{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Подготовка данных"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "По причине нечитаемости файла wiki.en.vec под Windows, этот файл был отфильтрован на другой машине и результата выполнения здесь не будет. Соответственно данные лежат в отфильтрованном файле data.txt. Сначала загрузим данные и преобразуем в формат numpy.array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.cluster.vq import kmeans2\n",
    "from matplotlib import pyplot as plt\n",
    "from sklearn.metrics.pairwise import cosine_similarity, euclidean_distances\n",
    "from sklearn.cluster import KMeans"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = list(open('data.txt').read().split('\\n'))\n",
    "a = len(data)\n",
    "traindata = []\n",
    "for j in range(a):\n",
    "    i = a - j - 1\n",
    "    if data[i] is not '': \n",
    "        data[i] = data[i].split(' ')\n",
    "        traindata.append(data[i][1:-1])\n",
    "    else:\n",
    "        data.pop(i)\n",
    "traindata = np.array(traindata, dtype=np.float)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Анализ данных"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Посмотрев на гистограммы и средние можно сказать, что распределине близко к нормальному, но тем не менее отклонение от \n",
    "выборочного среднего достигает 0.25, тем не менее общее среднее очень близо к 0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(19924, 300)\n",
      "-0.045342032386438476\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.02935998801816904\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.1540862898480225\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.16802282231500706\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.1206643013014706\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.016813838235580206\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.06415388072400122\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.14503732678528405\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.0020340770753864684\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.10622762763165026\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(traindata.shape)\n",
    "\n",
    "for i in range(10):\n",
    "    print(np.mean(traindata[:, i]))\n",
    "    plt.hist(traindata[:, i], bins=100, range=(-1, 1))\n",
    "    plt.title(\"Признак {}\".format(i+1))\n",
    "    plt.xlabel(\"Значение\")\n",
    "    plt.ylabel(\"Количество элементов\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Эксперимент"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "В результате эксперимента хотлесь бы оценить точность кластеризации для различных К алгоритмом K-means. Так же хотелось бы определить оптимальное количество кластеров."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1000\n",
      "1200\n",
      "1400\n",
      "1600\n",
      "1800\n",
      "2000\n",
      "2200\n",
      "2400\n",
      "2600\n",
      "2800\n",
      "3000\n",
      "3200\n",
      "3400\n",
      "3600\n",
      "3800\n",
      "4000\n",
      "4200\n",
      "4400\n",
      "4600\n",
      "4800\n",
      "5000\n",
      "5200\n",
      "5400\n",
      "5600\n",
      "5800\n",
      "6000\n",
      "6200\n",
      "6400\n",
      "6600\n",
      "6800\n",
      "7000\n",
      "7200\n",
      "7400\n",
      "7600\n",
      "7800\n",
      "8000\n",
      "8200\n",
      "8400\n",
      "8600\n",
      "8800\n",
      "9000\n",
      "9200\n",
      "9400\n",
      "9600\n",
      "9800\n"
     ]
    }
   ],
   "source": [
    "a = len(traindata)\n",
    "half = int(a/2)\n",
    "out = []\n",
    "for k in range(1000, half, 200):\n",
    "    b = KMeans(k, random_state=10).fit(traindata)\n",
    "    print(k)\n",
    "    out.append(b)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Введем функции для оценки внутрикластерного и межкластерного расстояния двумя метриками: косинусной мерой и евклидовым расстоянием."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "def clusters(out, K, traindata):\n",
    "    clust = [[] for T in range(K)]\n",
    "    \n",
    "    Y = out.labels_\n",
    "    for i in range(len(Y)):\n",
    "        clust[Y[i]].append(traindata[i])\n",
    "    #print(clust[1])\n",
    "    return clust\n",
    "def int_dist(clust):\n",
    "    #avgeu = []\n",
    "    #avgcos = [] \n",
    "    full = 0\n",
    "    eud = 0\n",
    "    cos = 0\n",
    "    for cluster in clust:\n",
    "        #print(cluster)\n",
    "        l = len(cluster)\n",
    "        cs = cosine_similarity(cluster)\n",
    "        eu = euclidean_distances(cluster)\n",
    "        for i in range(l):\n",
    "            for j in range(i + 1, l):\n",
    "                full += 1\n",
    "                cos += cs[i, j]\n",
    "                eud += eu[i, j]\n",
    "    return eud/full, cos/full\n",
    "def ext_dist(centers):\n",
    "    cs = cosine_similarity(centers)\n",
    "    eu = euclidean_distances(centers)\n",
    "    l = len(centers)\n",
    "    full = l*(l - 1)//2\n",
    "    eud = 0\n",
    "    cos = 0\n",
    "    for i in range(l):\n",
    "            for j in range(i + 1, l):\n",
    "                cos += cs[i, j]\n",
    "                eud += eu[i, j]\n",
    "    return eud/full, cos/full"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Воспользуемся этими функциями и рассчитаем значения функционалов для всех К. Так же дополнительно для каждой метрики посчитаем отношения внутрикластерных расстояний к межкластерным."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Для K = 1000 \n",
      "Средняя косинусная схожесть между кластерами 0.2849025448291311 \n",
      "Среднее евклидово расстояние между кластерами 4.439397734072058 \n",
