Kmeans.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# To find out where the pyspark\n",
    "import findspark\n",
    "findspark.init()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Creating Spark Context\n",
    "from pyspark import SparkContext\n",
    "sc = SparkContext(\"local\", \"first app\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import math\n",
    "import time\n",
    "import copy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_dataset(N, D=10, K=None):\n",
    "    if K is None:\n",
    "        K = math.ceil(math.sqrt(N)/2)\n",
    "        \n",
    "    def create_normal_dist(n):\n",
    "        mu = np.random.randint(-100, 100, size=(D,)) / 100. * D\n",
    "        \n",
    "        L = np.random.randint(-70, 70, size=(D,D)) / 100.\n",
    "        cov = np.dot(L, L.transpose())\n",
    "        \n",
    "        t = np.random.multivariate_normal(mu, cov, n)\n",
    "        return t\n",
    "    \n",
    "    dataset = list()\n",
    "    Csize = int(N / K)\n",
    "    for k in range(K):\n",
    "        dataset_c = np.zeros((Csize, D+1))\n",
    "        #gen IDs\n",
    "        dataset_c[:, 0] = k\n",
    "        dataset_c[:, 1:D+1] = create_normal_dist(Csize)\n",
    "        dataset.extend(dataset_c)\n",
    "        \n",
    "    return np.array(dataset)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 가장 가까운 클러스터의 idx를 반환하는 함수"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def find_closest(point, center, K):\n",
    "    centerId = -1\n",
    "    min_dist = np.Inf\n",
    "\n",
    "    for i in range(K):\n",
    "        dist = np.sqrt(np.sum((center[i][1] - point)**2))\n",
    "        if(dist < min_dist):\n",
    "            min_dist = dist\n",
    "            centerId = center[i][0]\n",
    "\n",
    "    return centerId"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Quiz 해답"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Quiz(N, cluster=[10,20,40,80], convergenceTol=0.001, maxIter=50):\n",
    "    duration = []\n",
    "    result = []\n",
    "    \n",
    "    for k in cluster:\n",
    "        dataset = create_dataset(N, K=k)\n",
    "        \n",
    "        start = time.time()\n",
    "        \n",
    "        inputRDD = sc.parallelize(dataset).map(lambda s: (s[0], s[1:])).cache()\n",
    "        center = inputRDD.map(lambda s: (s[0], (1,s[1]))).reduceByKey(lambda x,y: ((x[0]+y[0]), x[1]+y[1])).mapValues(lambda v: v[1]/v[0]).collect()\n",
    "        pr = sc.broadcast(center)\n",
    "        \n",
    "        prev = inputRDD.map(lambda t: np.sqrt(np.sum((pr.value[int(t[0])][1] - t[1])**2))).sum()\n",
    "        \n",
    "        for _ in range(maxIter):\n",
    "            inputRDD = inputRDD.map(lambda s: (find_closest(s[1], center, k), s[1])).cache()\n",
    "            center = inputRDD.map(lambda s: (s[0], (1,s[1]))).reduceByKey(lambda x,y: ((x[0]+y[0]), x[1]+y[1])).mapValues(lambda v: v[1]/v[0]).collect()\n",
    "            pr = sc.broadcast(center)\n",
    "            \n",
    "            # test convergence\n",
    "            err = inputRDD.map(lambda t: np.sqrt(np.sum((pr.value[int(t[0])][1] - t[1])**2))).sum()\n",
    "            if abs(prev - err) < convergenceTol:\n",
    "                prev = err\n",
    "                break\n",
    "\n",
    "            # save prev-error value\n",
    "            prev = err\n",
    "        \n",
    "        end = time.time()\n",
    "        \n",
    "        result.append(center)\n",
    "        duration.append(end-start)\n",
    "        \n",
    "    return duration    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Quiz 실행코드"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = [1000, 2000, 4000, 8000, 16000]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[Dataset: 1000]\n",
