chp01/dpmeans.ipynb

{
 "metadata": {
  "name": "dpmeans.ipynb"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Dirichlet Process K-Means"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Dirichlet Process (DP) K-Means is a Bayesian non-parametric extension of the K-means algorithm based on small variance assymptotics (SVA) approximation of the Dirichlet Process Mixture Model. DP-means is similar to K-Means except that new clusters are created whenever a point is sufficiently far away from all existing cluster centroids. Therefore, the number of clusters grows with data. DP means converges to a local optimum of a K means like objective that includes a penalty for the number of clusters."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline \n",
      "\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "\n",
      "import time\n",
      "from sklearn import metrics\n",
      "from sklearn.datasets import load_iris\n",
      "\n",
      "np.random.seed(0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "class dpmeans:\n",
      "    \n",
      "    def __init__(self,X):\n",
      "        # Initialize parameters for DP means\n",
      "                    \n",
      "        self.K = 1\n",
      "        self.K_init = 4\n",
      "        self.d = X.shape[1]\n",
      "        self.z = np.mod(np.random.permutation(X.shape[0]),self.K)+1\n",
      "        self.mu = np.random.standard_normal((self.K, self.d))\n",
      "        self.sigma = 1\n",
      "        self.nk = np.zeros(self.K)\n",
      "        self.pik = np.ones(self.K)/self.K \n",
      "        \n",
      "        #init mu\n",
      "        self.mu = np.array([np.mean(X,0)])\n",
      "        \n",
      "        #init lambda\n",
      "        self.Lambda = self.kpp_init(X,self.K_init)\n",
      "        \n",
      "        self.max_iter = 100\n",
      "        self.obj = np.zeros(self.max_iter)\n",
      "        self.em_time = np.zeros(self.max_iter)   \n",
      "        \n",
      "    def kpp_init(self,X,k):\n",
      "        #k++ init\n",
      "        #lambda is max distance to k++ means\n",
      "\n",
      "        [n,d] = np.shape(X)\n",
      "        mu = np.zeros((k,d))        \n",
      "        dist = np.inf*np.ones(n)\n",
      "                \n",
      "        mu[0,:] = X[np.ceil(np.random.rand()*n-1),:]\n",
      "        for i in range(1,k):\n",
      "            D = X-np.tile(mu[i-1,:],(n,1))\n",
      "            dist = np.minimum(dist, np.sum(D*D,1))\n",
      "            idx = np.where(np.random.rand() < np.cumsum(dist/float(sum(dist))))\n",
      "            mu[i,:] = X[idx[0][0],:]\n",
      "            Lambda = np.max(dist)\n",
      "        \n",
      "        print \"Lambda: \", Lambda\n",
      "        \n",
      "        return Lambda\n",
      "        \n",
      "    def fit(self,X):\n",
      "\n",
      "        obj_tol = 1e-3\n",
      "        max_iter = self.max_iter        \n",
      "        [n,d] = np.shape(X)\n",
      "        \n",
      "        obj = np.zeros(max_iter)\n",
      "        em_time = np.zeros(max_iter)\n",
      "        print 'running dpmeans...'\n",
      "        \n",
      "        for iter in range(max_iter):\n",
      "            tic = time.time()\n",
      "            dist = np.zeros((n,self.K))\n",
      "            \n",
      "            #assignment step\n",
      "            for kk in range(self.K):\n",
      "                Xm = X - np.tile(self.mu[kk,:],(n,1))\n",
      "                dist[:,kk] = np.sum(Xm*Xm,1)\n",
      "            \n",
      "            #update labels\n",
      "            dmin = np.min(dist,1)\n",
      "            self.z = np.argmin(dist,1)\n",
      "            idx = np.where(dmin > self.Lambda)\n",
      "            \n",
      "            if (np.size(idx) > 0):\n",
      "                self.K = self.K + 1\n",
      "                self.z[idx[0]] = self.K-1 #cluster labels in [0,...,K-1]\n",
      "                self.mu = np.vstack([self.mu,np.mean(X[idx[0],:],0)])                \n",
      "                Xm = X - np.tile(self.mu[self.K-1,:],(n,1))\n",
      "                dist = np.hstack([dist, np.array([np.sum(Xm*Xm,1)]).T])\n",
      "             \n",
      "            #update step\n",
      "            self.nk = np.zeros(self.K)\n",
      "            for kk in range(self.K):\n",
      "                self.nk[kk] = self.z.tolist().count(kk)\n",
      "                idx = np.where(self.z == kk)\n",
      "                self.mu[kk,:] = np.mean(X[idx[0],:],0)\n",
      "            \n",
      "            self.pik = self.nk/float(np.sum(self.nk))\n",
      "            \n",
      "            #compute objective\n",
      "            for kk in range(self.K):\n",
      "                idx = np.where(self.z == kk)\n",
      "                obj[iter] = obj[iter] + np.sum(dist[idx[0],kk],0)                \n",
      "            obj[iter] = obj[iter] + self.Lambda * self.K\n",
      "            \n",
      "            #check convergence\n",
      "            if (iter > 0 and np.abs(obj[iter]-obj[iter-1]) < obj_tol*obj[iter]):\n",