      "Средняя косинусная схожесть внутри кластера 0.4080731749947111 \n",
      "Среднее евклидово расстояние внутри кластеров 4.532455650912566 \n",
      "Отношение в косинусной мере 1.4323254825240364 \n",
      "Отношение в евклидовой метрике 1.0209618336573665\n",
      "Для K = 1200 \n",
      "Средняя косинусная схожесть между кластерами 0.27421467038169756 \n",
      "Среднее евклидово расстояние между кластерами 4.552870053813335 \n",
      "Средняя косинусная схожесть внутри кластера 0.41008739163780594 \n",
      "Среднее евклидово расстояние внутри кластеров 4.580229944099753 \n",
      "Отношение в косинусной мере 1.4954976371868731 \n",
      "Отношение в евклидовой метрике 1.0060093721022199\n",
      "Для K = 1400 \n",
      "Средняя косинусная схожесть между кластерами 0.2614862941105615 \n",
      "Среднее евклидово расстояние между кластерами 4.756429437679993 \n",
      "Средняя косинусная схожесть внутри кластера 0.4107335317953991 \n",
      "Среднее евклидово расстояние внутри кластеров 4.603577453396553 \n",
      "Отношение в косинусной мере 1.5707650498183776 \n",
      "Отношение в евклидовой метрике 0.9678641328992371\n",
      "Для K = 1600 \n",
      "Средняя косинусная схожесть между кластерами 0.2482574232571355 \n",
      "Среднее евклидово расстояние между кластерами 4.9626264550804695 \n",
      "Средняя косинусная схожесть внутри кластера 0.4082079256924501 \n",
      "Среднее евклидово расстояние внутри кластеров 4.512077845132141 \n",
      "Отношение в косинусной мере 1.6442929292375843 \n",
      "Отношение в евклидовой метрике 0.9092116616016744\n",
      "Для K = 1800 \n",
      "Средняя косинусная схожесть между кластерами 0.2440303831337221 \n",
      "Среднее евклидово расстояние между кластерами 4.980376520261026 \n",
      "Средняя косинусная схожесть внутри кластера 0.4196547290573161 \n",
      "Среднее евклидово расстояние внутри кластеров 4.509422978685123 \n",
      "Отношение в косинусной мере 1.7196822939353276 \n",
      "Отношение в евклидовой метрике 0.9054381652351016\n",
      "Для K = 2000 \n",
      "Средняя косинусная схожесть между кластерами 0.23569827856947473 \n",
      "Среднее евклидово расстояние между кластерами 5.1140661604978 \n",
      "Средняя косинусная схожесть внутри кластера 0.4196496306672191 \n",
      "Среднее евклидово расстояние внутри кластеров 4.509882908022253 \n",
      "Отношение в косинусной мере 1.7804526754043417 \n",
      "Отношение в евклидовой метрике 0.8818585380958903\n",
      "Для K = 2200 \n",
      "Средняя косинусная схожесть между кластерами 0.23067404800142632 \n",
      "Среднее евклидово расстояние между кластерами 5.164465381728354 \n",
      "Средняя косинусная схожесть внутри кластера 0.4233108868851542 \n",
      "Среднее евклидово расстояние внутри кластеров 4.513808809600239 \n",
      "Отношение в косинусной мере 1.835104081073467 \n",
      "Отношение в евклидовой метрике 0.8740127924121424\n",
      "Для K = 2400 \n",
      "Средняя косинусная схожесть между кластерами 0.22353829738556635 \n",
      "Среднее евклидово расстояние между кластерами 5.29062036816851 \n",
      "Средняя косинусная схожесть внутри кластера 0.42445972114451347 \n",
      "Среднее евклидово расстояние внутри кластеров 4.448559081157274 \n",
      "Отношение в косинусной мере 1.8988232714879774 \n",
      "Отношение в евклидовой метрике 0.8408388377140851\n",
      "Для K = 2600 \n",
      "Средняя косинусная схожесть между кластерами 0.22017613381027248 \n",
      "Среднее евклидово расстояние между кластерами 5.325477188015468 \n",
      "Средняя косинусная схожесть внутри кластера 0.4275225657738951 \n",
      "Среднее евклидово расстояние внутри кластеров 4.447251593716978 \n",
      "Отношение в косинусной мере 1.9417298250058959 \n",
      "Отношение в евклидовой метрике 0.8350897838272856\n",
      "Для K = 2800 \n",
      "Средняя косинусная схожесть между кластерами 0.214668255875133 \n",
      "Среднее евклидово расстояние между кластерами 5.421558799587563 \n",
      "Средняя косинусная схожесть внутри кластера 0.4305732119866381 \n",
      "Среднее евклидово расстояние внутри кластеров 4.388795906708441 \n",
      "Отношение в косинусной мере 2.005760983296438 \n",
      "Отношение в евклидовой метрике 0.809508126526694\n",
      "Для K = 3000 \n",
      "Средняя косинусная схожесть между кластерами 0.21085083006149052 \n",
      "Среднее евклидово расстояние между кластерами 5.471343355260775 \n",
      "Средняя косинусная схожесть внутри кластера 0.43500558033047637 \n",
      "Среднее евклидово расстояние внутри кластеров 4.385557996010169 \n",
      "Отношение в косинусной мере 2.063096361553879 \n",
      "Отношение в евклидовой метрике 0.8015504988904402\n",
      "Для K = 3200 \n",
      "Средняя косинусная схожесть между кластерами 0.20729483447159525 \n",
      "Среднее евклидово расстояние между кластерами 5.51006226944155 \n",
      "Средняя косинусная схожесть внутри кластера 0.4399135676367622 \n",
      "Среднее евклидово расстояние внутри кластеров 4.348034133697272 \n",
      "Отношение в косинусной мере 2.1221636745465635 \n",
      "Отношение в евклидовой метрике 0.7891079848246342\n",
      "Для K = 3400 \n",
      "Средняя косинусная схожесть между кластерами 0.20509213276523222 \n",
      "Среднее евклидово расстояние между кластерами 5.540448492694646 \n",
      "Средняя косинусная схожесть внутри кластера 0.4484134310865372 \n",
      "Среднее евклидово расстояние внутри кластеров 4.272365938787849 \n",
      "Отношение в косинусной мере 2.186399961035236 \n",
      "Отношение в евклидовой метрике 0.7711227609860779\n",
      "Для K = 3600 \n",
      "Средняя косинусная схожесть между кластерами 0.19982298125578674 \n",
      "Среднее евклидово расстояние между кластерами 5.628524176254878 \n",
