enhancedSoftKmen.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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D3wEeAlZXvr8ROFB5/6t4wb1HgROV/67PWO5tFZmfAnZVvrsLeGfl\nfQFvE91TeEpoPEt5I8j/EPB8zTP/UtYyh5G/oe3XyEl2UFDZgXvwNlc+hrcBM3O5Q/ztXAccw8sc\nehR4W9YyN8h/EG9m/xO8Da4fBm4HfqOmzZ/iZUE9lrO/nZayA/cB/1zz73YuSL/aLCaEEH1M1u4g\nIYQQGSIjIIQQfYyMgBBC9DEyAkII0cfICAghRB8jIyCEEH2MjIAQQvQxMgJCCNHH/H/1HIIz5Sy+\nWwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108f9d710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[60.968073849997282, 43.497384629253268, 36.337612014376873, 59.196929506372555]\n",
      "[60.88484421070185, 42.96555802080411, 39.043916629596232, 57.105681138897793]\n",
      "[63.987644677286994, 34.835231785156516, 36.066140163359165, 65.110983374197332]\n",
      "[69.482887714345438, 19.570329819749244, 30.552107603792258, 80.394674862113064]\n",
      "[77.66720838910183, 5.9754878588353124, 22.415456828600224, 93.94184692346262]\n",
      "[88.687295702815561, 0.006954568477618165, 11.625191602974567, 99.680558125732219]\n",
      "[99.499398244380558, 2.4467633158101972e-37, 1.0331095889834985, 99.467492166635836]\n"
     ]
    },
    {
     "data": {
      "image/png": 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vFULcibDc+lc10S/f+Q5w/vnAzTcDw4cXbl/QVMd+Njr97Q0NZtPXnXeaBdvZ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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108e6efd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.141360622756 0.0 0.00477753996787 0.142411752757\n",
      "0.0197599392275 nan 0.00200194103472 0.0204760110039\n"
     ]
    }
   ],
   "source": [
    "import random\n",
    "import numpy as np\n",
    "from numpy import linalg as LA\n",
    "import matplotlib.pyplot as plt\n",
    "import math\n",
    "\n",
    "data1=[]\n",
    "for i in range(100):\n",
    "\tdata1=data1+[[0.5+0.5*random.random(),0.5+0.5*random.random()]]\n",
    "\t\n",
    "data2=[]\n",
    "for i in range(100):\n",
    "\tdata2=data2+[[0.5*random.random(),0.5*random.random()]]\n",
    "\n",
    "#data3 =[]\n",
    "#for i in range(30):\n",
    "#\tdata3=data3+[[0.8,random.random()]]\n",
    "\n",
    "data=data1+data2#+data3\n",
    "\n",
    "\n",
    "\n",
    "datax=[]\n",
    "for i in range(len(data)):\n",
    "\tdatax=datax+[data[i][0]]\n",
    "\t\n",
    "datay=[]\n",
    "for i in range(len(data)):\n",
    "\tdatay=datay+[data[i][1]]\n",
    "\n",
    "plt.scatter(datax,datay)\n",
    "plt.show()\n",
    "\n",
    "\n",
    "\t\n",
    "assign = []\n",
    "for j in range(4):\n",
    "\tassign=assign+[[random.random(),random.random()]]\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "sum=[]\n",
    "for i in range(len(data)):\n",
    "\tsum=sum+[[]]\n",
    "r=[]\t\n",
    "for i in range(4):\n",
    "\tr=r+[[]]\n",
    "\tfor j in range(len(data)):\n",
    "\t\tr[i]=r[i]+[[]]\n",
    "update_assign=[]\n",
    "for k in range(4):\n",
    "\tupdate_assign=update_assign+[[]]\t\n",
