axisAlignedGaussianSoftKmean.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1109f7410>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[21.898904199213032, 79.132000105607148, 7.944351938292634, 21.024743756887187]\n",
      "[26.012086043866923, 87.966183482280556, 11.854819030129631, 4.1669114437229346]\n",
      "[27.166416109215948, 89.43222865895217, 12.494418002370757, 0.90693722946109434]\n",
      "[28.032985224909755, 88.79689400773087, 12.959620118742153, 0.21050064861719417]\n",
      "[28.952578998107484, 87.557272326470752, 13.438292906085394, 0.051855769336438241]\n",
      "[29.858149880377706, 86.224760970652738, 13.903604470848075, 0.013484678121505807]\n",
      "[30.704509677581942, 84.955408573643709, 14.336401774062765, 0.0036799747116162498]\n",
      "[31.476814181609608, 83.791386874191971, 14.730750755956294, 0.0010481882421497844]\n",
      "[32.174993366246319, 82.737467080646667, 15.087229426879986, 0.00031012622708014216]\n",
      "[32.804654576216748, 81.786363904098664, 15.408886601642122, 9.4918042506433122e-05]\n",
      "[0.3478799330186515, 0.34006308772956717, 0.34743248597318344, 0.35045734263573414] [0.40349576974397916, 0.39241320239952904, 0.40337377457299795, 0.40736194388285663]\n"
     ]
    },
    {
     "data": {
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aTWz7t1ZbiIMH22PAgEtQKIJEjSe/Ih9dP+uKzGczERUYJUpGY+G5zc9BKVfi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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1106f1190>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.3478799330186515, 0.34006308772956717, 0.34743248597318344, 0.35045734263573414] [0.40349576974397916, 0.39241320239952904, 0.40337377457299795, 0.40736194388285663]\n"
     ]
    }
   ],
   "source": [
    "import random\n",
    "import numpy as np\n",
    "from numpy import linalg as LA\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.patches import Ellipse\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+[[random.random(),0.8+0.1*random.random()]]\n",
    "\n",
    "data=data2+data3#+data1\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",
    "assignx = []\n",
    "assigny = []\n",
    "\n",
    "for k in range(4):\n",
    "\tassignx=assignx+[random.random()]\n",
    "\n",
    "for k in range(4):\n",
    "\tassigny=assigny+[random.random()]\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_assignx=[[],[],[],[]]\n",
    "update_assigny=[[],[],[],[]]\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "vx=[random.random(),random.random(),random.random(),random.random()]\n",
    "vy=[random.random(),random.random(),random.random(),random.random()]\n",
    "\n",
    "p=[random.random(),random.random(),random.random(),random.random()]\n",
    "rsum=[[],[],[],[]]\n",
    "turn = 0\n",
    "while turn<10:\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]/(2*np.pi*np.sqrt(vx[k]*vy[k]))*np.exp(-(assignx[k]-datax[n])**2/(2*vx[k])-(assigny[k]-datay[n])**2/(2*vy[k]))\n",
    "\t\tsum[n]=s\n",
    "\t\tfor k in range(4):\n",
    "\t\t\tr[k][n]=p[k]/(2*np.pi*np.sqrt(vx[k]*vy[k]))*np.exp(-(assignx[k]-datax[n])**2/(2*vx[k])-(assigny[k]-datay[n])**2/(2*vy[k]))/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\trsum[k]=rs\n",
    "\t\t\t\n",
    "\t\tua=[0,0]\n",
    "\t\tfor n in range(len(data)):\n",
    "\t\t\tua[0]=ua[0]+r[k][n]*datax[n]/float(rsum[k])\n",
    "\t\t\tua[1]=ua[1]+r[k][n]*datay[n]/float(rsum[k])\n",
    "\t\t\tupdate_assignx[k]=ua[0]\n",
    "\t\t\tupdate_assigny[k]=ua[1]\n",
    "\t\t\t\n",
    "\t\t\t\n",
    "\tassignx= update_assignx\n",
    "\tassigny= update_assigny\n",
    "\n",
    "\tfor k in range(4):\n",
    "\t\tfor n in range(len(data)):\n",
    "\t\t\tvx[k]=vx[k]+r[k][n]*(datax[n]-assignx[k])**2/float(rsum[k])\n",
    "\t\t\tvy[k]=vy[k]+r[k][n]*(datay[n]-assigny[k])**2/float(rsum[k])\n",
    "\t\t\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",
    "print assignx, assigny\n",
    "\n",
    "c=[[],[],[],[]]\n",
    "\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",
    "ell0= Ellipse(xy=[assignx[0],assigny[0]],width=np.sqrt(vx[0]),height=np.sqrt(vy[0]),color='r',fill=False)\n",
    "ell1= Ellipse(xy=[assignx[1],assigny[1]],width=np.sqrt(vx[1]),height=np.sqrt(vy[1]),color='g',fill=False)\n",
    "ell2= Ellipse(xy=[assignx[2],assigny[2]],width=np.sqrt(vx[2]),height=np.sqrt(vy[2]),color='y',fill=False)\n",
    "ell3= Ellipse(xy=[assignx[3],assigny[3]],width=np.sqrt(vx[3]),height=np.sqrt(vy[3]),color='b',fill=False)\n",
    "\n",
    "fig=plt.figure(0) \n",
    "ax=fig.add_subplot(111, aspect='equal')\n",
    "plt.xlim([-0.3,1.3])\n",
    "plt.ylim([-0.3,1.3])\n",
    "ax.add_artist(ell0)\n",
    "ax.add_artist(ell1)\n",
    "ax.add_artist(ell2)\n",
    "ax.add_artist(ell3)\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 assignx, assigny\n",
    "\t\n",
    "\n",
    "\n",