      "Средняя косинусная схожесть внутри кластера 0.4408135550397838 \n",
      "Среднее евклидово расстояние внутри кластеров 4.304460383954352 \n",
      "Отношение в косинусной мере 2.2060203099237774 \n",
      "Отношение в евклидовой метрике 0.7647582650730417\n",
      "Для K = 3800 \n",
      "Средняя косинусная схожесть между кластерами 0.1977083531795413 \n",
      "Среднее евклидово расстояние между кластерами 5.636479719936874 \n",
      "Средняя косинусная схожесть внутри кластера 0.4453621652692246 \n",
      "Среднее евклидово расстояние внутри кластеров 4.2727734206999015 \n",
      "Отношение в косинусной мере 2.2526218953671924 \n",
      "Отношение в евклидовой метрике 0.7580570911284596\n",
      "Для K = 4000 \n",
      "Средняя косинусная схожесть между кластерами 0.19544628532685596 \n",
      "Среднее евклидово расстояние между кластерами 5.684078290641675 \n",
      "Средняя косинусная схожесть внутри кластера 0.4479120133687332 \n",
      "Среднее евклидово расстояние внутри кластеров 4.22190115400502 \n",
      "Отношение в косинусной мере 2.291739710579121 \n",
      "Отношение в евклидовой метрике 0.7427591489997599\n",
      "Для K = 4200 \n",
      "Средняя косинусная схожесть между кластерами 0.1932109525231684 \n",
      "Среднее евклидово расстояние между кластерами 5.705755064120349 \n",
      "Средняя косинусная схожесть внутри кластера 0.4529809039004855 \n",
      "Среднее евклидово расстояние внутри кластеров 4.225143324991399 \n",
      "Отношение в косинусной мере 2.3444887465485036 \n",
      "Отношение в евклидовой метрике 0.7405055557958455\n",
      "Для K = 4400 \n",
      "Средняя косинусная схожесть между кластерами 0.19106850336887854 \n",
      "Среднее евклидово расстояние между кластерами 5.737123508101132 \n",
      "Средняя косинусная схожесть внутри кластера 0.45399756491349724 \n",
      "Среднее евклидово расстояние внутри кластеров 4.190054484279555 \n",
      "Отношение в косинусной мере 2.3760983987874 \n",
      "Отношение в евклидовой метрике 0.7303406451618079\n",
      "Для K = 4600 \n",
      "Средняя косинусная схожесть между кластерами 0.1891143388186527 \n",
      "Среднее евклидово расстояние между кластерами 5.763458407701363 \n",
      "Средняя косинусная схожесть внутри кластера 0.4657345080261133 \n",
      "Среднее евклидово расстояние внутри кластеров 4.159529659524312 \n",
      "Отношение в косинусной мере 2.46271388481399 \n",
      "Отношение в евклидовой метрике 0.7217072398694128\n",
      "Для K = 4800 \n",
      "Средняя косинусная схожесть между кластерами 0.1873423682818134 \n",
      "Среднее евклидово расстояние между кластерами 5.804050450035903 \n",
      "Средняя косинусная схожесть внутри кластера 0.4672212122311046 \n",
      "Среднее евклидово расстояние внутри кластеров 4.076471591636492 \n",
      "Отношение в косинусной мере 2.4939431294488497 \n",
      "Отношение в евклидовой метрике 0.702349441433831\n",
      "Для K = 5000 \n",
      "Средняя косинусная схожесть между кластерами 0.1849593284598245 \n",
      "Среднее евклидово расстояние между кластерами 5.8213468838431055 \n",
      "Средняя косинусная схожесть внутри кластера 0.4616128266900252 \n",
      "Среднее евклидово расстояние внутри кластеров 4.128555234931547 \n",
      "Отношение в косинусной мере 2.4957531503489068 \n",
      "Отношение в евклидовой метрике 0.7092096240459698\n",
      "Для K = 5200 \n",
      "Средняя косинусная схожесть между кластерами 0.18390722110879276 \n",
      "Среднее евклидово расстояние между кластерами 5.82673817191359 \n",
      "Средняя косинусная схожесть внутри кластера 0.4743308675184057 \n",
      "Среднее евклидово расстояние внутри кластеров 4.0939480008803075 \n",
      "Отношение в косинусной мере 2.579185660348861 \n",
      "Отношение в евклидовой метрике 0.7026140320864619\n",
      "Для K = 5400 \n",
      "Средняя косинусная схожесть между кластерами 0.18191376308653212 \n",
      "Среднее евклидово расстояние между кластерами 5.866818908997949 \n",
      "Средняя косинусная схожесть внутри кластера 0.4679416267031479 \n",
      "Среднее евклидово расстояние внутри кластеров 4.0449995434031925 \n",
      "Отношение в косинусной мере 2.572326682509223 \n",
      "Отношение в евклидовой метрике 0.6894706664968592\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Для K = 5600 \n",
      "Средняя косинусная схожесть между кластерами 0.18180049861249498 \n",
      "Среднее евклидово расстояние между кластерами 5.856403667332999 \n",
      "Средняя косинусная схожесть внутри кластера 0.48049272337680626 \n",
      "Среднее евклидово расстояние внутри кластеров 4.024022149638105 \n",
      "Отношение в косинусной мере 2.642967027285053 \n",
      "Отношение в евклидовой метрике 0.6871148879446421\n",
      "Для K = 5800 \n",
      "Средняя косинусная схожесть между кластерами 0.17966076576974901 \n",
      "Среднее евклидово расстояние между кластерами 5.87990347280742 \n",
      "Средняя косинусная схожесть внутри кластера 0.48163132000414555 \n",
      "Среднее евклидово расстояние внутри кластеров 4.02486773481528 \n",
      "Отношение в косинусной мере 2.680781849841374 \n",
      "Отношение в евклидовой метрике 0.6845125525323574\n",
      "Для K = 6000 \n",
      "Средняя косинусная схожесть между кластерами 0.17845064848857825 \n",
      "Среднее евклидово расстояние между кластерами 5.895458467294324 \n",
      "Средняя косинусная схожесть внутри кластера 0.4848811106321581 \n",
      "Среднее евклидово расстояние внутри кластеров 4.00485909286449 \n",
      "Отношение в косинусной мере 2.717172029011668 \n",
      "Отношение в евклидовой метрике 0.6793125785012085\n",
      "Для K = 6200 \n",
      "Средняя косинусная схожесть между кластерами 0.17741622039151397 \n",