      "                print('converged in %d iterations\\n'% iter)\n",
      "                break\n",
      "            em_time[iter] = time.time()-tic\n",
      "        #end for\n",
      "        self.obj = obj\n",
      "        self.em_time = em_time\n",
      "        return self.z, obj, em_time\n",
      "        \n",
      "    def compute_nmi(self, z1, z2):\n",
      "        # compute normalized mutual information\n",
      "        \n",
      "        n = np.size(z1)\n",
      "        k1 = np.size(np.unique(z1))\n",
      "        k2 = np.size(np.unique(z2))\n",
      "        \n",
      "        nk1 = np.zeros((k1,1))\n",
      "        nk2 = np.zeros((k2,1))\n",
      "\n",
      "        for kk in range(k1):\n",
      "            nk1[kk] = np.sum(z1==kk)\n",
      "        for kk in range(k2):\n",
      "            nk2[kk] = np.sum(z2==kk)\n",
      "            \n",
      "        pk1 = nk1/float(np.sum(nk1))\n",
      "        pk2 = nk2/float(np.sum(nk2))\n",
      "        \n",
      "        nk12 = np.zeros((k1,k2))\n",
      "        for ii in range(k1):\n",
      "            for jj in range(k2):\n",
      "                nk12[ii,jj] = np.sum((z1==ii)*(z2==jj))\n",
      "        pk12 = nk12/float(n)        \n",
      "        \n",
      "        Hx = -np.sum(pk1 * np.log(pk1 + np.finfo(float).eps))\n",
      "        Hy = -np.sum(pk2 * np.log(pk2 + np.finfo(float).eps))\n",
      "        \n",
      "        Hxy = -np.sum(pk12 * np.log(pk12 + np.finfo(float).eps))\n",
      "        \n",
      "        MI = Hx + Hy - Hxy;\n",
      "        nmi = MI/float(0.5*(Hx+Hy))\n",
      "        \n",
      "        return nmi\n",
      "                \n",
      "\n",
      "    def generate_plots(self,X):\n",
      "\n",
      "        plt.close('all')\n",
      "        plt.figure(0)\n",
      "        for kk in range(self.K):\n",
      "            #idx = np.where(self.z == kk)\n",
      "            plt.scatter(X[self.z == kk,0], X[self.z == kk,1], \\\n",
      "                        s = 100, marker = 'o', color = np.random.rand(3,1), label = str(kk))\n",
      "        #end for\n",
      "        plt.xlabel('X1')\n",
      "        plt.ylabel('X2')\n",
      "        plt.legend()\n",
      "        plt.title('DP-means clusters')\n",
      "        plt.grid(True)\n",
      "        plt.show()\n",
      "        \n",
      "        plt.figure(1)\n",
      "        plt.plot(self.obj)\n",
      "        plt.title('DP-means objective function')\n",
      "        plt.xlabel('iterations')\n",
      "        plt.ylabel('penalized l2 squared distance')\n",
      "        plt.grid(True)\n",
      "        plt.show()\n",
      "        \n",
      "        #plt.figure(2)\n",
      "        #plt.plot(self.em_time)\n",
      "        #plt.title('DP-means time per iteration')\n",
      "        #plt.xlabel('iterations')\n",
      "        #plt.ylabel('time, sec')\n",
      "        #plt.grid(True)\n",
      "        #plt.show()        \n",
      "                                                \n",
      "                            \n",
      "    def display_params(self):\n",
      "        \n",
      "        print 'K = %d'% self.K\n",
      "        print 'd = %d'% self.d\n",
      "        print 'Labels:'\n",
      "        print self.z\n",
      "        print 'Means:'\n",
      "        print self.mu\n",
      "        print 'Sigma:'\n",
      "        print self.sigma\n",
      "        print 'Counts:'\n",
      "        print self.nk\n",
      "        print 'Proportions:'\n",
      "        print self.pik\n",
      "        print 'Lambda: %.2f'% self.Lambda\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "iris = load_iris()\n",
      "X = iris.data\n",
      "y = iris.target\n",
      "    \n",
      "dp = dpmeans(X)\n",
      "labels, obj, em_time = dp.fit(X)\n",
      "dp.generate_plots(X)\n",
      "\n",
      "nmi = dp.compute_nmi(y,labels)\n",
      "ari = metrics.adjusted_rand_score(y,labels)\n",
      "    \n",
      "print \"NMI: %.4f\" % nmi\n",
      "print \"ARI: %.4f\" % ari        "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Lambda:  6.01\n",
        "running dpmeans...\n",
        "converged in 8 iterations\n",
        "\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "-c:33: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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A6upq7NmzB3FxcRZjpkyZgo0bN4JhGOTm5sLPz0/0+wmAODUAUjen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\nCGFRUiCEEMKipEAIIYT1/2SmtWaIox0BAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x6d32eb8>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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3czYd+sq7VVcxff/99wgPDwcA7N27F0FBQfDy8mr1Sezt7TFlyhScPHkSTk5O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\nCCIi0ogFgoiINPr/fh1sKxxIkaEAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x90abc50>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "NMI: 0.7582\n",
        "ARI: 0.7302\n"
       ]
      }
     ],
     "prompt_number": 3
    }
   ],
   "metadata": {}
  }
 ]
}