mbeltagy/GMM_for_clustering.ipynb

## GMM_for_clustering.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Experimenting with Gausian Mixture models for clustering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "using RDatasets\n",
    "using PyPlot\n",
    "using Clustering"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the IRIS dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element DataArrays.DataArray{String,1}:\n",
       " \"setosa\"    \n",
       " \"versicolor\"\n",
       " \"virginica\" "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris = dataset(\"datasets\", \"iris\")\n",
    "classes=unique(iris[:,5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above is a listing of the three species of flowers in the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"data-frame\"><tr><th></th><th>SepalLength</th><th>SepalWidth</th><th>PetalLength</th><th>PetalWidth</th><th>Species</th></tr><tr><th>1</th><td>5.1</td><td>3.5</td><td>1.4</td><td>0.2</td><td>setosa</td></tr><tr><th>2</th><td>4.9</td><td>3.0</td><td>1.4</td><td>0.2</td><td>setosa</td></tr><tr><th>3</th><td>4.7</td><td>3.2</td><td>1.3</td><td>0.2</td><td>setosa</td></tr><tr><th>4</th><td>4.6</td><td>3.1</td><td>1.5</td><td>0.2</td><td>setosa</td></tr><tr><th>5</th><td>5.0</td><td>3.6</td><td>1.4</td><td>0.2</td><td>setosa</td></tr><tr><th>6</th><td>5.4</td><td>3.9</td><td>1.7</td><td>0.4</td><td>setosa</td></tr></table>"
      ],
      "text/plain": [
       "6×5 DataFrames.DataFrame\n",
       "│ Row │ SepalLength │ SepalWidth │ PetalLength │ PetalWidth │ Species  │\n",
       "├─────┼─────────────┼────────────┼─────────────┼────────────┼──────────┤\n",
       "│ 1   │ 5.1         │ 3.5        │ 1.4         │ 0.2        │ \"setosa\" │\n",
       "│ 2   │ 4.9         │ 3.0        │ 1.4         │ 0.2        │ \"setosa\" │\n",
       "│ 3   │ 4.7         │ 3.2        │ 1.3         │ 0.2        │ \"setosa\" │\n",
       "│ 4   │ 4.6         │ 3.1        │ 1.5         │ 0.2        │ \"setosa\" │\n",
       "│ 5   │ 5.0         │ 3.6        │ 1.4         │ 0.2        │ \"setosa\" │\n",
       "│ 6   │ 5.4         │ 3.9        │ 1.7         │ 0.4        │ \"setosa\" │"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "head(iris)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The data has four parameters and an associated species. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "breakDataByClass (generic function with 2 methods)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function breakDataByClass(f,classes=classes)\n",
    "    dataByClass=Array{Array{Float64}}(length(classes))\n",
    "    for i=1:length(classes)\n",
    "        dataByClass[i]=Float64[]\n",
    "    end\n",
    "    for i=1:size(iris,1)\n",
    "        current_class=f(i)\n",
    "        for j=1:4\n",
    "            push!(dataByClass[current_class],iris[i,j])\n",
    "        end\n",
    "    end\n",
    "    for i=1:length(classes)\n",
    "        dataByClass[i]=reshape(dataByClass[i],4,div(length(dataByClass[i]),4))\n",
