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  1. {
  2.  "cells": [
  3.   {
  4.    "cell_type": "code",
  5.    "execution_count": 1,
  6.    "metadata": {},
  7.    "outputs": [],
  8.    "source": [
  9.     "using Distributions\n",
  10.     "using GaussianMixtures\n",
  11.     "using PyPlot"
  12.    ]
  13.   },
  14.   {
  15.    "cell_type": "code",
  16.    "execution_count": 2,
  17.    "metadata": {},
  18.    "outputs": [
  19.     {
  20.      "data": {
  21.       "image/png": 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",
  22.       "text/plain": [
  23.        "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
  24.       ]
  25.      },
  26.      "metadata": {},
  27.      "output_type": "display_data"
  28.     },
  29.     {
  30.      "data": {
  31.       "text/plain": [
  32.        "PyObject <matplotlib.collections.PathCollection object at 0x7fb7fd8c7780>"
  33.       ]
  34.      },
  35.      "execution_count": 2,
  36.      "metadata": {},
  37.      "output_type": "execute_result"
  38.     }
  39.    ],
  40.    "source": [
  41.     "# create 5 evenly distributed cluster centers\n",
  42.     "m = convert(Array{Float64,2}, [3 3; 3 15; 15 15; 15 3; 9 9])\n",
  43.     "scatter(m[:,1], m[:,2])"
  44.    ]
  45.   },
  46.   {
  47.    "cell_type": "code",
  48.    "execution_count": 3,
  49.    "metadata": {},
  50.    "outputs": [
  51.     {
  52.      "data": {
  53.       "text/plain": [
  54.        "2×2 Array{Int64,2}:\n",
  55.        " 1  0\n",
  56.        " 0  1"
  57.       ]
  58.      },
  59.      "execution_count": 3,
  60.      "metadata": {},
  61.      "output_type": "execute_result"
  62.     }
  63.    ],
  64.    "source": [
  65.     "# create covariation matrix\n",
  66.     "s = [1 0; 0 1]"
  67.    ]
  68.   },
  69.   {
  70.    "cell_type": "code",
  71.    "execution_count": 4,
  72.    "metadata": {},
  73.    "outputs": [
  74.     {
  75.      "data": {
  76.       "text/plain": [
  77.        "5"
  78.       ]
  79.      },
  80.      "execution_count": 4,
  81.      "metadata": {},
  82.      "output_type": "execute_result"
  83.     }
  84.    ],
  85.    "source": [
  86.     "# number of classes in source data\n",
  87.     "classes = size(m)[1]"
  88.    ]
  89.   },
  90.   {
  91.    "cell_type": "code",
  92.    "execution_count": 5,
  93.    "metadata": {},
  94.    "outputs": [],
  95.    "source": [
  96.     "# for each class generate 2d mixed gaussians with 1000 points each and concatenate them in a single vector\n",
  97.     "for i=1:classes\n",
  98.     "    mvn = MvNormal(m[i,:], s)\n",
  99.     "    arr = rand(mvn,1000)\n",
  100.     "    \n",
  101.     "    # arr is an 2 element column vector where each element is an row vector of (1000,) size\n",
  102.     "    if i==1\n",
  103.     "        global xfull = arr[1,:]'\n",
  104.     "        global yfull = arr[2,:]'\n",
  105.     "    else\n",
  106.     "        xfull = hcat(xfull, arr[1,:]')\n",
  107.     "        yfull = hcat(yfull, arr[2,:]')        \n",
  108.     "    end\n",
  109.     "        \n",
  110.     "end"
  111.    ]
  112.   },
  113.   {
  114.    "cell_type": "code",
  115.    "execution_count": 6,
  116.    "metadata": {},
  117.    "outputs": [
  118.     {
  119.      "data": {
  120.       "text/plain": [
  121.        "(1, 5000)"
  122.       ]
  123.      },
  124.      "execution_count": 6,
  125.      "metadata": {},
  126.      "output_type": "execute_result"
  127.     }
  128.    ],
  129.    "source": [
  130.     "size(xfull)"
