word cvsroot\n",
      "Unknown word messageslog\n",
      "Unknown word inlog\n",
      "Unknown word profileprofile\n",
      "Unknown word thiscategory\n",
      "Unknown word faqfaq\n",
      "Unknown word usergroupsusergroups\n",
      "Unknown word phantomnode\n",
      "Unknown word ionamin\n",
      "Unknown word mcsg\n",
      "Unknown word bontril\n",
      "Unknown word libstdc\n",
      "Unknown word bbbonline\n",
      "Unknown word fomit\n",
      "Unknown word typekey\n",
      "Unknown word vgroup\n",
      "Unknown word oldmedline\n",
      "Unknown word sleazydream\n",
      "Unknown word asnblock\n",
      "Unknown word memberlistmemberlist\n",
      "Unknown word vdata\n",
      "Unknown word commentsblog\n",
      "Unknown word prolyte\n",
      "Unknown word ivtools\n",
      "Unknown word bizjournalshire\n"
     ]
    }
   ],
   "source": [
    "X = []\n",
    "for w in google_words:\n",
    "    try:\n",
    "        X.append(model[w])\n",
    "    except KeyError:\n",
    "        print('Unknown word ' + w)\n",
    "X = np.array(X)\n",
    "np.savetxt(\"drive/My Drive/model.csv\", X, delimiter=\",\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "В дальнейшем будем пользоваться сохраненными векторами, что бы не хдать каждый раз когда загрузится модель"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.genfromtxt(\"model.csv\", delimiter=',')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "idFbqvcSG4f5"
   },
   "source": [
    "# DATASET ANALYSIS"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "DTs520pqQ0d0"
   },
   "source": [
    "Посмотрим на гистограммы слов по признакам. Особо ничего интересного сказать нельзя. Получилось нормальное распределение вокруг 0, как и предполагалось в FastText. Выбросы отсутствуют."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 107717
    },
    "colab_type": "code",
    "id": "JRXmzUZdHmzw",
    "outputId": "429f7bea-10be-43b0-8054-e1f2de9774cf"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(3):\n",
    "    plt.hist(X[:, i], bins=100)\n",
    "    plt.title(\"feature {}\".format(i))\n",
    "    plt.xlabel(\"feature value\")\n",
    "    plt.ylabel(\"num of samples\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "gfrkpOw3Ydmn"
   },
   "source": [
    "# MODEL"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "AoL4Dj67Yj7C"
   },
   "source": [
    "Будем использовать K-means и попробуем искать наилучшее количество кластеров по различным метрикам: евклидово расстояние и косинусная мера (внутрикластерное расстояние и межкластерное расстояние). Итого 4 метрики. За расстояние между кластерами принято расстояние между центрами кластеров, что немного лукавство, ну да ладно... Нам хотелось бы минимизировать внутрикластерное расстояние и косинусную похожесть между кластерами, а максимизировать межкластерное евклидово расстояние и внутрикластерную косинусную схожесть. В идеале нам хотелось бы что бы (межкластерное расстояние - внутрикластерное) / max(внутрикластерное, межкластерное) -> 1. Приложены графики:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "hKh15cXlrbQ2"
   },
   "outputs": [],
   "source": [
    "def int_metr(X, Y, n_clusters):\n",
    "    clust = [[] for _ in range(n_clusters)]\n",
    "    for i in range(len(X)):\n",
    "        clust[Y[i]].append(X[i])\n",
    "    \n",
    "    eu_avg = 0\n",
    "    cos_average = []\n",
    "    for i in range(n_clusters):\n",
    "        cs = cosine_similarity(clust[i])\n",
    "        cs_avg = 0\n",
    "        for k in range(len(cs)):\n",
    "            for j in range(k+1, len(cs)):\n",
    "                cs_avg += cs[k][j]\n",
    "        if len(clust[i]) == 1:\n",
    "            cos_average.append(cs[0][0])\n",
    "        else:\n",
    "            cos_average.append(cs_avg / (((len(clust[i])**2) - len(clust[i])) / 2))\n",
    "        max_row = 0\n",
    "        cs = euclidean_distances(clust[i])\n",
    "        for k in range(len(cs) // 2):\n",
    "            max_row = max(max_row, max(cs[k]))\n",
    "        eu_avg += max_row\n",
    "    \n",
    "    return np.array(cos_average).mean(), eu_avg / n_clusters\n",
    "\n",
    "def ext_metr(centers):\n",
    "    cosine = cosine_similarity(centers)\n",
    "    cs = []\n",
    "    for i in range(len(cosine)):\n",
    "        for j in range(i+1, len(cosine)):\n",
    "            cs.append(cosine[i][j])\n",
    "    cosine = np.array(cs).mean()\n",
    "    distances = euclidean_distances(centers)\n",
    "    cs = []\n",
    "    for i in range(len(distances)):\n",
    "        for j in range(i+1, len(distances)):\n",
    "            cs.append(distances[i][j])\n",
    "    dist = np.array(cs).mean()\n",
    "    return cosine, dist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "G-uPV73C4Z4M"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For n_clusters = 1000 \n",