    "    end\n",
    "    dataByClass\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A convience method the helps in the plotting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "orgPlot (generic function with 1 method)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataByClass= breakDataByClass(x->findfirst(iris[x,5].==classes))\n",
    "function orgPlot(dataByClass,classes) # Poltiong the classes\n",
    "    p_syms=[\"*\",\"+\",\"o\",\"k+\"]\n",
    "    for i=1:length(classes)\n",
    "        plot( dataByClass[i][1,:],dataByClass[i][3,:], p_syms[i], label=classes[i])\n",
    "    end\n",
    "    legend(bbox_to_anchor=(0., 1.02, 1., .102), loc=3,\n",
    "               ncol=3, mode=\"expand\", borderaxespad=0.)\n",
    "    xlabel(\"$(names(iris)[1])\")\n",
    "    ylabel(\"$(names(iris)[3])\");\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We start with a KNN type analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7f696c1b6910>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "srand(67)\n",
    "R=kmeans(Array(iris[:,1:4])',3)\n",
    "dataByCluster=breakDataByClass(z->R.assignments[z])\n",
    "figure(\"Comparing stuff\", figsize=(15,7))\n",
    "title(\"GMM prediction\")\n",
    "subplot(1,2,1)\n",
    "orgPlot(dataByCluster,[\"Cluster$i\" for i=1:3]);\n",
    "subplot(1,2,2)\n",
    "orgPlot(dataByClass,classes);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The figure on the left shows the KNN clusters and one on the right shows the\n",
    "original classification. Note how the KNN cluster are limited by the spherical\n",
    "Euclidean distance metric and hence struggle to separate the top most clusters\n",
    "into their original classes. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "using GaussianMixtures"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  Iters               objv        objv-change | affected \n",
      "-------------------------------------------------------------\n",
      "      0       2.260000e+02\n",
      "      1       7.918304e+01      -1.468170e+02 |        2\n",
      "      2       7.885144e+01      -3.315966e-01 |        0\n",
      "      3       7.885144e+01       0.000000e+00 |        0\n",
      "K-means converged with 3 iterations (objv = 78.85144142614651)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO: Initializing GMM, 3 Gaussians diag covariance 4 dimensions using 150 data points\n",
      "INFO: K-means with 150 data points using 3 iterations\n",
      "10.0 data points per parameter\n",
      "INFO: Running 10 iterations EM on diag cov GMM with 3 Gaussians in 4 dimensions\n",
      "INFO: iteration 1, average log likelihood -0.515143\n",
      "INFO: iteration 2, average log likelihood -0.512267\n",
      "INFO: iteration 3, average log likelihood -0.511997\n",
      "INFO: iteration 4, average log likelihood -0.511967\n",
      "INFO: iteration 5, average log likelihood -0.511964\n",
      "INFO: iteration 6, average log likelihood -0.511963\n",