  131.    ]
  132.   },
  133.   {
  134.    "cell_type": "code",
  135.    "execution_count": 7,
  136.    "metadata": {},
  137.    "outputs": [
  138.     {
  139.      "data": {
  140.       "image/png": 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",
  141.       "text/plain": [
  142.        "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
  143.       ]
  144.      },
  145.      "metadata": {},
  146.      "output_type": "display_data"
  147.     },
  148.     {
  149.      "data": {
  150.       "text/plain": [
  151.        "PyObject <matplotlib.collections.PathCollection object at 0x7fb7fd8e00b8>"
  152.       ]
  153.      },
  154.      "execution_count": 7,
  155.      "metadata": {},
  156.      "output_type": "execute_result"
  157.     }
  158.    ],
  159.    "source": [
  160.     "# display generated clusters data. each cluster contains 1000 points of 2d mixed gaussians\n",
  161.     "scatter(xfull, yfull)"
  162.    ]
  163.   },
  164.   {
  165.    "cell_type": "code",
  166.    "execution_count": 8,
  167.    "metadata": {},
  168.    "outputs": [
  169.     {
  170.      "data": {
  171.       "text/plain": [
  172.        "5000×2 Array{Float64,2}:\n",
  173.        "  2.68897   3.42787 \n",
  174.        "  1.69879   3.03419 \n",
  175.        "  2.15612   2.64969 \n",
  176.        "  3.51008   2.05623 \n",
  177.        "  3.53597   3.01573 \n",
  178.        "  4.13259   3.10096 \n",
  179.        "  1.35953   3.40438 \n",
  180.        "  1.60389   3.77203 \n",
  181.        "  1.63905   3.68828 \n",
  182.        "  4.96802   1.86317 \n",
  183.        "  2.71256   2.66798 \n",
  184.        "  3.18305   0.196338\n",
  185.        "  3.81788   4.28388 \n",
  186.        "  ⋮                 \n",
  187.        "  6.61715   9.73912 \n",
  188.        "  9.98262   9.26157 \n",
  189.        "  9.34681   9.2978  \n",
  190.        "  8.33693   8.64992 \n",
  191.        "  7.10736  10.4348  \n",
  192.        "  5.80049  10.391   \n",
  193.        " 10.2621    9.18297 \n",
  194.        "  8.84101  11.4162  \n",
  195.        "  8.44779   9.19123 \n",
  196.        "  9.90137   8.89936 \n",
  197.        "  9.35692   8.14735 \n",
  198.        "  8.523     9.29872 "
  199.       ]
  200.      },
  201.      "execution_count": 8,
  202.      "metadata": {},
  203.      "output_type": "execute_result"
  204.     }
  205.    ],
  206.    "source": [
  207.     "# create source data array as concatenation of 5 separate in space 2d mixed gaussians\n",
  208.     "X = hcat(xfull', yfull')"
  209.    ]
  210.   },
  211.   {
  212.    "cell_type": "code",
  213.    "execution_count": 9,
  214.    "metadata": {},
  215.    "outputs": [
  216.     {
  217.      "name": "stderr",
  218.      "output_type": "stream",
  219.      "text": [
  220.       "┌ Info: Initializing GMM, 5 Gaussians LinearAlgebra.diag covariance 2 dimensions using 5000 data points\n",
  221.       "└ @ GaussianMixtures /home/toleg/.julia/packages/GaussianMixtures/RGtTJ/src/train.jl:77\n",
  222.       "┌ Warning: implicit `dims=2` argument now has to be passed explicitly to specify that distances between columns should be computed\n",
  223.       "│   caller = ip:0x0\n",
  224.       "└ @ Core :-1\n"
  225.      ]
  226.     },
  227.     {
  228.      "name": "stdout",
  229.      "output_type": "stream",
  230.      "text": [
  231.       "  Iters               objv        objv-change | affected \n",
  232.       "-------------------------------------------------------------\n",
  233.       "      0       1.675874e+04\n",