      "average between clusters cosine similarity is 0.28508220882638224 \n",
      "average between clusters euclidean distance is 4.43051855378622 \n",
      "average among clusters cosine similarity is 0.5220442426059242 \n",
      "average among clusters euclidean distance is 5.716753060475638\n",
      "For n_clusters = 1200 \n",
      "average between clusters cosine similarity is 0.27376919765463764 \n",
      "average between clusters euclidean distance is 4.582534779463035 \n",
      "average among clusters cosine similarity is 0.5429387840096667 \n",
      "average among clusters euclidean distance is 5.5076374023608\n",
      "For n_clusters = 1400 \n",
      "average between clusters cosine similarity is 0.2592292657407178 \n",
      "average between clusters euclidean distance is 4.807426887297778 \n",
      "average among clusters cosine similarity is 0.5681579826334481 \n",
      "average among clusters euclidean distance is 5.239628506558609\n",
      "For n_clusters = 1600 \n",
      "average between clusters cosine similarity is 0.2530602724078216 \n",
      "average between clusters euclidean distance is 4.853522267647604 \n",
      "average among clusters cosine similarity is 0.5809587608920418 \n",
      "average among clusters euclidean distance is 5.0868180532553415\n",
      "For n_clusters = 1800 \n",
      "average between clusters cosine similarity is 0.24390760533307987 \n",
      "average between clusters euclidean distance is 4.979173488205444 \n",
      "average among clusters cosine similarity is 0.5975848209961699 \n",
      "average among clusters euclidean distance is 4.880299352001343\n",
      "For n_clusters = 2000 \n",
      "average between clusters cosine similarity is 0.2386734841886413 \n",
      "average between clusters euclidean distance is 5.060428426197632 \n",
      "average among clusters cosine similarity is 0.6102819991878232 \n",
      "average among clusters euclidean distance is 4.707763812093987\n",
      "For n_clusters = 2200 \n",
      "average between clusters cosine similarity is 0.22917542667833155 \n",
      "average between clusters euclidean distance is 5.189386435724067 \n",
      "average among clusters cosine similarity is 0.6302335833904884 \n",
      "average among clusters euclidean distance is 4.487932915839568\n",
      "For n_clusters = 2400 \n",
      "average between clusters cosine similarity is 0.22509795612846123 \n",
      "average between clusters euclidean distance is 5.244145178934603 \n",
      "average among clusters cosine similarity is 0.6395771580303115 \n",
      "average among clusters euclidean distance is 4.359222170762623\n",
      "For n_clusters = 2600 \n",
      "average between clusters cosine similarity is 0.21972627243942988 \n",
      "average between clusters euclidean distance is 5.335489908829679 \n",
      "average among clusters cosine similarity is 0.65531054599174 \n",
      "average among clusters euclidean distance is 4.177078982242871\n",
      "For n_clusters = 2800 \n",
      "average between clusters cosine similarity is 0.21512432986971536 \n",
      "average between clusters euclidean distance is 5.397892031404066 \n",
      "average among clusters cosine similarity is 0.6676556697475778 \n",
      "average among clusters euclidean distance is 4.021572218300688\n",
      "For n_clusters = 3000 \n",
      "average between clusters cosine similarity is 0.2087341120145789 \n",
      "average between clusters euclidean distance is 5.516606990054527 \n",
      "average among clusters cosine similarity is 0.6889583036285245 \n",
      "average among clusters euclidean distance is 3.791477197967287\n",
      "For n_clusters = 3200 \n",
      "average between clusters cosine similarity is 0.20819996447471692 \n",
      "average between clusters euclidean distance is 5.498206365401357 \n",
      "average among clusters cosine similarity is 0.687114284607629 \n",
      "average among clusters euclidean distance is 3.7889662460942226\n",
      "For n_clusters = 3400 \n",
      "average between clusters cosine similarity is 0.20408083258839363 \n",
      "average between clusters euclidean distance is 5.553735849766324 \n",
      "average among clusters cosine similarity is 0.7000600627809165 \n",
      "average among clusters euclidean distance is 3.6392750655921366\n",
      "For n_clusters = 3600 \n",
      "average between clusters cosine similarity is 0.2013905742825641 \n",
      "average between clusters euclidean distance is 5.595029446761155 \n",
      "average among clusters cosine similarity is 0.708951049378337 \n",
      "average among clusters euclidean distance is 3.527827379071479\n",
      "For n_clusters = 3800 \n",
      "average between clusters cosine similarity is 0.1985564771245103 \n",
      "average between clusters euclidean distance is 5.63571478605656 \n",
