{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## This notebook shows an application of kneed in selecting the optimal number of clusters from kmeans clustering algorithm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Look at the K means tutorial posted [here](https://pythonprogramminglanguage.com/kmeans-elbow-method/)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1073a8400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x103643588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# clustering dataset\n",
    "# determine k using elbow method\n",
    " \n",
    "from sklearn.cluster import KMeans\n",
    "from sklearn import metrics\n",
    "from scipy.spatial.distance import cdist\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    " \n",
    "x1 = np.array([3, 1, 1, 2, 1, 6, 6, 6, 5, 6, 7, 8, 9, 8, 9, 9, 8])\n",
    "x2 = np.array([5, 4, 5, 6, 5, 8, 6, 7, 6, 7, 1, 2, 1, 2, 3, 2, 3])\n",
    " \n",
    "plt.plot()\n",
    "plt.xlim([0, 10])\n",
    "plt.ylim([0, 10])\n",
    "plt.title('Dataset')\n",
    "plt.scatter(x1, x2)\n",
    "plt.show()\n",
    " \n",
    "# create new plot and data\n",
    "plt.plot()\n",
    "X = np.array(list(zip(x1, x2))).reshape(len(x1), 2)\n",
    "colors = ['b', 'g', 'r']\n",
    "markers = ['o', 'v', 's']\n",
    " \n",
    "# k means determine k\n",
    "distortions = []\n",
    "K = range(1,10)\n",
    "for k in K:\n",
    "    kmeanModel = KMeans(n_clusters=k).fit(X)\n",
    "    kmeanModel.fit(X)\n",
    "    distortions.append(sum(np.min(cdist(X, kmeanModel.cluster_centers_, 'euclidean'), axis=1)) / X.shape[0])\n",
    "\n",
    "# Plot the elbow\n",
    "plt.plot(K, distortions, 'bx-')\n",
    "plt.xlabel('k')\n",
    "plt.ylabel('Distortion')\n",
    "plt.title('The Elbow Method showing the optimal k')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## focus on the second plot showing the distortion as a function of k clusters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "range(1, 10) \n",
      " [3.4577032384495707, 1.7687413573405673, 0.8819889697423957, 0.7587138847606585, 0.6635212812400347, 0.5808803063754726, 0.5093717077076824, 0.42618267462691206, 0.3529411764705882]\n"
     ]
    }
   ],
   "source": [
    "print(K, '\\n', distortions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Use kneed to determine best k"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "sys.path.append('..')\n",
    "\n",
    "from kneed import KneeLocator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "kn = KneeLocator(list(K), distortions, S=1.0, curve='convex', direction='decreasing')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kn.knee"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c127b2ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel('k')\n",
    "plt.ylabel('Distortion')\n",
    "plt.title('The Elbow Method showing the optimal k')\n",
    "plt.plot(K, distortions, 'bx-')\n",
    "plt.vlines(kn.knee, plt.ylim()[0], plt.ylim()[1], linestyles='dashed')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}