      "INFO: iteration 7, average log likelihood -0.511963\n",
      "INFO: iteration 8, average log likelihood -0.511963\n",
      "INFO: iteration 9, average log likelihood -0.511963\n",
      "INFO: iteration 10, average log likelihood -0.511963\n",
      "INFO: EM with 150 data points 10 iterations avll -0.511963\n",
      "5.8 data points per parameter\n"
     ]
    }
   ],
   "source": [
    "gm=GMM(3,Array(iris[:,1:4]));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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jk3ujW2nutKr/8jbl+fzs3uiO2PK4z4/sPs/NzdVf//pXdevWTf/7v/9b7/MigTFGrcrLVVv/KktSXHl5wOb7CXZ53Ot13+svv/yy5syZowceeEC5ubnq2rWr0tPTo34iW9Qumtt5lmUpJibGb2+Tdu3aSZI2bNigd999VxdddJHGjRvnc8wxxxyj2bNn65dfftGSJUvqVWZ5ebmee+45OZ1OzZ0712ffiSeeqClTpqi8vFzPPPOMT5zNmzf32wuhMs5K1XvXVDd16lQZY7Ry5cp6xRlJormNJkn/8z//I8uytGjRIp/t+/fv10svvaROnTopOTlZkvTII4/Isiw9/vjjat26tc/xV155pU499VS/7wdJmjdvXo131OHeXVLd76/vv/9eL730krp06aIHHnigxv5WrVrpmGOOkSRt27ZNb7zxhnr06KFbbrnF57izzjpLl156qXbu3KlXXnnlsGUuXbpUO3fuVHp6ugYOHOiz79Zbb1VCQoLeeOMNffPNNzV+19tuu03HH3/8Ya8fiaK9fScd2XNyOJZl6e67767Rm02qWHm5WbNmuueee3y2x8fH6+abbz7i3ychIUGZmZk+20aNGqXjjz9ea9eurfP8vLw8ff311zr//PN18cUX19j/28UMIuH90GSGczocDk2efI0efXSZqi/Q2KaNpcmTr4n48kLl0ksvVXZ2ts4//3xNmDBBI0aM0KBBg9SzZ88jus7atWt18OBBSRXdu39r//79kqQvvviixr4zzjijAZFHp/Q+6T6Txqa505Sbnhs15YVKpN3nhYWFuvzyy+V0OrVkyZKoW4HKsiyVORwykt+Gj5FU5nAEbILvYJcXSpFyr7vdbrndbu3Zs0effvqpZs+ereuuu04ffvihHn/88SOKFdEhmtt5l19+uaZNm6ZevXrp0ksv1ZAhQzRo0CCfFduKiookVQxJ8/fM/fe//5Uxxu8z58+XX36pn3/+WWeffbbfd8iIESOUlZWl9evX+8T56KOPqlevXrr44os1ZMgQuVyuquRDdXv37tXDDz+spUuXatOmTfJ4PFV/2FmWpW3bttUrzkgS7W20bt266ZxzztGbb76pL774QieffLKkiiGLu3bt0q233lo1BOuDDz6Qw+HQiy++6Pda+/fv1/fff19jyFuLFi3Up0+fGsefcsopOu200+R2u7V161alpaVp0KBBGjBgQL2mtFi7dq28Xq+GDBmiFi1aHPbYjz/+WJJ09tln+x1SNmLECD333HNav369rrjiisNex7IsDRs2rMa+mJgYDRkyRM8884w+/vhjde/e3Wd/tP7t0xTad0fynNTF333g8Xi0efNmHX/88X4TrYMHDz7imE899VS/ddC9e3d98MEHdZ7/wQcfyLKseiUHpch4PzSZJFolr/eAWrZ8Um3bvqhduy6R13sg4svr0qWLvvjii5DcUAMGDNDq1auVlZWll19+Wc8884yMMTr55JM1a9Ysv9lmf3744QdJFS+x2jLalmWprKysxvbOnTs3/BdAxOA+r999vnr1ao0ZM0YxMTFavny5Tj/99HqdF2kGpaZqRU6OzxwWlV63bQ1OS4vY8rjX6/9veuvWrXXmmWcqLy9PAwYM0JNPPqmbb765zrnkEL2isZ03depUdezYUf/3f/+nRx55RA8//LAkafjw4XrggQd02mmnVT1zBQUFKigo8Hud2p45f3bv3i2p9uexstdn5XGS9PDDD+uEE07QwoULdd999+nee+9VTEyMzjvvPD300ENKTEyUVLF69PDhw7V27Vr16dNHl156qTp27FiV7Jg1a5b27dtXrzgRXq666iq98cYbWrRoke69915JFb1iLMvSlVdeWXXcDz/8oIMHD/qdF7OSZVnas2ePTxKtU6dOfo+1bVtvvfWW5syZo5dfflm33367jDE65phjNHHixKr5PGuza9cuSTV7xPjTkGcj0NeJ5r99orl9V6m+z0ld/K2m+dNPP9W673DbD6e2L+NjYmLk9VNvv3Ukz1ekvB+azHDOSv36Jer++y199dUy3X+/pX79EiO+vMGDB8sYozfffPOor1WZ+fb3QFQ+AL81cOBA5ebmaufOnSosLNRdd92l7du367LLLtOqVavqVW7lwzl16lQdPHiw1v/eeOONGudGQ+8P1I37vO77/J133tGYMWPUvHlzrVy5Ui6Xq15xRaJpWVl6KClJ+batyk7pRlK+bWt+UpJu/c3wo0gqj3v9yP9Nj4mJ0TnnnCOpYlgbmq5obOdJ0hVXXKH3339fP/zwg1577TVde+21WrVqlUaPHq0ffvih6pnLzs4+7DP35JNP1qu8yutVDi//rf/85z8+x0kVz+6UKVP08ccfa/v27frHP/6hcePGadmyZRozZowOHKhIMC5btkxr167VpEmT9Mknn+ixxx7T3Xffrbvuukv/7//9vwbXEUJv3LhxcjqdevbZZ2WM0ffff6+VK1fq1