      "Среднее евклидово расстояние между кластерами 5.911856252483661 \n",
      "Средняя косинусная схожесть внутри кластера 0.4771836586682534 \n",
      "Среднее евклидово расстояние внутри кластеров 3.999087592668947 \n",
      "Отношение в косинусной мере 2.6896281389335566 \n",
      "Отношение в евклидовой метрике 0.6764521026689154\n",
      "Для K = 6400 \n",
      "Средняя косинусная схожесть между кластерами 0.17665223541837527 \n",
      "Среднее евклидово расстояние между кластерами 5.915861112232224 \n",
      "Средняя косинусная схожесть внутри кластера 0.4786066309667663 \n",
      "Среднее евклидово расстояние внутри кластеров 3.9680820718794103 \n",
      "Отношение в косинусной мере 2.7093154515325306 \n",
      "Отношение в евклидовой метрике 0.670753081689935\n",
      "Для K = 6600 \n",
      "Средняя косинусная схожесть между кластерами 0.1755403917545228 \n",
      "Среднее евклидово расстояние между кластерами 5.921379419541899 \n",
      "Средняя косинусная схожесть внутри кластера 0.4869838791646543 \n",
      "Среднее евклидово расстояние внутри кластеров 3.9345018262737503 \n",
      "Отношение в косинусной мере 2.7741984297588713 \n",
      "Отношение в евклидовой метрике 0.6644569698217614\n",
      "Для K = 6800 \n",
      "Средняя косинусная схожесть между кластерами 0.1742504097915752 \n",
      "Среднее евклидово расстояние между кластерами 5.945292009765007 \n",
      "Средняя косинусная схожесть внутри кластера 0.48765197245993175 \n",
      "Среднее евклидово расстояние внутри кластеров 3.9131442156444236 \n",
      "Отношение в косинусной мере 2.7985700179599187 \n",
      "Отношение в евклидовой метрике 0.6581920970773468\n",
      "Для K = 7000 \n",
      "Средняя косинусная схожесть между кластерами 0.1737460100098719 \n",
      "Среднее евклидово расстояние между кластерами 5.946317689940568 \n",
      "Средняя косинусная схожесть внутри кластера 0.49220249681148937 \n",
      "Среднее евклидово расстояние внутри кластеров 3.9103099128264547 \n",
      "Отношение в косинусной мере 2.832885179829588 \n",
      "Отношение в евклидовой метрике 0.6576019171396705\n",
      "Для K = 7200 \n",
      "Средняя косинусная схожесть между кластерами 0.1725583075299284 \n",
      "Среднее евклидово расстояние между кластерами 5.962314399220996 \n",
      "Средняя косинусная схожесть внутри кластера 0.4905858918150706 \n",
      "Среднее евклидово расстояние внутри кластеров 3.890658327143469 \n",
      "Отношение в косинусной мере 2.843015203599999 \n",
      "Отношение в евклидовой метрике 0.6525416250528153\n",
      "Для K = 7400 \n",
      "Средняя косинусная схожесть между кластерами 0.17179196885939632 \n",
      "Среднее евклидово расстояние между кластерами 5.963778682643595 \n",
      "Средняя косинусная схожесть внутри кластера 0.4925291962007767 \n",
      "Среднее евклидово расстояние внутри кластеров 3.8845319778988174 \n",
      "Отношение в косинусной мере 2.8670094386303284 \n",
      "Отношение в евклидовой метрике 0.651354147195969\n",
      "Для K = 7600 \n",
      "Средняя косинусная схожесть между кластерами 0.1711935698803183 \n",
      "Среднее евклидово расстояние между кластерами 5.969406355900676 \n",
      "Средняя косинусная схожесть внутри кластера 0.5003816774252424 \n",
      "Среднее евклидово расстояние внутри кластеров 3.8677644919733387 \n",
      "Отношение в косинусной мере 2.922899953398133 \n",
      "Отношение в евклидовой метрике 0.6479311779721791\n",
      "Для K = 7800 \n",
      "Средняя косинусная схожесть между кластерами 0.17056974090785768 \n",
      "Среднее евклидово расстояние между кластерами 5.976442106320828 \n",
      "Средняя косинусная схожесть внутри кластера 0.5017838011653454 \n",
      "Среднее евклидово расстояние внутри кластеров 3.8230986858281963 \n",
      "Отношение в косинусной мере 2.941810185643716 \n",
      "Отношение в евклидовой метрике 0.6396947578200073\n",
      "Для K = 8000 \n",
      "Средняя косинусная схожесть между кластерами 0.1698759342868815 \n",
      "Среднее евклидово расстояние между кластерами 5.980211433056854 \n",
      "Средняя косинусная схожесть внутри кластера 0.5088950168557493 \n",
      "Среднее евклидово расстояние внутри кластеров 3.811669723109949 \n",
      "Отношение в косинусной мере 2.995686345991436 \n",
      "Отношение в евклидовой метрике 0.6373804280631546\n",
      "Для K = 8200 \n",
      "Средняя косинусная схожесть между кластерами 0.1692126506482103 \n",
      "Среднее евклидово расстояние между кластерами 5.984205219955994 \n",
      "Средняя косинусная схожесть внутри кластера 0.5112388412394786 \n",
      "Среднее евклидово расстояние внутри кластеров 3.7839255177508875 \n",
      "Отношение в косинусной мере 3.0212802605541227 \n",
      "Отношение в евклидовой метрике 0.6323188090429013\n",
      "Для K = 8400 \n",
      "Средняя косинусная схожесть между кластерами 0.16872901583411942 \n",
      "Среднее евклидово расстояние между кластерами 5.988213693216306 \n",
      "Средняя косинусная схожесть внутри кластера 0.5230856896390906 \n",
      "Среднее евклидово расстояние внутри кластеров 3.7449243724695402 \n",
      "Отношение в косинусной мере 3.1001525555826492 \n",
      "Отношение в евклидовой метрике 0.6253825538510666\n",
      "Для K = 8600 \n",
      "Средняя косинусная схожесть между кластерами 0.16790174067994879 \n",
      "Среднее евклидово расстояние между кластерами 5.994465338634625 \n",
      "Средняя косинусная схожесть внутри кластера 0.5122957166774318 \n",
      "Среднее евклидово расстояние внутри кластеров 3.747559959775721 \n",
      "Отношение в косинусной мере 3.051163821189683 \n",
      "Отношение в евклидовой метрике 0.6251700106801038\n",
      "Для K = 8800 \n",