    "\n",
    "I = 2 # dimension\n",
    "\n",
    "v=[] # variance or 1/beta\t\n",
    "for k in range(4):\n",
    "\tv=v+[np.var(data)]\n",
    "\n",
    "p=[]\n",
    "for k in range(4):\n",
    "\tp=p+[1]\n",
    "rsum=[[],[],[],[]]\n",
    "turn = 0\n",
    "while turn<7:\n",
    "\tturn = turn+1\n",
    "\tsum=[]\n",
    "\tfor n in range(len(data)):\n",
    "\t\tsum=sum+[[]]\n",
    "\tfor n in range(len(data)):\n",
    "\t\ts=0\n",
    "\t\tfor k in range(4):\n",
    "\t\t\ts=s+p[k]/(np.sqrt(2*np.pi*v[k]))**I*np.exp(-1/v[k]*(LA.norm(np.array(assign[k])-np.array(data[n]))))\n",
    "\t\t\tsum[n]=s\n",
    "\t\tfor k in range(4):\n",
    "\t\t\tr[k][n]=p[k]/(np.sqrt(2*np.pi*v[k]))**I*np.exp(-1/v[k]*(LA.norm(np.array(assign[k])-np.array(data[n]))))/s\n",
    "\t\t\t#print a,j,n,r[j][n]\n",
    "\n",
    "\tfor k in range(4):\n",
    "\t\trs=0\n",
    "\t\tfor n in range(len(data)):\n",
    "\t\t\trs=rs+r[k][n]\n",
    "\t\t\trsum[k]=rs\n",
    "\t\t\t\n",
    "\n",
    "\t\tua=[0,0]\n",
    "\t\tfor n in range(len(data)):\n",
    "\t\t\tua[0]=ua[0]+r[k][n]*data[n][0]/float(rsum[k])\n",
    "\t\t\tua[1]=ua[1]+r[k][n]*data[n][1]/float(rsum[k])\n",
    "\t\t\tupdate_assign[k]=ua\n",
    "\t\t\t\n",
    "\tassign= update_assign\n",
    "\tv=[0,0,0,0]\n",
    "\tfor k in range(4):\n",
    "\t\tfor n in range(len(data)):\n",
    "\t\t\tv[k]=v[k]+r[k][n]*LA.norm(np.array(data[n])-np.array(assign[k]))**2/float(I*rsum[k])\n",
    "\tprint rsum\n",
    "\trsumsum=0\n",
    "\tfor k in range(4):\n",
    "\t\trsumsum=rsumsum+rsum[k]\n",
    "\t\n",
    "\tp[k]=rsum[k]/float(rsumsum)\t\n",
    "\n",
    "\n",
    "c=[[],[],[],[]]\n",
    "for n in range(len(data)):\n",
    "\ta=[]\n",
    "\tfor k in range(4):\n",
    "\t\ta=a+[r[k][n]]\n",
    "\ti=a.index(max(a))\n",
    "\tc[i]=c[i]+[data[n]]\n",
    "\"\"\n",
    "\n",
    "circle0= plt.Circle(assign[0],np.sqrt(v[0]),color='r',fill=False)\n",
    "circle1= plt.Circle(assign[1],np.sqrt(v[1]),color='g',fill=False)\n",
    "circle2= plt.Circle(assign[2],np.sqrt(v[2]),color='y',fill=False)\n",
    "circle3= plt.Circle(assign[3],np.sqrt(v[3]),color='b',fill=False)\n",
    "\n",
    "fig, ax=plt.subplots()\n",
    "plt.xlim([-0.3,1.3])\n",
    "plt.ylim([-0.3,1.3])\n",
    "ax.add_artist(circle0)\n",
    "ax.add_artist(circle1)\n",
    "ax.add_artist(circle2)\n",
    "ax.add_artist(circle3)\n",
    "\n",
    "ax.scatter([x for x,y in c[0]],[y for x,y in c[0]],color='r')\n",
    "ax.scatter([x for x,y in c[1]],[y for x,y in c[1]],color='g')\n",
    "ax.scatter([x for x,y in c[2]],[y for x,y in c[2]],color='y')\n",
    "ax.scatter([x for x,y in c[3]],[y for x,y in c[3]],color='b')\n",
    "\n",
    "\n",
    "plt.show()\n",
    "\n",
    "print np.sqrt(v[0]),np.sqrt(v[1]),np.sqrt(v[2]),np.sqrt(v[3])\n",
    "print np.var(c[0]),np.var(c[1]),np.var(c[2]),np.var(c[3])\n",
    "\n",
    "\t"
   ]
  },
  {
   "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",
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