{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import style\n",
    "style.use('ggplot')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# input features\n",
    "X = np.array([\n",
    "    [1, 3],\n",
    "    [2, 1.8],\n",
    "    [5, 8],\n",
    "    [8, 8],\n",
    "    [1., 0.8],\n",
    "    [9, 11]\n",
    "    ])\n",
    "plt.scatter(X[:,0], X[:,1], s=100)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "# colors for our groups \n",
    "colors = 5*['r', 'b', 'g', 'm', 'y', 'c']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "class K_Means:\n",
    "    def __init__(self, k=2, tol=0.01, max_iter=300):\n",
    "        self.k = k # num groups to cluster\n",
    "        self.tol = tol # tolerance: how much centroid can  move before converging\n",
    "        self.max_iter = max_iter # if tolerance is not reached (did not converge)\n",
    "    def fit(self, data):\n",
    "        self.centroids = {}\n",
    "        # first k centroids are chosen arbitraraly\n",
    "        # in this case the first k features are the initial centroids\n",
    "        for i in range(self.k):\n",
    "            self.centroids[i] = data[i]\n",
    "\n",
    "        for i in range(self.max_iter):\n",
    "            # contains (centroid, fetures) pairs\n",
    "            self.classifications = {}\n",
    "\n",
    "            for i in range(self.k):\n",
    "                self.classifications[i] = []\n",
    "\n",
    "            for featureset in data:\n",
    "                # list of distances from each centroid from the feature\n",
    "                distances = [np.linalg.norm(featureset - self.centroids[centroid]) for centroid in self.centroids]\n",
    "                classification = distances.index(min(distances))\n",
    "                self.classifications[classification].append(featureset)\n",
    "            prev_centroids = dict(self.centroids)\n",
    "\n",
    "            for classification in self.classifications:\n",
    "                # centroid changes to mean of features\n",
    "                self.centroids[classification] = np.average(self.classifications[classification], axis=0)\n",
    "            # see if converged\n",
    "            converged = True\n",
    "            for c in self.centroids:\n",
    "                origanal_centroid = prev_centroids[c]\n",
    "                current_centroid = self.centroids[c]\n",
    "                if np.sum((current_centroid-origanal_centroid) / origanal_centroid*100.0) > self.tol:\n",
    "                    print('centroid moved: ', np.sum((current_centroid-origanal_centroid) / origanal_centroid*100.0))\n",
    "                    converged = False\n",
    "    def predict(self, data):\n",
    "        distances = [np.linalg.norm(data - self.centroids[centroid]) for centroid in self.centroids]\n",
    "        classification = distances.index(min(distances))\n",
    "        return classification"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "centroid moved:  625.0\n",
      "centroid moved:  47.53623188405797\n",
      "centroid moved:  32.478632478632456\n"
     ]
    }
   ],
   "source": [
    "clf = K_Means(k=2)\n",
    "clf.fit(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for centroid in clf.centroids:\n",
    "    plt.scatter(clf.centroids[centroid][0], clf.centroids[centroid][1],\n",
    "        marker = 'o', c='k',s=60)\n",
    "for classification in clf.classifications:\n",
    "    color = colors[classification]\n",
    "    for featureset in clf.classifications[classification]:\n",
    "        plt.scatter(featureset[0], featureset[1], marker='x', c=color, s=70,linewidth=3)\n",
    "# plt.show()"
   ]
  }
 ],
 "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
}