      "Средняя косинусная схожесть между кластерами 0.1674889808580331 \n",
      "Среднее евклидово расстояние между кластерами 5.993639125200632 \n",
      "Средняя косинусная схожесть внутри кластера 0.5223323892349716 \n",
      "Среднее евклидово расстояние внутри кластеров 3.7121150300166637 \n",
      "Отношение в косинусной мере 3.118607484260177 \n",
      "Отношение в евклидовой метрике 0.6193424316136824\n",
      "Для K = 9000 \n",
      "Средняя косинусная схожесть между кластерами 0.16661542213646227 \n",
      "Среднее евклидово расстояние между кластерами 6.001553415521553 \n",
      "Средняя косинусная схожесть внутри кластера 0.5098228971294846 \n",
      "Среднее евклидово расстояние внутри кластеров 3.7187567500824192 \n",
      "Отношение в косинусной мере 3.0598781949003895 \n",
      "Отношение в евклидовой метрике 0.6196323672575775\n",
      "Для K = 9200 \n",
      "Средняя косинусная схожесть между кластерами 0.16642368275745667 \n",
      "Среднее евклидово расстояние между кластерами 6.007278072938436 \n",
      "Средняя косинусная схожесть внутри кластера 0.5241684870103833 \n",
      "Среднее евклидово расстояние внутри кластеров 3.6711843468200467 \n",
      "Отношение в косинусной мере 3.1496027387778605 \n",
      "Отношение в евклидовой метрике 0.6111227584682627\n",
      "Для K = 9400 \n",
      "Средняя косинусная схожесть между кластерами 0.16591494509920635 \n",
      "Среднее евклидово расстояние между кластерами 6.002829226325309 \n",
      "Средняя косинусная схожесть внутри кластера 0.52404529391057 \n",
      "Среднее евклидово расстояние внутри кластеров 3.657308493477967 \n",
      "Отношение в косинусной мере 3.1585177188060123 \n",
      "Отношение в евклидовой метрике 0.6092641245629479\n",
      "Для K = 9600 \n",
      "Средняя косинусная схожесть между кластерами 0.1653749657463808 \n",
      "Среднее евклидово расстояние между кластерами 6.005208149335568 \n",
      "Средняя косинусная схожесть внутри кластера 0.5251373116133828 \n",
      "Среднее евклидово расстояние внутри кластеров 3.637343051531873 \n",
      "Отношение в косинусной мере 3.175434136861645 \n",
      "Отношение в евклидовой метрике 0.6056980809123691\n",
      "Для K = 9800 \n",
      "Средняя косинусная схожесть между кластерами 0.1651977727243326 \n",
      "Среднее евклидово расстояние между кластерами 6.006483408585621 \n",
      "Средняя косинусная схожесть внутри кластера 0.534448313112521 \n",
      "Среднее евклидово расстояние внутри кластеров 3.606380092534799 \n",
      "Отношение в косинусной мере 3.2352028983124423 \n",
      "Отношение в евклидовой метрике 0.6004145599369953\n"
     ]
    }
   ],
   "source": [
    "ic = []\n",
    "ie = []\n",
    "ec = []\n",
    "ee = []\n",
    "iec = []\n",
    "iee = []\n",
    "K = np.arange(1000, half, 200)\n",
    "for k in K:\n",
    "    i = (k-1000)//200\n",
    "    clust = clusters(out[i], k, traindata)\n",
    "    avg_ie, avg_ic  = int_dist(clust)\n",
    "    avg_ee, avg_ec  = ext_dist(out[i].cluster_centers_)\n",
    "    ic.append(avg_ic)\n",
    "    ie.append(avg_ie)\n",
    "    ec.append(avg_ec)\n",
    "    ee.append(avg_ee)\n",
    "    iec.append(avg_ic/avg_ec)\n",
    "    iee.append(avg_ie/avg_ee)\n",
    "    \n",
    "    print(\"Для K =\", k,\n",
    "        '\\nСредняя косинусная схожесть между кластерами', avg_ec, \n",
    "        '\\nСреднее евклидово расстояние между кластерами', avg_ee,\n",
    "        '\\nСредняя косинусная схожесть внутри кластера', avg_ic, \n",
    "        '\\nСреднее евклидово расстояние внутри кластеров', avg_ie, \n",
    "        '\\nОтношение в косинусной мере', iec[i], \n",
    "        '\\nОтношение в евклидовой метрике', iee[i])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Построим графики для каждого функционала и посмотрим на них:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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LewO7AMUzz5UxxjS4f3waz9GiEh65ZCgizWtt8KbCTfLYpqojAURknaqO8HJMxhhTpe92ZPDJuv3cPqkvfbs237mjGjs3bR7BIhIkIh2BKBH5t4i09nZgxhhTUX5RCfd/spHoLiHcclZfX4fTorlJHm8BicA24F5gAfClm4uLyPkisk1EEkTk7kqenyUi6SKyznncVO65mSKyw3nMdPd2jDHNVU5BMf/72Vb2HMzjkUuG0jqw5jU2jPe4GST4sIg87WxnA4jI+prOExF/4Hk8M/AmAatFZIGqxlc49F1Vva3CuZ2BvwOxeNpX1jjnHsIY02IczClg2ZZUlmxO5bsdGRSWlHL56Egm9Av1dWgtnttBgtki0tWZURegyMVpY4EEVd0FICLvANOAismjMucBX6hqpnPuF8D5wNtu4jXGNF3p2QUsWL+fJZsPELcnk1KFyE7BXHdqL84f0p3RzXzCwabCTVfdqcATQA8gDegFbAEG13BqBJ7qrjJJwLhKjrtMRCYC2/FMfZJYxbnWH8+YZi6/qIRLX/iexMyjnNKtHbdN6sd5g7sxKLy99apqZNzceTyMZ16rZao6UkTOAq5ycV5l/9JaYX8h8LaqFojIb4HXgEkuz0VEZuNM0hgV1fxnsTSmuZv7/W4SM48yb9YYzhrQ1dfhmGq4aTAvUtWDgJ+I+Knq14Cb7rpJQM9y+5HA/vIHqOpBVS1wdl8GRrs91zl/jqrGqmpsWFiYi5CMMY1VenYB//p6J+cM7GaJowlwkzwOi0hbYAXwlog8AxS7OG810E9EYkQkCJiBp6fWMSISXm53Kp7qMIAlwLki0slpZznXKTPGNFNPLdtOflEJ9144wNehGBfcVFtNA/KBO4FrgA7AQzWdpKrFInIbnl/6/sBcVd0sIg8Bcaq6ALjdaVMpBjKBWc65mSLyMJ4EBPBQWeO5Mab52XYgm3dW7WPmadH0DrOBf02BqJ7QlNAkxcbGalxcnK/DMMbUkqpy/dxVbEg6wjd/PpOOITbJYUMSkTWqGlvb89z0tsrG01gdDBzF05itqtq+1lEaY0wFy7en8+2ODP528SBLHE2Im0GC7QBE5OeyOa6MMaY+FJeU8o9PtxDdJYTrxvfydTimFmqznkfzqN8yxjQab69OJCEth3suHGhLyDYxbqqtRjmbwSIyEmcMhqqu9WZgxpjmLSu/iKe+2M743p05d1A3X4djaslNb6snnJ8HgCedbcUzmM8YY+rk+a8SOJRXyP0XDbLR402QmzaPsxoiEGNMy7HvYB7zvt/DZaMiGRLRwdfhmDqosZJRRB511vIo2+8kIo94NyxjTFOQmJnHog37yS1wM24YikpKWbh+P795PQ5/P+HP553i5QiNt7iptrpAVe8t21HVQyJyIXC/98IyxjR2ezJyuXLOj6RmFRAc6M8FQ7rzX6MiOK1PKP5+x1dDHckr4u3V+3jthz2kHMknuksIT105gm7tbV25pspN8vAXkVZlc1CJSDDQyrthGWMas8TMPK5++ScKi0t59qqR/Lgzg0UbUvjo52S6tW/FJSMjuHRkJAH+wr+/38MHa5I4WlTCaX268PC0IUwa0BU/P2vnaMpqHGEuIn/BM+/UPDwN5TcCC1T1Me+H556NMDemYaQcOcoVL/3ouZuYPZ7BPTxtFvlFJXy5JY2Pf05i+bZ0iks9v1uC/P2YNqIHN5wew6AeNra4sanrCHNX05OIyPnAOXi66S5V1UY3SaElD2O8Ly0rnyvn/ERGdgFv3jSO4T07VnrcwZwCFm1IIa+whOmjIwlrZ5UVjZU3pye5DXhLVT+vU2TGmGYhI6eAq19ZSWpWPm/8emyViQOgS9tWzDwtuuGCMw3OzZDO7njWH