    "\t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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4uJo1a64JveGs9nm/BUH7Emotrx5hB5re3t78yqQd5FJZwxw//nO6uroC71uk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\ndRVuAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11700a490>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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FFgHHu/vSjG0OBx5w99fN7PNAu7sfH9GWknwu5SShZ54J0xdkylVrLnU/hZ4X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\nASCpkcu4jHSqAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117cd31d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.138173693885 0.000280920654126 1.96261557335e-17 0.206507473625\n",
      "0.0192882547628 nan nan 0.0675261626156\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",
    "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+[[random.random(),0.8+0.1*random.random()]]\n",
    "\n",
    "data=data2+data3#+data1\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",
    "shrink = False\n",
    "while not shrink:\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",
    "\t\tif v[k] < 0.00000001:\n",
    "\t\t\tshrink = True\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([-.3,1.3])\n",
    "plt.ylim([-.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\n",
    "\n",
    "\n",
    "\t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.039273813535920021, 2.2236483340438421e-10, nan, 0.024458712514676729]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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I+vaVhjmnTvVfr7F8+XKv+hbp7sZSxXu17sZWAC0V7/8AkKqSV0QuWCCOHCF6+WWi1q2J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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110b6b150>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import random\n",
    "import numpy as np\n",
    "from numpy import linalg as LA\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.patches import Ellipse\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(100):\n",
    "\tdata3=data3+[[random.random(),0.8+0.1*random.random()]]\n",
    "\n",
    "data=data3+data2#+data1\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",
    "\n",
    "\t\n",
    "assignx = []\n",
    "assigny = []\n",
    "\n",
    "for k in range(4):\n",
    "\tassignx=assignx+[random.random()]\n",
    "\n",
    "for k in range(4):\n",
    "\tassigny=assigny+[random.random()]\n",
    "\n",
    "\n",
    "\n",
    "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_assignx=[[],[],[],[]]\n",
    "update_assigny=[[],[],[],[]]\n",
    "\n",
    "\n",
    "\n",
    "vx, vy = [0.2,0.2,0.2,0.2], [0.2,0.2,0.2,0.2]\n",
    "p=[0.5,0.5,0.5,0.5]\n",
    "\n",
    "\n",
    "rsum=[[],[],[],[]]\n",
    "\n",
    "\n",
    "turns = 0\n",
    "shrink = False\n",
    "while turns < 100 and not shrink :\n",
    "\tT = 0.04\n",
    "\tif turns > 500:\n",
    "\t\tT = 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]/(2*np.pi*np.sqrt(vx[k]*vy[k]))*np.exp(-(assignx[k]-datax[n])**2/(2*T*vx[k])-(assigny[k]-datay[n])**2/(2*T*vy[k]))\n",
    "\t\t\tsum[n]=s\n",
    "\t\tfor k in range(4):\n",
    "\t\t\tr[k][n]=p[k]/(2*np.pi*np.sqrt(vx[k]*vy[k]))*np.exp(-(assignx[k]-datax[n])**2/(2*T*vx[k])-(assigny[k]-datay[n])**2/(2*T*vy[k]))/s\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\trsum[k]=rs\n",
    "\t\t\t\n",
    "\t\tua=[0,0]\n",
    "\n",
    "\t\tfor n in range(len(data)):\n",
    "\t\t\tua[0]=ua[0]+r[k][n]*datax[n]/float(rsum[k])\n",
    "\t\t\tua[1]=ua[1]+r[k][n]*datay[n]/float(rsum[k])\n",
    "\t\tupdate_assignx[k]=ua[0]\n",
    "\t\tupdate_assigny[k]=ua[1]\n",
    "\t\t\t\n",
    "\t\t\t\n",
    "\tassignx= update_assignx\n",
    "\tassigny= update_assigny\n",
    "\tfor k in range(4):\n",
    " \t\t for n in range(len(data)):\n",
    "\t\t\tvx[k]=vx[k]+r[k][n]*(datax[n]-assignx[k])**2/float(rsum[k])\n",
    "\t\t\tvy[k]=vy[k]+r[k][n]*(datay[n]-assigny[k])**2/float(rsum[k])\n",
    "\n",
    "    \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",
    "\tturns += 1\n",
    "\n",
    "c=[[],[],[],[]]\n",
    "\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",
    "ell =[]\n",
    "\n",
    "colors = ['r','g','b','y']\n",
    "\n",
    "for i in range(4):\n",
    "\tif c[i] != []:\n",
    "\t\tell.append(Ellipse(xy=[assignx[i],assigny[i]],width=np.sqrt(vx[i]/4),height=np.sqrt(vy[i]/4),color=colors[i],fill=False))\n",
    "        \n",
    "\n",
    "fig=plt.figure(0) \n",
    "ax=fig.add_subplot(111, aspect='equal')\n",
    "plt.xlim([-0.3,1.3])\n",
    "plt.ylim([-0.3,1.3])\n",
    "for i in range(len(ell)):\n",
    "\tax.add_artist(ell[i])\n",
    "\n",
    "for i in range(4):\n",
    "\tax.scatter([x for x,y in c[i]],[y for x,y in c[i]],color=colors[i])\n",
    "\n",
    "plt.show()\n",
    "\n",
    "\n",
    "\n"
   ]
  }
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