  234.       "      1       9.739258e+03      -7.019478e+03 |        0\n",
  235.       "      2       9.739258e+03       0.000000e+00 |        0\n",
  236.       "K-means converged with 2 iterations (objv = 9739.258387061276)\n"
  237.      ]
  238.     },
  239.     {
  240.      "name": "stderr",
  241.      "output_type": "stream",
  242.      "text": [
  243.       "┌ Warning: implicit `dims=2` argument now has to be passed explicitly to specify that distances between columns should be computed\n",
  244.       "│   caller = macro expansion at printf.jl:161 [inlined]\n",
  245.       "└ @ Core ./printf.jl:161\n",
  246.       "┌ Info: K-means with 5000 data points using 2 iterations\n",
  247.       "│ 333.3 data points per parameter\n",
  248.       "└ @ GaussianMixtures /home/toleg/.julia/packages/GaussianMixtures/RGtTJ/src/train.jl:138\n",
  249.       "┌ Info: Running 0 iterations EM on full cov GMM with 5 Gaussians in 2 dimensions\n",
  250.       "└ @ GaussianMixtures /home/toleg/.julia/packages/GaussianMixtures/RGtTJ/src/train.jl:242\n",
  251.       "┌ Info: EM with 5000 data points 0 iterations avll -2.209936\n",
  252.       "│ 172.4 data points per parameter\n",
  253.       "└ @ GaussianMixtures /home/toleg/.julia/packages/GaussianMixtures/RGtTJ/src/gmms.jl:71\n"
  254.      ]
  255.     },
  256.     {
  257.      "data": {
  258.       "text/plain": [
  259.        "GMM{Float64} with 5 components in 2 dimensions and full covariance\n",
  260.        "Mix 1: weight 0.200000\n",
  261.        " mean: [9.01301, 9.01512]\n",
  262.        " covariance: 2×2 Array{Float64,2}:\n",
  263.        "  1.01478    -0.0118714\n",
  264.        " -0.0118714   0.986692 \n",
  265.        "Mix 2: weight 0.200000\n",
  266.        " mean: [14.9994, 3.0264]\n",
  267.        " covariance: 2×2 Array{Float64,2}:\n",
  268.        " 0.971859   0.0287232\n",
  269.        " 0.0287232  0.942263 \n",
  270.        "⋮\n",
  271.        "Mix 4: weight 0.200000\n",
  272.        " mean: [3.02209, 2.98229]\n",
  273.        " covariance: 2×2 Array{Float64,2}:\n",
  274.        "  0.939732   -0.0301108\n",
  275.        " -0.0301108   0.976562 \n",
  276.        "Mix 5: weight 0.200000\n",
  277.        " mean: [2.91973, 14.975]\n",
  278.        " covariance: 2×2 Array{Float64,2}:\n",
  279.        "  0.916032    -0.00912194\n",
  280.        " -0.00912194   1.04543   \n"
  281.       ]
  282.      },
  283.      "execution_count": 9,
  284.      "metadata": {},
  285.      "output_type": "execute_result"
  286.     },
  287.     {
  288.      "name": "stdout",
  289.      "output_type": "stream",
  290.      "text": [
  291.       "4 (1:2, 4:5)\n"
  292.      ]
  293.     }
  294.    ],
  295.    "source": [
  296.     "# creating a model with 100 iterations for K-means initialization and without any fitting\n",
  297.     "gmm = GMM(classes, X, kind=:full, nInit=100, nIter=0)"
  298.    ]
  299.   },
  300.   {
  301.    "cell_type": "code",
  302.    "execution_count": 10,
  303.    "metadata": {},
  304.    "outputs": [
  305.     {
  306.      "name": "stderr",
  307.      "output_type": "stream",
  308.      "text": [
  309.       "┌ Info: Running 1 iterations EM on full cov GMM with 5 Gaussians in 2 dimensions\n",
  310.       "└ @ GaussianMixtures /home/toleg/.julia/packages/GaussianMixtures/RGtTJ/src/train.jl:242\n",
  311.       "┌ Info: iteration 1, average log likelihood -2.209936\n",
  312.       "└ @ GaussianMixtures /home/toleg/.julia/packages/GaussianMixtures/RGtTJ/src/gmms.jl:71\n"
  313.      ]
  314.     },