39PRM4X65BtTItzKLeQa19ZSdKhPObNGsPoXp19HZLxsRqTh6reD/QDXsUzZfoOp/tuHy/HZozxsez8ItYnHua6uSvZlZHLK9ePYVzvLr4OyzQCbnpboaoqIgfwjDIvBjoBH4jIF6r6F28GaIzxvtJSZcWOdHak5rArI5dd6Z6f6dmehT4D/YU518UyoV+ojyM1jYWbNo/bgZlABvAK8GdVLRIRP2AHYMnDmCbu2a928PSyHQB0Cgmkd1hbzuwfRkxYG3qHtmVoZAciOgb7OErTmLi58wgFLlXVveULVbVURC72TljGmIZyMKeAl1fsYvKgbjx22TA6tbE1NUzN3CSPVwBEJKp8oaruU9UtlZ9ijGkqnv96J0eLSvjr+QMscRjX3PS2+tR5bAEWOduLvBmUMaZq89clM+GfX/HN9vSTvlby4aO8+dNeLh/dk75dbe1w456bWXWHgq0kaIyv5RUW8/f5m3l/TRJ+Ag/M38TSOyfSKsC/ztd8+ovtIPCHc/rVY6SmJbCVBI1pArakZDHlue/4YG0Sv5/Ul1dnjmHvwTz+/f2eOl8zIS2bD9cmcd34XvSwxnBTS256W13qbHYst42qfuS1qIwxAKgqb67cx8OL4ukQHMibvx7H6X093WXPHtCV575K4NJRdZv+44ml2wkO9OeWM23Ilqk9N3ceU5zHN+W2rZeVMV52JK+I3725lr99sonxvbvw2R/OOJY4AO67aCAFxSU8vmRbra+9Iekwn206wE1n9KZLW5t3ytSemzaPG+p6cWdCxWcAf+AVVf3fKo6bDrwPjFHVOBEJxNPLa5QT4+uq+j91jcOYpiI1K58fdx7kh50ZfLU1ncN5hdx74QBumtD7hCnMe4e1Zeap0bz6/W6uO7VXrVbk+39LttEpJJCbzoip77dgWgg31VbPVlauqrfXcJ4/8DwwGUjCMz/WAlWNr3BcO+B2YGW54suBVqo6VERCgHgReVtV99QUrzFNyZG8In7YmcEPTsLYmZ4LQIfgQMb37szvzuzLiGomIPz92f346OdkHloYz7s3j3e1FvgPOzP4dkcG9180kHatA+vtvZiWxc04j4uBLOAFIL8W1x4LJKjqLgAReQeYBsRXOO5h4DHgT+XKFGgjIgFAMFDoxGBMs5FfVMJ5T6/gQFY+bYL8GRvTmRljoji1TxcGhrc/YTW+ynQIDuSuc/tz38ebWLzxABcNC6/2eFXlsc+3Ed6hNdeO71Vfb8W0QG6SR3/gZuAm4CVgrqqWujgvAkgst58EjCt/gIiMBHqq6iIRKZ88PsCTaFKAEOBOVc2s+AIiMhuYDRAVFVXxaWMatWVbUjmQlc+TVwxnyvAeBPrXpvPjL2aMieKNH/fy6OItnD2wK60Dq+66+0V8KusSD/O/lw6t9jhjauJmVt1iVX0emAiEAT84bRQ1qezPpmPdfZ25sZ4C7qrkuLFACdADiAHuEpHelcQ2R1VjVTU2LCzMRUjGNB7z1+2nW/tWTBsRUefEAeDvJzwwZRDJh4/yyre7qjyupFR5fOk2eoe2YfroyDq/njHgrs1jI7/80hegA/Aunkbw6iQBPcvtRwL7y+23A4YAy5162u7AAhGZClwNfK6qRUCaiHwPxAJV/88wpgk5klfE8m1pzDw12lX1VE1O6xPKeYO78a/lO7k8tifd2rcGoLiklFW7M/l88wGWbD5AalYB/3f1SAJOIlkZA+7bPOpiNdBPRGKAZGAGnqQAgKoewTPpIgAishz4k9Pb6mxgkoi8iafaajzwdB3jMKbR+WxTCkUlyrQREfV2zfsuHMQ5T37D/yzewtQRPfh80wG+iE/lUF4RrQP9+FX/MKYOj+DCod3r7TVNy+UmeYQDm1U1G471jhoE7K3uJFUtdpawXYLnLmWuqm4WkYeAOFVdUM3pzwPzgE147nbmqeoGF7Ea0yR8si6Z3qFtGBLRvt6uGdUlhBsnxPDiNzv5ZN1+2rUKYNLArlwwpDsT+4cREuRq+R5jXHHzbXoBz3iLMrmVlFVKVRcDiyuUPVDFsWeW287B013XmGYn5chRVu7O5A9n93PVtbY2bj+7LyFB/gyN6MBpfbuc1LxXxlTHTfIQVT3W0O2s42F/whhTR4vWp6BKvVZZlQkJCuD2s22SQ+N9blrNdonI7SIS6Dz+gDVcG1Nn89cnMzyyAzGhbXwdijF15iZ5/BY4DU+jdzKesRqzvRmUMU3Nqt2ZbEo+UuNxCWk5bErOYqoX7jqMaUhu5rZKw9NTyhhTicLiUma/EYe/CEvunEhoNRMNLliXjAhMqWEkuDGNXY13HiISKSIfi0iaiKSKyIciYiOMjHF8l5DO4bwiDuYWcveHGynXRHgcVWX++v2c1qcLXZ1xGMY0VW6qreYBC/CM9o4AFjplxhhgwbr9dAgO5C/nn8KyLam8H5dU6XHrk46w92Ae04ZblZVp+twkjzBVnedMU1Ksqv/GM02JMS3e0cISlsancsGQ7vx2Yh/G9+7Mgws3k5iZd8Kx89clExTgx/k2SM80A26SR4aIXCsi/s7jWuCgtwMzpin4cmsqeYUlTB3eAz8/4fHLh+Mnwl3vraek9Jfqq5JSZeH6FCad0pX2Ng26aQbcJI8bgSuAA3hmuZ3ulBnT4i1Yt5+u7VoxrncXACI7hfDfUwezak/mcZMU/rAzg4ycAqaN6OGrUI2pV25m1d2nqlNVNUxVu6rqJUBqA8RmTKN25GgRy7elc9Gw8OMmN7x0VATnD+7OE0u3syXFswzNfGe6kLMGdPVVuMbUKze9rR6osH8OnkkPjWnRlm4+QGFJKVOHH383ISI8eulQ2gcHcue768jKL+LzTQc4b0h3W0PDNBtuqq26i8iLIhIqIq8Bf8GzUJMxLdqC9fuJ6hxS6TKxndsE8dj0oWw9kM11r6wkp6DYqqxMs+Km2uoWPOtwJAI/quq5ZUvLGtNSZeQU8MPOg0wZHl7l5IaTBnTjqrFRrE86QmjbVpzqtIsY0xy4WQzqUjxToy8DrhWRNABV/cjLsRnToFSVzfuzCPAXBnSvfqr0xRtTKClVptYwZuP+iwby875DnDe4uy3AZJoVN7PjTnF+ZjiPKXhWFrTkYZo8VSU+JYtPN6Tw6cYU9h7Mo3WgHx/fcjoDw6tOIAvW7eeUbu04pXu7aq/fplUAn98xsb7DNsbn3MxtdUNDBGJMQ1FVth7IPpYwdmfk4u8nnNanCzdNiOG5rxL47ZtrWHDrBDqEnDgmI/nwUeL2HuLP553ig+iNaRxsXQ7T4rzwzU4e+3wbfuJZ+3v2xN6cN7g7ndsEATCoR3tmzPmJO979mVdnjsGvwhrjC9fvB2DKMGsANy2XJQ/TohSXlDLv+z2c1qcLz141stIZcEf36swDFw/ib/M38+xXO7jjnP7HPb9g3X5G9OxIVJeQhgrbmEbHWvBMi7JiRzrp2QXMPC262qnTrx3fi8tGRfL0sh18ueWXMbEJaTnEp2SdMLbDmJbGTW+rqtYcf6j+wzHGuz5Yk0SXNkFMqmGkt4jwj/8awtYDWdzx7joW3jaB6NA2LFi/Hz+Bi209DtPCubnzmA3kALnAb5yfud4MyhhvOJRbyLL4NKaNiCDQRbfZ1oH+vHjtaPz9hJvfWENuQTEL1+9nfG9bj8MYN8kjXVWfVNUngHzgLWfbmCZlwfr9FJaUMn20+7XMenYO4dkZI9mels11r65kd0auVVkZg7vkISLyXyIyEygAPhaRM91cXETOF5FtIpIgIndXc9x0EVERiS1XNkxEfhSRzSKyUUTsTz1zUj5Yk8TgHu0Z1KP6AYAVTewfxp/OPYW1+w4T6C9cMMSqrIxx09vqN8BfgRLgcjwz6s4Dlld3koj4A88Dk4EkYLWILFDV+ArHtQNuB1aWKwsA3gSuU9X1ItIFKHL5now5wdYDWWxMPsLfpwyq0/m3nNmHlCNHCQkKqHTshzEtjZtBgqvxrOFRnpuJEccCCWXzYInIO8558RWOexh4DPhTubJzgQ2qut6JwRafMiflg7gkAv2FaSPqtgSsiPDIJUPrOSpjmi5X4zxE5CJgMHCs6shFb6sIPJMplkkCxlW47kigp6ouEpHyyaM/oCKyBM+St++o6mNuYjWmoqKSUj5Zl8zZA7odGwhojDk5brrqvgiEAGcBr+C5C1nl4tqVTTV6bF1OEfEDngJmVRHXBGAMkAd8KSJrVPXLCrHNxtMbjKioKBchmZZo+bZ0MnIKuTzWfUO5MaZ6bho1IjXOAAAXoElEQVTMT1PV64FDqvogcCrQ08V5SRWOi8QztXuZdsAQYLmI7AHGAwucRvMk4BtVzVDVPGAxMKriC6jqHFWNVdXYsLAwFyGZluj9uERC27biV/3tO2JMfXGTPI46P/NEpAeehusYF+etBvqJSIyIBAEzgAVlT6rqEVUNVdVoVY0GfgKmqmocsAQYJiIhTuP5rzixrcSYGh3MKeCrrWlcOirCpkQ3ph65afNYJCIdgf8HrMVT9fRKTSeparGI3IYnEfgDc1V1s4g8BMSp6oJqzj0kIk/iSUAKLFbVT13EasxxPlm3n+JSrdXYDmNMzURVaz6q7GCRVkBrVT3ivZDqJjY2VuPi4nwdhmlkLnjmW4L8hfm3TfB1KMY0Sk57cmzNRx7PTYP59ZWUoaqv1/bFjGlIm5KPsCUli4enDfZ1KMY0O26qrcY4P68A3nO2FbDkYRq1D9YkEeTvV+NSscaY2nMzSPD3ACIyoWzbmMausLiU+euSmTy4m40IN8YLarMYlPvGEWN85MjRItbuO8TSzakcyiuyhnJjvMRNm8dzeBJHpIg8W1auqrd7MzBj3Nh3MI/VezKJ23uItXsPsT0tG1Xw9xPOGdiNif1sbIcx3uDmzqOsC9MabwZiTG09s2wHTy3bDkC71gGMiurExcPCGR3dieGRHWnTylZZNsZb3LR5vOYM8huA5w5km6oWej0yY6rxXlwiTy3bzrQRPfjdmX3o37Udfn6VzYhjjPEGN9VWFwIvATvxzFcVIyI3q+pn3g7OmMp8tyODez/ayBn9Qnn88uGuVgU0xtQvN/f1TwJnqWoCgIj0AT4FLHmYBrclJYvfvrmGvl3b8q9rRlniMMZH3PzPSytLHI5dQJqX4jGmSgeO5HPDvNW0bRXAvBvG0K61dcE1xlfc3HlsFpHFeAYIKp7VBFeLyKUAqvqRF+MzBoDs/CJu+PdqcgqKee/mUwnvEOzrkIxp0dwkj9Z4lp79lbOfDnQGpuBJJpY8jFcVlZRy639+ZntqNvNmjan1GuTGmPrnprfVDQ0RiGn6DucVctNrcdz8qz5MHtStXq6pqtz/8SZWbE/nscuGMdHW5DCmUaixzUNE+ovIlyKyydkfJiL3ez8009S8tGIXcXsPcf8nG8ktKD7p6207kM11r67i3bhEbp/UlyvGuFmDzBjTENw0mL8M3INnEShUdQOehZ2MOSYtO59/f7+H4ZEdSM0q4PmvE2o+qQqHcgt5YP4mLnhmBRuTj/Dg1MHcObl/PUZrjDlZbto8QlR1lchxA7BO/s9K06z86+udFJaU8vSMkTz35Q5e+XY3V47pSa8ubVxfo6iklLd+2stTy3aQU1DMteN7cec5/enUJsiLkRtj6sLNnUeGM7ZDAURkOpDi1ahMk5J8+Cj/WbmPy0dHEhPahr9eMIAAf+GRT7e4vsa3O9K58Jlv+e+F8QyJaM/i28/goWlDLHEY00i5ufO4FZgDDBCRZGA3cI1XozJNyrPLdgDw+7P7AdCtfWtum9SXxz7fxrc70jmjhskJ56zYyaOLt9