adds maximum loglikelihood estimation note and other notes

Kmeans.ipynb

@@ -0,0 +1,244 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "%matplotlib inline\n",
+    "import numpy as np\n",
+    "import pandas as pd\n",
+    "from IPython import display\n",
+    "import matplotlib.pylab as plt\n",
+    "import time\n",
+    "from IPython import display\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "a:  [0 1 0 1 1 1]\n",
+      "\n",
+      "mu, c 0 0\n",
+      "[[ 0.18709855  0.        ]\n",
+      " [-0.12785456  0.        ]]\n",
+      "\n",
+      "mu, c 1 1\n",
+      "[[ 0.18709855 -0.14170366]\n",
+      " [-0.12785456  0.41424891]]\n",
+      "\n",
+      "mu, c 0 2\n",
+      "[[ 0.52861541 -0.14170366]\n",
+      " [ 0.00111371  0.41424891]]\n",
+      "\n",
+      "mu, c 1 3\n",
+      "[[ 0.52861541  0.89944324]\n",
+      " [ 0.00111371  1.09908324]]\n",
+      "\n",
+      "mu, c 1 4\n",
+      "[[  5.28615411e-01   1.89455526e+00]\n",
+      " [  1.11371268e-03   1.83856955e+00]]\n",
+      "\n",
+      "mu, c 1 5\n",
+      "[[  5.28615411e-01   2.55948263e+00]\n",
+      " [  1.11371268e-03   2.44099325e+00]]\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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ysvKcrxEALoTJZJLJZPKsv6+6eyYLqKqlJJ/o7p/Y5r3Lu/uxzcfXJ/lwdy/tsJ2e1ZoA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\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x10e26d550>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "\n",
+    "N = 6\n",
+    "D = 2\n",
+    "X1 = np.random.randn(D,N/2)\n",
+    "X2 = 0.8*np.random.randn(D,N/2) + 3*np.ones((D, N/2))\n",
+    "\n",
+    "X = np.hstack((np.mat(X1), np.mat(X2)))\n",
+    "\n",
+    "#plt.plot(X[0,:], X[1,:],'x')\n",
+    "#plt.show()\n",
+    "\n",
+    "K = 2;\n",
+    "\n",
+    "W = np.mat('[3,0;0,1]')\n",
+    "mu = X[:,0:K]\n",
+    "#plt.plot(mu[0,:],mu[1,:],'ro')\n",
+    "\n",
+    "EP = 200\n",
+    "\n",
+    "fig = plt.figure(figsize=(8,10))\n",
+    "plt.plot(X[0,:], X[1,:],'kx')\n",
+    "\n",
+    "ax = fig.gca()\n",
+    "ln = plt.Line2D(xdata=mu[0,:], ydata=mu[1,:], marker='o', color='r',linestyle=None,linewidth=0)\n",
+    "ax.add_line(ln)\n",
+    "\n",
+    "eta = 0.3\n",
+    "#print X\n",
+    "#print mu\n",
+    "\n",
+    "dist = np.zeros((N,K))\n",
+    "for i in range(N):\n",
+    "    for c in range(K):\n",
+    "        err = X[:,i]-mu[:,c]\n",
+    "        dist[i,c] = float(err.T*W.I*err)\n",
+    "#         print\n",
+    "#         print \"i, c\", i, c\n",
+    "#         print dist\n",
+    "\n",
+    "a = np.argmin(dist, axis=1)\n",
+    "print \"a: \", a\n",
+    "\n",
+    "mu = np.mat(np.zeros((D,K)))\n",
+    "count = np.zeros((K))\n",
+    "for i,c in enumerate(a):\n",
+    "    # count[c] += 1\n",
+    "    #mu[:,c] = (count[c]-1)/count[c]*mu[:,c] + 1/count[c]*X[:,i]\n",
+    "    mu[:,c] = (1-eta)*mu[:,c] + eta*X[:,i]\n",
+    "    print \"\\nmu, c\", c, i\n",
+    "    print mu\n",
+    "\n",
+    "# ------------\n",
+    "\n",
+    "for e in range(0):\n",
+    "    \n",
+    "    dist = np.zeros((N,K))\n",
+    "    for i in range(N):\n",
+    "        for c in range(K):\n",
+    "            err = X[:,i]-mu[:,c]\n",
+    "            dist[i,c] = float(err.T*W.I*err)\n",
+    "    \n",
+    "    # Assignments\n",
+    "    a = np.argmin(dist, axis=1)\n",
+    "    \n",
+    "    mu = np.mat(np.zeros((D,K)))\n",
+    "    count = np.zeros((K))\n",
+    "    for i,c in enumerate(a):\n",
+    "        count[c] += 1\n",
+    "        #mu[:,c] = (count[c]-1)/count[c]*mu[:,c] + 1/count[c]*X[:,i]\n",
+    "        mu[:,c] = (1-eta)*mu[:,c] + eta*X[:,i]\n",
+    "    \n",
+    "    ln.set_xdata(mu[0,:])\n",
+    "    ln.set_ydata(mu[1,:])\n",
+    "    \n",
+    "    #plt.subplot(EP,1,e+1)\n",
+    "    display.clear_output(wait=True)\n",
+    "    display.display(plt.gcf())\n",
+    "    time.sleep(0.1)\n",
+    "    plt.plot(X[0,:], X[1,:],'kx')\n",
+    "    #plt.plot(mu[0,:],mu[1,:],'ro')\n",
+    "\n",
+    "plt.show()\n",
+    "    "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "matrix([[4, 2, 7],\n",
+       "        [0, 7, 1],\n",
+       "        [9, 3, 2]])"
+      ]
+     },
+     "execution_count": 19,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "a = np.mat([ [4, 2, 7], [0, 7, 1], [9, 3, 2] ])\n",
+    "a"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "matrix([[1],\n",
+       "        [0],\n",
+       "        [2]])"
+      ]
+     },
+     "execution_count": 23,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "np.argmin(a, axis=1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 2",
+   "language": "python",
+   "name": "python2"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 2
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython2",
+   "version": "2.7.10"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}