      "\n",
      "# of cluster : 10\n",
      "Duration: 10.415163040161133\n",
      "\n",
      "# of cluster : 20\n",
      "Duration: 2.476116418838501\n",
      "\n",
      "# of cluster : 40\n",
      "Duration: 2.8163578510284424\n",
      "\n",
      "# of cluster : 80\n",
      "Duration: 3.3927273750305176\n",
      "\n",
      "================================\n",
      "\n",
      "[Dataset: 2000]\n",
      "\n",
      "# of cluster : 10\n",
      "Duration: 2.455453634262085\n",
      "\n",
      "# of cluster : 20\n",
      "Duration: 4.275258302688599\n",
      "\n",
      "# of cluster : 40\n",
      "Duration: 3.7587835788726807\n",
      "\n",
      "# of cluster : 80\n",
      "Duration: 7.180518627166748\n",
      "\n",
      "================================\n",
      "\n",
      "[Dataset: 4000]\n",
      "\n",
      "# of cluster : 10\n",
      "Duration: 2.7537453174591064\n",
      "\n",
      "# of cluster : 20\n",
      "Duration: 5.840237379074097\n",
      "\n",
      "# of cluster : 40\n",
      "Duration: 8.93427848815918\n",
      "\n",
      "# of cluster : 80\n",
      "Duration: 19.88587474822998\n",
      "\n",
      "================================\n",
      "\n",
      "[Dataset: 8000]\n",
      "\n",
      "# of cluster : 10\n",
      "Duration: 4.03127384185791\n",
      "\n",
      "# of cluster : 20\n",
      "Duration: 13.555373191833496\n",
      "\n",
      "# of cluster : 40\n",
      "Duration: 19.05179262161255\n",
      "\n",
      "# of cluster : 80\n",
      "Duration: 16.347975492477417\n",
      "\n",
      "================================\n",
      "\n",
      "[Dataset: 16000]\n",
      "\n",
      "# of cluster : 10\n",
      "Duration: 10.294225215911865\n",
      "\n",
      "# of cluster : 20\n",
      "Duration: 10.829514026641846\n",
      "\n",
      "# of cluster : 40\n",
      "Duration: 34.18788290023804\n",
      "\n",
      "# of cluster : 80\n",
      "Duration: 50.37799048423767\n",
      "\n",
      "================================\n",
      "\n"
     ]
    }
   ],
   "source": [
    "durations = []\n",
    "\n",
    "for x in X:\n",
    "    print(\"[Dataset: {}]\".format(x))\n",
    "    print()\n",
    "\n",
    "    duration = Quiz(x)\n",
    "\n",
    "    print(\"# of cluster : 10\")\n",
    "    print(\"Duration: {}\".format(duration[0]))\n",
    "    print()\n",
    "    print(\"# of cluster : 20\")\n",
    "    print(\"Duration: {}\".format(duration[1]))\n",
    "    print()\n",
    "    print(\"# of cluster : 40\")\n",
    "    print(\"Duration: {}\".format(duration[2]))\n",
    "    print()\n",
    "    print(\"# of cluster : 80\")\n",
    "    print(\"Duration: {}\".format(duration[3]))\n",
    "    print()\n",
    "    print(\"================================\")\n",
    "    print()\n",
    "\n",
    "    durations.append(duration)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 그래프"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "th = [10, 20, 40, 80]\n",
    "marker = ['^', 's', 'h', 'o']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(4):\n",
    "    result = []\n",
    "    for j in range(5):\n",
    "        result.append(durations[j][i])\n",
    "    \n",
    "    plt.plot(X, result, marker=marker[i], label=\"# of cluster = {}\".format(th[i]))\n",
    "\n",
    "\n",
    "plt.xlabel(\"Number of data\")\n",
    "plt.ylabel(\"Execution time\")\n",
    "\n",
    "plt.yscale('log')\n",
    "plt.legend(loc='upper left', fontsize=10)\n",
    "\n",
    "plt.show()"
   ]
  }
 ],
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