KrSwhzrhvN5EHdqHCna4xpZNzceeSp6jlAGDBAVSeo6l4vx2WaiN0ZuXywNomrx0UR0fGXsRe/nhBDry4hPLgwnqKS0irPn/f9bh5dvJWLhoWz9M6JnDu4uyUOY5oAN8ljMYCq5qpqtpfjMU3MU19sJ8jfj1vP6ntceasAf+6/aBAJaTm88WPlf2u8tXIvDy6M57zB3Xj6yhG0CvBviJCNMfXAJgYydbYlJYsF6/dzw+nRhLVrdcLz5wzsyhn9Qnlq2XYO5hQc99z7cYnc9/EmJg3oynNX2RxVxjQ1bv7HDhORrHKPbBHJ8npkptF7Yul22rUO4OaJfSp9XkT4+5RBHC0s4fGl24+Vz1+XzF8+3MAZ/UL51zWjCAqwxGFMU+Pmf+1GVW1f7tFOVV3NDyEi54vINhFJEJG7qzluuoioiMRWKI8SkRwR+ZOb1zMN5+d9h1i2JZXZZ/Sudo3wvl3bcf2p0byzeh+bko+weGMKf3xvPeNiOjPnulhaB1pVlTFNkdeWWhMRf+B5YDKQhGcyxQWqGl/huHbA7cDKSi7zFDb1e6P0xNLtdG4TxA0TYmo89g/n9OOTdcn8/u2fSczMY2TPjrw6cwzBQZY4jGmq3Nx5XFbHa48FElR1l7Py4DvAtEqOexh4DMgvXygil+CZ/n1zHV/feMkPOzP4LiGDW87sQ1sXS712CA7kT+eewu6MXAZHdGDeDWNsiVhjmjg3yePvItKxbEdEOonIXBfnRQCJ5faTnLJjRGQk0FNVF1UobwP8FXjQxeuYBlRcUspjn2+je/vWXDu+l+vzZozpyQvXjOKNX4+1dTiMaQbc/Pk3TFUPl+2o6iHnl35NKuusr8eeFPHDUy01q5LjHgSeUtWc6vr8i8hsYDZAVFSUi5DMyVBV7v9kE+sSD/PkFcNr1V7h5ydcMDTci9EZYxqSm+ThJyKdVPUQgIh0dnleElB+GtRIYH+5/XbAEGC5kyC6AwtEZCowDpguIo8BHYFSEclX1f8r/wKqOgfP6HdiY2MV41VPfbGdd1YncttZfbl0VKSvwzHG+JCbJPAE8IOIfODsXw78w8V5q4F+IhIDJOOZiffqsidV9QgQWrYvIsuBP6lqHHBGufL/BnIqJg7TsN74aS/PfpXAFbGR3HWuzXBrTEvnZjGo10VkDXAWnqqoSyv2mKrivGIRuQ1YAvgDc1V1s4g8BMSp6oKTjN00kM83pfDA/E2cPaArj/7XUJs+xBiDqLqr7RGRrniWpAVAVfd5K6i6iI2N1bi4OF+H0eys3HWQ6+auYnCP9vznpvHWvdaYZkZE1qhqbM1HHs/NSoJTRWQHntl0vwH2YGMvWoStB7K46fU4enYKZq6NyzDGlOOmq+7DwHhgu6rGAGcD33s1KuNzyYePMnPuKkKC/Hn91+NsXQ1jzHHcJI8iVT2Ip9eVn6p+DYzwclzGh9Ky87nu1ZXkFZbw2o1jj5tq3RhjwF1vq8Mi0hZYAbwlImnYMrTNVlp2PlfN+YkDR/J57caxDOjuahozY0wL4+bOYxpwFLgT+BzYCUzxZlDGN9Ky87n65ZWkHMln3qwxjInu7OuQjDGNlJs7j1bOA2ChF2MxPpSeXcDVL68k+dBR/n3DGMb17uLrkIwxjZib5JGCZ5Cf4JlepOxnby/GZRpQenYBV738kyUOY4xrbpJHvKq6mcvKNEHlE8c8SxzGGJfcJI8OIjINKMAzN1W8qlqDeTPgqaryJI65s8Yw3hKHMcYlN8njGzxregQDPYBeIvIbVbWBgk3Ymr2HuPPddaRl5zNv1lhO7WOJwxjjnpu5rW4ovy8ifYFPsFHmTVJhcSnPfLmdF5bvJLxDMG/dNI7RvaxXlTGmdmq9nJuqJojIZG8EY7xr24Fs7nx3HfEpWVwRG8nfLh5kCzMZY+rEzdxWD1TYnwws9VpEpt6VlCovr9jFlOe+IzUrnznXjeax6cMtcRhj6szNnUd3EXkRuB/P2h7hVL4WuWmEEjPzuOv99azancm5g7rx6KVDCW3bquYTjTGmGm7aPG5x7j4SgTtV9UXvh2VOlqrywZokHlzoWXrl8cuHc9moCFuLwxhTL2pMHiJyKbAJWAZc68xthap+5OXYTB0dzCngno82sjQ+lfG9O/P45cOJ7BTi67CMMc2Im2qrsnmsMpzHFDwjzC15NELL4lO5+6MNZB0t5v6LBnLj6TH4+dndhjGmftW6q65pnHIKinlkUTzvrE5kYHh73rppBKd0b+frsIwxzZSbaqv+wAtAN1UdIiLDgKmq+ojXozM1ysgp4PuEDB5fuo3kQ0e55cw+3HFOf4IC3EyYbIwxdeOm2upl4M/ASwCqukFE/gNY8vCBrPwiVu3K5IedB/lhZwZbD2QDENU5hPduPpVYm0bdGNMA3CSPEFVdVaGXjs1t1cA+25jCSyt2sTH5CCWlSqsAP8ZEd+bP5/Xg9L6hDOnRngB/u9swxjQMN8kjQ0T64GkkR0Sm45mm3TSA0lLlqWXbee6rBPp3a8stZ/bhtD6hjIzqSOtAf1+HZ4xpodwkj1uBOcAAEUkGdgPXeDUqA0BuQTF/fG8dSzanckVsJI9cMtTaMowxjUKNv4lUdZeqngOEAQNUdYKq7nVzcRE5X0S2iUiCiNxdzXHTRURFJNbZnywia0Rko/Nzkts31FwkHcpj+os/8kV8Kn+7eBD/vGyYJQ5jTKPhprdVF+DvwARAReQ74CFVPVjDef7A88BkIAlYLSILVDW+wnHtgNuBleWKM4ApqrpfRIYAS4AI92+raVuzN5Ob31hDQVEpc2eN4cxTuvo6JGOMOY6bP2XfAdLxrOkx3dl+18V5Y4EE586l0LlOZXNiPQw8BuSXFajqz6q639ndDLQWkRYxIdP7cYlcNWclbVsF8PGtp1viMMY0Sm7aPDqr6sPl9h8RkUtcnBeBZz6sMknAuPIHiMhIoKeqLhKRP1VxncuAn1W1oOITIjIbmA0QFRXlIiTf+2prKne8s46SUj1WVr4nW05BMaf37cLzV4+iY0iQL0I0xpgauUkeX4vIDOA9Z3868KmL8yqbE+PYb0wR8QOeAmZVeQGRwcA/gXMre15V5+BpzCc2NlYrO6axeXnFboKD/JkyrMexsvKBh3dozczTogm0brfGmEbMTfK4Gfgj8Iaz7w/kisgfAVXV9lWclwT0LLcfiWcN9DLtgCHAcucv7+7AAhGZqqpxIhIJfAxcr6o73b6hxmzvwVx+3HWQuyb35/dn9/N1OMYYU2du5raq6wRJq4F+IhIDJAMzgKvLXfcIEFq2LyLLgT85iaMjnrube1T1+zq+fqPzflwSfgLTYyN9HYoxxpwUNysJLqrLhVW1GLgNT0+pLcB7qrpZRB4Skak1nH4b0Bf4m4iscx5NuuW4pNSzvsbE/mGEdwj2dTjGGHNS3FRb9aj5kMqp6mJgcYWyB6o49sxy24/QzObOWrEjnQNZ+fx9yiBfh2KMMSfNTfLoLSILKhaqak13D6ac91Yn0rlNEGcP7ObrUIwx5qS5SR7peNYuN3V0MKeAZVtSuf7UaBslboxpFtwkjxxV/cbrkTRjH/+cTFGJcuWYnjUfbIwxTYCbP4Mf9XoUzZiq8u7qREb07Ej/braynzGmeXCTPP4qIreKSCevR9MM/Zx4mB1pOXbXYYxpVtwkjxl4elytFpF3ROQ8qbAylKnae6sTCQ705+Jh4b4OxRhj6o2bKdkTVPU+oD/wH2AusE9EHhQRW/O0GrkFxSxcv5+LhoXTrnWgr8Mxxph646rrj4gMw9Pj6v8BH+KZ3yoL+Mp7oTV9izemkFtYYlVWxphmx816HmuAw8CrwN3lZrddKSKnezO4xqCkVNl/+Ci7MnLZk5HLbuex52AumTmFXD0uilsn9aV9JXcW78Ul0ju0DbG9rLnIGNO8uOmqe7mq7qrsCVW9tJ7jaTQSM/N49bvdvB+XSG5hybHyNkH+RIe2YUhEB1CY8+0uPliTxF3nnsKVY3ri7+dpDtqZnsPqPYf46/kDsCYiY0xz4yZ5XFvZLz9Vfaj+w/G9DUmHmbNiF4s3puAnwpThPRgX05mY0DbEhLYhrF2r45LBxqQjPLRoM/d+vJHXf9zDAxcP4rS+obwXl4i/n3DZ6BazAKIxpgVxkzxynZ93AE97MRafKS1Vlm9PY86KXfy0K5N2rQL4zRm9mXV6dI2TGA6N7MB7N5/KZ5sO8OjiLVz9ykomD+rGz/sOc9YpXenarnUDvQtjjGk4bqZkfwJARK4t225OEjPzuPHfq9mRlkN4h9bcd+FAZoztWaveUSLChUPDmTSgK69+t5t/fZ1gDeXGmGbNzZ1HmSaxUl9thXdoTVTnEG45qw8XD+txUiv4tQ7059az+nL56EhW7s7k7AFNehZ5Y4ypkqhWnxNEZCGexDERWFFW3thm1Y2NjdW4uDhfh2GMMU2KiKxR1djanufmzuNx52ezq7IyxhhTN27aPI7NqCsiocBBrel2xRhjTLNWZQW/iIwXkeUi8pGIjBSRTcAmIFVEzm+4EI0xxjQ21d15/B9wL9ABzzQkF6jqTyIyAHgb+LwB4jPGGNMIVde1KEBVl6rq+8ABVf0JQFW3NkxoxhhjGqvqkkdpue2jFZ6zNg9jjGnBqqu2Gi4iWYAAwc42zr4NmzbGmBasyuShqv4NGYgxxpimo8ZBgk2FiKQDe30dRz0IBTJ8HUQjY59J5exzOZF9Jieq6TPppaphtb1os0kezYWIxNVltGdzZp9J5exzOZF9Jify1mdS94mcjDHGtFiWPIwxxtSaJY/GZ46vA2iE7DOpnH0uJ7LP5ERe+UyszcMYY0yt2Z2HMcaYWrPk4WUi0lNEvhaRLSKyWUT+4JR3FpEvRGSH87OTUy4i8qyIJIjIBhEZVe5aM53jd4jITF+9p/oiIv4i8rOILHL2Y0RkpfP+3hWRIKe8lbOf4DwfXe4a9zjl20TkPN+8k/ojIh1F5AMR2ep8Z05t6d8VEbnT+b+zSUTeFpHWLe27IiJzRSTNmaC2rKzevhciMlpENjrnPCsiUmNQqmoPLz6AcGCUs90O2A4MAh4D7nbK7wb+6WxfCHyGZyT/eGClU94Z2OX87ORsd/L1+zvJz+aPwH+ARc7+e8AMZ/tF4HfO9i3Ai872DOBdZ3sQsB5oBcQAOwF/X7+vk/xMXgNucraDgI4t+bsCRAC7geBy35FZLe27gmcxvlHApnJl9fa9AFYBpzrnfIZnItzqY/L1h9LSHsB8YDKwDQh3ysKBbc72S8BV5Y7f5jx/FfBSufLjjmtqDyAS+BKYBCxyvrQZeCbkxPkiL3G2lwCnOtsBznEC3APcU+6ax45rig+gvfOLUiqUt9jvipM8Ep1feAHOd+W8lvhdAaIrJI96+V44z20tV37ccVU9rNqqATm30COBlUA3VU0BcH6WLXhe9p+lTJJTVlV5U/U08Bd+mYCzC3BYVYud/fLv79h7d54/4hzf3D6T3kA6MM+pzntFRNrQgr8rqpqMZzXTfUAKnn/7Ndh3BervexHhbFcsr5YljwYiIm2BD4E7VDWrukMrKdNqypscEbkYSFPVNeWLKzlUa3iu2XwmjgA8VRMvqOpIIBdPdURVmv3n4tTjT8NT1dQDaANcUMmhLe27Up3afgZ1+mwseTQAEQnEkzjeUtWPnOJUEQl3ng8H0pzyJKBnudMjgf3VlDdFpwNTRWQP8A6eqqungY4iUjZZZ/n3d+y9O893ADJpXp8JeN5PkqqudPY/wJNMWvJ35Rxgt6qmq2oR8BFwGvZdgfr7XiQ52xXLq2XJw8ucXguvAltU9clyTy0Ayno7zMTTFlJWfr3TY2I8cMS5JV0CnCsinZy/xs51ypocVb1HVSNVNRpPo+ZXqnoN8DUw3Tms4mdS9llNd45Xp3yG08MmBuiHp+GvSVLVA0CiiJziFJ0NxNOCvyt4qqvGi0iI83+p7DNp0d8VR718L5znssWz9LgA15e7VtV83QjU3B/ABDy3gBuAdc7jQjz1sF8CO5yfnZ3jBXgeT2+QjUBsuWvdCCQ4jxt8/d7q6fM5k196W/XG8x86AXgfaOWUt3b2E5zne5c7/z7ns9qGix4ijf0BjADinO/LJ3h6xbTo7wrwILAV2AS8gafHVIv6ruBZ+jsFKMJzp/Dr+vxeALHO57sTzxLkUlNMNsLcGGNMrVm1lTHGmFqz5GGMMabWLHkYY4ypNUsexhhjas2ShzHGmFqz5GGMF4lITrntC53ZTKN8GZMx9SGg5kOMMSdLRM4GngPOVdV9vo7HmJNlycMYLxORM4CXgQtVdaev4zGmPtggQWO8SESKgGzgTFXd4Ot4jKkv1uZhjHcVAT/gmU7CmGbDkocx3lUKXAGMEZF7fR2MMfXF2jyM8TJVzXPWMPlWRFJV9VVfx2TMybLkYUwDUNVMETkfWCEiGapa85TXxjRi1mBujDGm1qzNwxhjTK1Z8jDGGFNrljyMMcbUmiUPY4wxtWbJwxhjTK1Z8jDGGFNrljyMMcbUmiUPY4wxtfb/AToW9vUrnFdRAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "K = np.arange(1000, 10000, 200)\n",