FNP9elB1qZNGx177LGHvVcPHDhQowfW4d4Pbdq00YMPPqivv/5a//rXv/TUU0/p5JNP1iOPPKIbb7zxsHFXTuJeny+vGvJsBPo60fy3TzS37yrV9zlpiMqev9urd5GuprbtjelInq9IeT80uSTaiy/maPLkaxQXF6fJk6/Riy/mRHx5kyZNksPh0JIlS+rspl85hKY2ld/2/Hb8vaQ6xzw7HA6deeaZmjVrlrKzs+X1erV06dKq/ZVzeVQO8anujDPOkG3beu+99w5bBo5Meu/0ug+KkPK4zw/vzTff1HnnnacWLVqooKAganugVXI6nVpSVKQ1GRkalZCg8+PjNSohQWsyMrSkqMhnRa9IK497vWG+/fZbSfI7dAxNRzS286o75phjlJycrMcff1wTJ07UDz/8oPfee09nnnmmJB3RM9esWTMZY/w+w7///e8VFxenTz75pKpnQ3VvvfWWJKl/f/+rkXbo0EEXXHCBXnjhBZ1zzjn617/+pU8//VSS9NVXX8myrBpzt0mqd6I+GkRTG61Sy5YtddFFF6m0tFRvvPGGnn32WR04cEBXXXWVz3Fnnnmmdu7cqeLi4kaJo2fPnpo0aZJWrVql1q1b1zk/WfV31i+//HLYYytX+Vy9erXfL6jeeustWZalfv361XkdY4zfe/7gwYNVz3Jd14k20dy+q1Tf56QhnE6nevbsqW3btmnr1q019ofib+0zzzxTxhitWLGizmMj5f3Q5JJo0ahHjx5VXRtTUlK0bt06v8fl5+fXORZ54MCBMsboiSee8Nn+5ptv6oUXXqhxfFFRkd+XTeW3KtXnFWjfvr2MMX7/mOvYsaMuv/xyffTRR5o7d67fl9LmzZtVUlJy2Pjhq/pcGJFeHvd57VauXKnU1FTFxcXpjTfeaDINLqfTqVnZ2SrYskVLv/lGBVu2aFZ2dqM0eIJZHve6fz/++KO2bNnid9+rr76qpUuXqn379ho6dGi9rwlEgtr+cKjsUdCiRQv1799fZ599tv7xj39o4cKFfo//9NNP9f3331f93L59e0n+k+wOh0OXX365fvrpJ82YMcNn37///W898sgjat68edWcT/v379f7779f4zrl5eVVQ00r//1ISEiQMUZvv/22z7GbN2/WHXfcEdW9bKqLpjZadRMnTpQxRosWLdIzzzwjh8Ohyy67zOeYygnCr7vuuqoeV9Xt3btXa9asqXeZJSUlft8PP/74o/bt21frggOVOnTooEsvvVTbtm3TbbfdVmN/WVlZVTI5Pj5e5557rkpKSjR//nyf49asWSO326127drpwgsvPGyZF1xwgdq1aye3213jd50/f762bNmic889NySLDIVatLbvqqvPc9JQV155pQ4ePKg777zTZ/s333yj7OzsoP8bm5qaqoSEBC1dulSLFy+usb96D7VIeT80uTnRotWdd96pgwcPavbs2Tr99NN11llnacCAAWrdurW2b9+ud999V//617/qnIhy0qRJmjdvnu69917985//1CmnnKJNmzbp9ddf17hx4/Tyyy/7HP/nP/9Zb731ls4++2wlJiaqdevW+uyzz5Sfn6927dr5dLscPny4bNvWHXfcoQ0bNlT1kKhc7ePRRx/VV199pZkzZ+qZZ57R4MGDddxxx6m0tFTFxcX66KOP5Ha7a12xw58vv/xS9957ryzLqpqQcOfOnZo0aVLVMQ8++GCNVaMQnrjPa9q0aZPOP/987d+/X2PHjtXSpUt9egtVmjlzZr2uF6mC/VJt7PK412v65ptv1L9/fw0YMEC///3vFR8fr127dumf//ynPvjgA7Vs2VJ///vfDzvvDRCJLrzwwqr5/yr/wHjvvfe0du1aDRgwQCNHjpQkPf/88xoxYoSuvfZaPfLIIxo4cKDatm2rb7/9Vhs2bNBnn32moqIidezYUZLkcrkUFxenhx9+WDt27KiaK2fKlClyOp2677779N577+nRRx/Vhx9+qOHDh+v777/X4sWLtWfPHuXk5KhHjx6SpJ9//lmDBw/W7373O/Xv3189evTQL7/8ooKCAn3xxRdKTU2tmkA7NTVVv/vd7zR//nxt3LhRp512mr7++mu99tprGjt2rN8EPyJH5ftj8eLFKi8vV1pams8iGJJ0zjnn6P7779edd96pE088USkpKUpMTNSePXv09ddf65133tHZZ5+t5cuX16vMTz75ROPGjdPpp5+upKQkde3aVd9//72WLVumAwcO6Pbbb6/zGo8++qg+++wz5eTk6M0339SoUaPUvHlzbd68WStXrlReXp6GDBkiSXrsscc0ePBg3XbbbVq5cqUGDBigrVu36uWXX1azZs20cOFCtWrVyuf6v10RsVWrVvrb3/6miy++WEOHDtWECRN0/PHHa926dVq5cqW6du2qxx57rF6/fzSLtvZdpfo8Jw112223aenSpXrhhRf0xRdfaNSoUdq1a5cWL16soUOH6pVXXqn34gUN8dt73eFwaPHixRo9erQuueQSPfbYYzrjjDP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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7f6967fdc150>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "prob_pos=gmmposterior(gm,Array(iris[:,1:4]))[1]\n",
    "ass=[indmax(prob_pos[i,:]) for i=1:size(iris,1)]\n",
    "dataByCluster=breakDataByClass(x->ass[x])\n",
    "figure(\"Comparing stuff\", figsize=(15,7))\n",
    "title(\"GMM prediction\")\n",
    "subplot(1,2,1)\n",
    "orgPlot(dataByCluster,[\"Cluster$i\" for i=1:3]);\n",
