Understanding KMedoids.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Understang KMedoids\n",
    "Doc : http://eric.univ-lyon2.fr/~ricco/cours/slides/classif_k_medoides.pdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt \n",
    "\n",
    "# 2D Points Dataset\n",
    "x = np.array([1,0,2.5,6,1,8,3,0,3,9,8,4,5,6.5])\n",
    "y = np.array([1,4,7,2,3,4,7,2,6,1,3,6,7,5])\n",
    "\n",
    "n = x.shape[0] #Nb of points\n",
    "k = 3 # Nb of clusters    k<n\n",
    "\n",
    "points = np.array([x,y])\n",
    "points = points.T # n 2D points  \n",
    "\n",
    "\n",
    "medoids = points[np.random.randint(low=0,high=n,size=k)]   #Get random points \n",
    "\n",
    "l = points.shape[1] #Len of vector : 2 (Point)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[6.5, 5. ],\n",
       "       [0. , 4. ],\n",
       "       [1. , 1. ]])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "medoids"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "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"
    }
   ],
   "source": [
    "plt.scatter(points[:,0],points[:,1],color='blue')\n",
    "plt.scatter(medoids[:,0],medoids[:,1],color='red')\n",
    "for i in range(0,n): \n",
    "    plt.text(points[i][0], points[i][1], str(i), fontsize=15)\n",
    "for i in range(0,k): \n",
    "    plt.text(medoids[i,0],medoids[i,1],chr(i+65), fontsize=15)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Euclidean distance calculation\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Inputs : \n",
    "\n",
    "<img src=\"img/Understanding_KMeans/Input.png\" width=150  />\n",
    "\n",
    "To compute the distance between each point and each middles we need to broadcast the two array \n",
    "<img src=\"img/Understanding_KMeans/step1.1.png\" width=450  />\n",
    "So now we can calculate substract each point by each middle and then pass the result to the the norm function\n",
    "<img src=\"img/Understanding_KMeans/norm.PNG\" width=300  />\n",
    "\n",
    "<img src=\"img/Understanding_KMeans/step2.png\" width=300  />\n",
    "Then for each point we can choose the min distance\n",
    "\n",
    "Our result will be :  [1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def euclid_distances(points,medoids):\n",
    "    \n",
    "    k = medoids.shape[0]\n",
    "    n = points.shape[0]\n",
    "    l = points.shape[1]\n",
    "\n",
    "    points=np.broadcast_to(points,(k,n,l)) \n",
    "    # (k,n,2)\n",
    "    \n",
    "    c = np.zeros((k,n,l))\n",
    "    for i in range(0,k):         #Need to find a numpy way to do this to avoid loops\n",
    "        c[i]=np.broadcast_to(medoids[i],(n,l))\n",
    "    # (k,n,2)\n",
    "    \n",
    "    d = np.linalg.norm(points-c,axis=2) # Euclidean Distance\n",
    "    # (k,n) because distance is a scalar here\n",
    " \n",
    "    args=np.argmin(d,axis=0) #For each point get the argument of the minimum distance\n",
    "    \n",
    "    return(args)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calc_new_medoids(points,belongs):\n",
    "    #Choose new medoid for each class\n",
    "    \n",
    "    k = len(np.unique(belongs))\n",
    "    l = points.shape[1]\n",
    "    \n",
    "    new_medoids = np.zeros((k,l))\n",
    "    \n",
    "    for i in range(k):\n",
    "        current_class_points = points[belongs == i]\n",
    "        \n",
    "        a,b = current_class_points.shape\n",
    "        \n",
    "        q = np.broadcast_to(current_class_points,(a,a,b))\n",
    "        \n",
    "        c = np.zeros((a,a,b))\n",
    "        for j in range(0,a):         #Need to find a numpy way to do this to avoid loops\n",
    "            c[j] = np.broadcast_to(current_class_points[j],(a,b))\n",
    "\n",
    "        v = np.linalg.norm(q-c,axis=2)\n",
    "        s = np.sum(v,axis=1)\n",
    "        ind = np.argmin(s)\n",
    "        new_medoids[i] = current_class_points[ind]\n",
    "        \n",
    "    return(new_medoids)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def scatter_plot(points,middles,belongs):\n",
    "    plt.scatter(points[:,0],points[:,1],color='blue')\n",
    "    plt.scatter(middles[:,0],middles[:,1],color='red')\n",
    "    \n",
    "    for i in range(0,n): \n",
    "        plt.text(points[i][0], points[i][1], chr(belongs[i]+65), fontsize=15)\n",
    "    for i in range(0,k): \n",
    "        plt.text(middles[i,0],middles[i,1], chr(i+65), fontsize=15)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Running the Algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "for p in range(5):\n",
    "    belongs = euclid_distances(points,medoids)\n",
    "    medoids = calc_new_medoids(points,belongs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "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"
    }
   ],
   "source": [
    "scatter_plot(points,medoids,belongs)"
   ]
  }
 ],
 "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": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}