    "plt.plot(K, ic)\n",
    "plt.xlabel(\"K\")\n",
    "plt.ylabel(\"Внутрекластерная косинусная схожесть\")\n",
    "plt.show()\n",
    "plt.plot(K, ie)\n",
    "plt.xlabel(\"K\")\n",
    "plt.ylabel(\"Внутрекластерное евклидово расстояние\")\n",
    "plt.show()\n",
    "plt.plot(K, ec)\n",
    "plt.xlabel(\"K\")\n",
    "plt.ylabel(\"Межкластерная косинусная схожесть\")\n",
    "plt.show()\n",
    "plt.plot(K, ee)\n",
    "plt.xlabel(\"K\")\n",
    "plt.ylabel(\"Межкластерное евклидово расстояние\")\n",
    "plt.show()\n",
    "plt.plot(K, iec)\n",
    "plt.xlabel(\"K\")\n",
    "plt.ylabel(\"Отношение косинусных критериев\")\n",
    "plt.show()\n",
    "plt.plot(K, iee)\n",
    "plt.xlabel(\"K\")\n",
    "plt.ylabel(\"Отношение евклидовых критериев\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "По графикам заметно, что где-то в районе К=5000 межкластерные расстояния меняются слабо, таким образом я предполагаю именно К=5000 наиболее оптимальным. Такое число достаточно хорошо соответствует интуитивному представлению, так как это около 4 слов на кластер в среднем. Интересно было бы посмотреть, что из себя представляют такие кластеры:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Кластер № 560\n",
      "parental\n",
      "grandparents\n",
      "maternal\n",
      "fathers\n",
      "pregnant\n",
      "generations\n",
      "relatives\n",
      "childhood\n",
      "parents\n",
      "child\n",
      "children\n",
      "family\n",
      "\n",
      "\n",
      "Кластер № 1750\n",
      "gratuite\n",
      "gratuit\n",
      "\n",
      "\n",
      "Кластер № 2285\n",
      "htdocs\n",
      "\n",
      "\n",
      "Кластер № 3237\n",
      "aussie\n",
      "outback\n",
      "australasia\n",
      "kangaroo\n",
      "australians\n",
      "darwin\n",
      "tasmania\n",
      "victoria\n",
      "wales\n",
      "australian\n",
      "australia\n",
      "\n",
      "\n",
      "Кластер № 4560\n",
      "disasters\n",
      "disaster\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "import random\n",
    "random.seed()\n",
    "best = out[20]\n",
    "for i in range(0,5):\n",
    "    p = random.randint(i*1000, (i + 1)*1000)\n",
    "    print(\"Кластер №\", p)\n",
    "    for j in range(0, len(traindata)):\n",
    "        if best.labels_[j] == p:\n",
    "            print(data[-j - 1][0])\n",
    "    print('\\n')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Как можно легко заметить, слова в одном кластере достаточно хорошо связаны по смыслу, а значит в этом плане кластеризация оказалась достаточно успешной. Посмотрим распределение количество слов по кластерам:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Кластеров с одним элементом: 1732\n"
     ]
    }
   ],
   "source": [
    "K = 5000\n",
    "arr =  out[int((K-1000)/200)].labels_\n",
    "num = 0\n",
    "for i in range(0, K):\n",
    "    if i not in arr:\n",
    "        num += 1\n",
    "plt.hist(arr, bins=K, range=(0, K))\n",
    "plt.title(\"K = {}\".format(K))\n",
    "plt.xlabel(\"Номер кластера\")\n",
    "plt.ylabel(\"Количество элеменктов в кластере\")\n",
    "plt.show()\n",
    "clust = clusters(out[int((K-1000)/200)], K, traindata)\n",
    "\n",
    "single = 0\n",
    "for cluster in clust:\n",
    "    if len(cluster) == 1:\n",
    "        single += 1\n",
    "print(\"Кластеров с одним элементом:\", single)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Видно, что распределение по кластерам достаточно неравномерно: присутствуют кластеры как с большим количеством элементов (до 20), один огромный кластер, в который попало около 90 слов. При этом около трети кластеров состоят всего из одного элемента."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Итоги"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "В результате эксперимента можно сказать, что наилучшим К можно считать 5000. Результаты работы самого алгоритма можно оценить как достаточно средние, так как схожесть слов в кластерах следует из того, что данные были очень хорошо предобработаны, а треть кластеров состоят всего из одного элемента."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Далее идут служебные блоки, связанные с сохранением и загрузкой промежуточных результатов. Файлы data.txt, all.pickle и out.pickle так же лежат на Github."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pickle\n",
    "with open('out.pickle', 'wb') as f:\n",
    "    pickle.dump(out, f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pickle\n",
    "with open('out.pickle', 'rb') as f:\n",
    "    out = pickle.load(f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [],
   "source": [
    "with open('all.pickle', 'wb') as f:\n",
    "    pickle.dump((ic, ie, ec, ee, iec, iee), f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "with open('all.pickle', 'rb') as f:\n",
    "    ic, ie, ec, ee, iec, iee = pickle.load(f)\n",
    "    "
   ]
  }
 ],
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