    "subplot(1,2,2)\n",
    "orgPlot(dataByClass,classes);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The default GMM building has uses a diagonal covariance matrix. This does not\n",
    "give it enough flexibility and hence, in this case, the results are not much better\n",
    "than KNN."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  Iters               objv        objv-change | affected \n",
      "-------------------------------------------------------------\n",
      "      0       1.858500e+02\n",
      "      1       1.027225e+02      -8.312751e+01 |        2\n",
      "      2       7.963488e+01      -2.308762e+01 |        2\n",
      "      3       7.899750e+01      -6.373778e-01 |        2\n",
      "      4       7.885567e+01      -1.418331e-01 |        0\n",
      "      5       7.885567e+01       0.000000e+00 |        0\n",
      "K-means converged with 5 iterations (objv = 78.85566582597703)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO: Initializing GMM, 3 Gaussians diag covariance 4 dimensions using 150 data points\n",
      "INFO: K-means with 150 data points using 5 iterations\n",
      "10.0 data points per parameter\n",
      "INFO: Running 10 iterations EM on full cov GMM with 3 Gaussians in 4 dimensions\n",
      "INFO: iteration 1, average log likelihood -0.334323\n",
      "INFO: iteration 2, average log likelihood -0.321513\n",
      "INFO: iteration 3, average log likelihood -0.317949\n",
      "INFO: iteration 4, average log likelihood -0.316207\n",
      "INFO: iteration 5, average log likelihood -0.314646\n",
      "INFO: iteration 6, average log likelihood -0.313034\n",
      "INFO: iteration 7, average log likelihood -0.311297\n",
      "INFO: iteration 8, average log likelihood -0.309474\n",
      "INFO: iteration 9, average log likelihood -0.307770\n",
      "INFO: iteration 10, average log likelihood -0.306245\n",
      "INFO: EM with 150 data points 10 iterations avll -0.306245\n",
      "3.4 data points per parameter\n"
     ]
    }
   ],
   "source": [
    "gm=GMM(3,Array(iris[:,1:4]),kind=:full);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7f6967fc3550>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "prob_pos=gmmposterior(gm,Array(iris[:,1:4]))[1]\n",
    "ass=[indmax(prob_pos[i,:]) for i=1:size(iris,1)]\n",
    "dataByCluster=breakDataByClass(x->ass[x])\n",
    "figure(\"Comparing stuff\", figsize=(15,7))\n",
    "title(\"GMM prediction\")\n",
    "subplot(1,2,1)\n",
    "orgPlot(dataByCluster,[\"Cluster$i\" for i=1:3]);\n",
    "subplot(1,2,2)\n",
    "orgPlot(dataByClass,classes);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A more flexible GMM building with a `full` covariance matrix does much better job. Note the leftmost Cluster1 point corresponding to *virginica*. "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 0.5.0-rc4",
   "language": "julia",
   "name": "julia-0.5"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "0.5.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}