      "average among clusters cosine similarity is 0.7207984404764073 \n",
      "average among clusters euclidean distance is 3.390508661239286\n"
     ]
    }
   ],
   "source": [
    "range_n_clusters = np.arange(1000, 4000, 200)\n",
    "'''\n",
    "ic = []\n",
    "ie = []\n",
    "ec = []\n",
    "ee = []\n",
    "'''\n",
    "for n_clusters in range_n_clusters:\n",
    "    clusterer = KMeans(n_clusters=n_clusters, random_state=10)\n",
    "    cluster_labels = clusterer.fit_predict(X)\n",
    "    avg_internal_cosine, avg_internal_eucl = int_metr(X, cluster_labels, n_clusters)\n",
    "    avg_external_cosine, avg_external_eucl = ext_metr(clusterer.cluster_centers_)\n",
    "    ic.append(avg_internal_cosine)\n",
    "    ie.append(avg_internal_eucl)\n",
    "    ec.append(avg_external_cosine)\n",
    "    ee.append(avg_external_eucl)\n",
    "\n",
    "    print(\"For n_clusters =\", n_clusters,\n",
    "        \"\\naverage between clusters cosine similarity is\", avg_external_cosine, \n",
    "        \"\\naverage between clusters euclidean distance is\", avg_external_eucl,\n",
    "        \"\\naverage among clusters cosine similarity is\", avg_internal_cosine, \n",
    "        \"\\naverage among clusters euclidean distance is\", avg_internal_eucl)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Посмотрим на графики. Косинусная схожесть увеличивается с возрастанием количества кластеров. Значит, что векторы в одном кластере в среднем становятся сонаправлеными и более кучно расположенными т.к. евклидово расстояние уменьшается. В то же время евклидово расстояние между кластерами увеличивается и косинусная похожесть между кластерами уменьшается. Последний график показывает зависимость метрики silhoutte от количества кластеров. Нам хочется что бы это значение приближалось к 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "RO4nAXVEbQta"
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "range_n_clusters = np.arange(1000, 4000, 200)\n",
    "plt.plot(range_n_clusters, ic)\n",
    "plt.xlabel(\"n clusters\")\n",
    "plt.ylabel(\"inner cluster cosine similarity\")\n",
    "plt.show()\n",
    "plt.plot(range_n_clusters, ie)\n",
    "plt.xlabel(\"n clusters\")\n",
    "plt.ylabel(\"inner cluster euclidean distance\")\n",
    "plt.show()\n",
    "plt.plot(range_n_clusters, ec)\n",
    "plt.xlabel(\"n clusters\")\n",
    "plt.ylabel(\"outer cluster cosine similarity\")\n",
    "plt.show()\n",
    "plt.plot(range_n_clusters, ee)\n",
    "plt.xlabel(\"n clusters\")\n",
    "plt.ylabel(\"outer cluster euclidean distance\")\n",
    "plt.show()\n",
    "silhouette = []\n",
    "for i in range(len(ie)):\n",
    "    silhouette.append((ee[i] - ie[i]) / max(ee[i], ie[i]))\n",
    "plt.plot(range_n_clusters, silhouette)\n",
    "plt.xlabel(\"n clusters\")\n",
    "plt.ylabel(\"silhouette metric\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Посмотрим наконец, какие слова вошли в один кластер. Видно, что в некоторых класстерах вместе оказались взаимозаменяемые  слова (по крайней мере кажется fasttext задумывался так, что взаимозаменяемое будет лежать рядом): lenght, distance, rush; historical, cultural, historic. Но вообще выглядит, что 4000 кластеров маловато и надо считать дальше, но слишком медленно, на моей машине выходит. Принцип понятен :) С Новым Годом!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "clusterer = KMeans(n_clusters=4000, random_state=10)\n",
    "Y = clusterer.fit_predict(X)\n",
    "clust = [[] for _ in range(4000)]\n",
    "for i in range(len(X)):\n",
    "    clust[Y[i]].append(google_words[i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2971 ['historical', 'cultural', 'historic', 'adapt']\n",
      "830 ['peak', 'advent']\n",
      "3034 ['cisco', 'wrought', 'phenotype']\n",
      "2917 ['proceeds', 'willis', 'sts', 'carmel', 'listeners', 'nineteenth', 'buster', 'waking', 'approving']\n",
      "3708 ['ordinary', 'np', 'frost', 'instrumentation', 'sac', 'precedent']\n",
      "3125 ['entertaining']\n",
      "1026 ['puerto', 'woods', 'subchapter']\n",
      "3104 ['rom', 'wasted']\n",
      "3857 ['auditing', 'sigh']\n",
      "2802 ['rhetoric']\n"
     ]
    }
   ],
   "source": [
    "from random import random\n",
    "\n",
    "for _ in range(10):\n",
    "    c = int(random() * 4000)\n",
    "    print(c, clust[c])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Эксперимент заключался в разделении заданной выборки слов на кластеры по взаимозаменяемости(в одном кластере взаимозаменяемые слова). В результате, как мы видим, действительно получились кластеры слов, но разделение ещё далеко от совершенства. Для более точного результата необходимо использовать большее количество кластеров, но это заняло бы слишком много времени."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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