  315.     {
  316.      "name": "stdout",
  317.      "output_type": "stream",
  318.      "text": [
  319.       "Iteration 1, previous: 0, current: -2.2099357850316164, delta: 2.2099357850316164\n",
  320.       "Iteration 2, previous: -2.2099357850316164, current: -2.209935536501018, delta: 2.485305983235264e-7\n",
  321.       "Log likelihood change delta is less than defined threshold: 1.0e-5. EM phase stopped"
  322.      ]
  323.     },
  324.     {
  325.      "name": "stderr",
  326.      "output_type": "stream",
  327.      "text": [
  328.       "┌ Info: EM with 5000 data points 1 iterations avll -2.209936\n",
  329.       "│ 172.4 data points per parameter\n",
  330.       "└ @ GaussianMixtures /home/toleg/.julia/packages/GaussianMixtures/RGtTJ/src/gmms.jl:71\n",
  331.       "┌ Info: Running 1 iterations EM on full cov GMM with 5 Gaussians in 2 dimensions\n",
  332.       "└ @ GaussianMixtures /home/toleg/.julia/packages/GaussianMixtures/RGtTJ/src/train.jl:242\n",
  333.       "┌ Info: iteration 1, average log likelihood -2.209936\n",
  334.       "└ @ GaussianMixtures /home/toleg/.julia/packages/GaussianMixtures/RGtTJ/src/gmms.jl:71\n",
  335.       "┌ Info: EM with 5000 data points 1 iterations avll -2.209936\n",
  336.       "│ 172.4 data points per parameter\n",
  337.       "└ @ GaussianMixtures /home/toleg/.julia/packages/GaussianMixtures/RGtTJ/src/gmms.jl:71\n"
  338.      ]
  339.     },
  340.     {
  341.      "name": "stdout",
  342.      "output_type": "stream",
  343.      "text": [
  344.       "\n"
  345.      ]
  346.     }
  347.    ],
  348.    "source": [
  349.     "# defining EM phase exit condition as log likelihood change delta is less than 1e-5\n",
  350.     "const delta = 1e-5\n",
  351.     "\n",
  352.     "# init iterations counter, total number of iterations, current and previous log likelihoods\n",
  353.     "i = 0\n",
  354.     "iter_max = 100\n",
  355.     "prev_prob, curr_prob = 0, 0\n",
  356.     "\n",
  357.     "# running iterations until likelihood change will become less than delta or max iterations exceeded\n",
  358.     "while i == 0 || (abs(curr_prob - prev_prob) >= delta && i <= iter_max)\n",
  359.     "    prev_prob = curr_prob\n",
  360.     "    curr_prob = GaussianMixtures.em!(gmm, X, nIter=1)[1]\n",
  361.     "    i += 1\n",
  362.     "    println(\"Iteration \", i, \", previous: \", prev_prob, \", current: \", curr_prob, \", delta: \", abs(curr_prob - prev_prob))\n",
  363.     "end\n",
  364.     "\n",
  365.     "if abs(curr_prob - prev_prob) < delta\n",
  366.     "    println(\"Log likelihood change delta is less than defined threshold: $delta. EM phase stopped\")\n",
  367.     "elseif i > iter_max\n",
  368.     "    println(\"Max iterations number exceeded. EM phase stopped\")\n",
  369.     "end\n",
  370.     "    "
  371.    ]
  372.   },
  373.   {
  374.    "cell_type": "code",
  375.    "execution_count": 11,
  376.    "metadata": {
  377.     "scrolled": true
  378.    },
  379.    "outputs": [
  380.     {
  381.      "data": {
  382.       "text/plain": [
  383.        "5×2 Array{Float64,2}:\n",
  384.        "  9.01301   9.01512\n",
  385.        " 14.9994    3.0264 \n",
  386.        " 14.9346   14.9271 \n",
  387.        "  3.02209   2.98229\n",
  388.        "  2.91973  14.975  "
  389.       ]
  390.      },
  391.      "execution_count": 11,
  392.      "metadata": {},
  393.      "output_type": "execute_result"
  394.     }
  395.    ],
  396.    "source": [
  397.     "GaussianMixtures.means(gmm)"
  398.    ]
  399.   },
  400.   {
  401.    "cell_type": "code",
  402.    "execution_count": 12,
  403.    "metadata": {},
  404.    "outputs": [
  405.     {
  406.      "data": {
  407.       "text/plain": [
  408.        "5-element Array{Array{Float64,2},1}:\n",
  409.        " [1.01378 -0.0118405; -0.0118405 0.98572]   \n",
  410.        " [0.970888 0.0286939; 0.0286939 0.941321]   \n",
  411.        " [0.938666 -0.00674876; -0.00674876 1.01503]\n",
  412.        " [0.938789 -0.0300856; -0.0300856 0.975581] \n",
  413.        " [0.915122 -0.00912054; -0.00912054 1.04439]"
  414.       ]
  415.      },
  416.      "execution_count": 12,
  417.      "metadata": {},
  418.      "output_type": "execute_result"
  419.     }
  420.    ],
  421.    "source": [
  422.     "GaussianMixtures.covars(gmm)"
  423.    ]
  424.   },
  425.   {
  426.    "cell_type": "code",
  427.    "execution_count": 13,
  428.    "metadata": {},
  429.    "outputs": [
  430.     {
  431.      "data": {
  432.       "text/plain": [
  433.        "5000-element Array{Int64,1}:\n",
  434.        " 4\n",
  435.        " 4\n",
  436.        " 4\n",
  437.        " 4\n",
  438.        " 4\n",
  439.        " 4\n",
  440.        " 4\n",
  441.        " 4\n",
  442.        " 4\n",
  443.        " 4\n",
  444.        " 4\n",
  445.        " 4\n",
  446.        " 4\n",
  447.        " ⋮\n",
  448.        " 1\n",
  449.        " 1\n",
  450.        " 1\n",
  451.        " 1\n",
  452.        " 1\n",
  453.        " 1\n",
  454.        " 1\n",
  455.        " 1\n",
  456.        " 1\n",
  457.        " 1\n",
  458.        " 1\n",
  459.        " 1"
  460.       ]
  461.      },
  462.      "execution_count": 13,
  463.      "metadata": {},
  464.      "output_type": "execute_result"
  465.     }
  466.    ],
  467.    "source": [
  468.     "# calc probability assignments\n",
  469.     "gp = gmmposterior(gmm, X)[1]\n",
  470.     "\n",
  471.     "# calc cluster assignments array\n",
  472.     "arr = [findmax(gp[i,:])[2] for i=1:size(X,1)]"
  473.    ]
  474.   },
  475.   {
  476.    "cell_type": "code",
  477.    "execution_count": 14,
  478.    "metadata": {},
  479.    "outputs": [
  480.     {
  481.      "data": {
  482.       "image/png": 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",
  483.       "text/plain": [
  484.        "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
  485.       ]
  486.      },
  487.      "metadata": {},
  488.      "output_type": "display_data"
  489.     },
  490.     {
  491.      "data": {
  492.       "text/plain": [
  493.        "PyObject <matplotlib.collections.PathCollection object at 0x7fb7fd74ed68>"
  494.       ]
  495.      },
  496.      "execution_count": 14,
  497.      "metadata": {},
  498.      "output_type": "execute_result"
  499.     }
  500.    ],
  501.    "source": [
  502.     "# display mapped cluster number via color\n",
  503.     "scatter(X[:,1],X[:,2],c=arr)"
  504.    ]
  505.   },
  506.   {
  507.    "cell_type": "code",
  508.    "execution_count": null,
  509.    "metadata": {},
  510.    "outputs": [],
  511.    "source": []
  512.   }
  513.  ],
  514.  "metadata": {
  515.   "kernelspec": {
  516.    "display_name": "Julia 1.0.2",
  517.    "language": "julia",
  518.    "name": "julia-1.0"
  519.   },
  520.   "language_info": {
  521.    "file_extension": ".jl",
  522.    "mimetype": "application/julia",
  523.    "name": "julia",
  524.    "version": "1.0.2"
  525.   }
  526.  },
  527.  "nbformat": 4,
  528.  "nbformat_minor": 2
  529. }
RAW Paste Data
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