1 | #region License Information
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2 | /* HeuristicLab
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3 | * Copyright (C) 2002-2012 Heuristic and Evolutionary Algorithms Laboratory (HEAL)
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4 | *
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5 | * This file is part of HeuristicLab.
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6 | *
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7 | * HeuristicLab is free software: you can redistribute it and/or modify
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8 | * it under the terms of the GNU General Public License as published by
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9 | * the Free Software Foundation, either version 3 of the License, or
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10 | * (at your option) any later version.
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11 | *
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12 | * HeuristicLab is distributed in the hope that it will be useful,
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13 | * but WITHOUT ANY WARRANTY; without even the implied warranty of
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14 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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15 | * GNU General Public License for more details.
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16 | *
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17 | * You should have received a copy of the GNU General Public License
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18 | * along with HeuristicLab. If not, see <http://www.gnu.org/licenses/>.
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19 | */
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20 | #endregion
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21 |
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22 | using System;
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23 | using System.Collections.Generic;
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24 | using System.Linq;
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25 | using HeuristicLab.Common;
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26 | using HeuristicLab.Core;
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27 | using HeuristicLab.Persistence.Default.CompositeSerializers.Storable;
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28 |
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29 | namespace HeuristicLab.Problems.DataAnalysis {
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30 | /// <summary>
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31 | /// Represents a threshold calculator that calculates thresholds as the cutting points between the estimated class distributions (assuming normally distributed class values).
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32 | /// </summary>
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33 | [StorableClass]
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34 | [Item("NormalDistributionCutPointsThresholdCalculator", "Represents a threshold calculator that calculates thresholds as the cutting points between the estimated class distributions (assuming normally distributed class values).")]
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35 | public class NormalDistributionCutPointsThresholdCalculator : ThresholdCalculator {
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36 |
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37 | [StorableConstructor]
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38 | protected NormalDistributionCutPointsThresholdCalculator(bool deserializing) : base(deserializing) { }
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39 | protected NormalDistributionCutPointsThresholdCalculator(NormalDistributionCutPointsThresholdCalculator original, Cloner cloner)
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40 | : base(original, cloner) {
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41 | }
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42 | public NormalDistributionCutPointsThresholdCalculator()
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43 | : base() {
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44 | }
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45 |
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46 | public override IDeepCloneable Clone(Cloner cloner) {
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47 | return new NormalDistributionCutPointsThresholdCalculator(this, cloner);
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48 | }
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49 |
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50 | public override void Calculate(IClassificationProblemData problemData, IEnumerable<double> estimatedValues, IEnumerable<double> targetClassValues, out double[] classValues, out double[] thresholds) {
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51 | NormalDistributionCutPointsThresholdCalculator.CalculateThresholds(problemData, estimatedValues, targetClassValues, out classValues, out thresholds);
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52 | }
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53 |
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54 | public static void CalculateThresholds(IClassificationProblemData problemData, IEnumerable<double> estimatedValues, IEnumerable<double> targetClassValues, out double[] classValues, out double[] thresholds) {
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55 | var estimatedTargetValues = Enumerable.Zip(estimatedValues, targetClassValues, (e, t) => new { EstimatedValue = e, TargetValue = t }).ToList();
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56 | double estimatedValuesRange = estimatedValues.Range();
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57 |
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58 | Dictionary<double, double> classMean = new Dictionary<double, double>();
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59 | Dictionary<double, double> classStdDev = new Dictionary<double, double>();
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60 | // calculate moments per class
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61 | foreach (var group in estimatedTargetValues.GroupBy(p => p.TargetValue)) {
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62 | IEnumerable<double> estimatedClassValues = group.Select(x => x.EstimatedValue);
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63 | double classValue = group.Key;
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64 | double mean, variance;
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65 | OnlineCalculatorError meanErrorState, varianceErrorState;
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66 | OnlineMeanAndVarianceCalculator.Calculate(estimatedClassValues, out mean, out variance, out meanErrorState, out varianceErrorState);
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67 |
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68 | if (meanErrorState == OnlineCalculatorError.None && varianceErrorState == OnlineCalculatorError.None) {
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69 | classMean[classValue] = mean;
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70 | classStdDev[classValue] = Math.Sqrt(variance);
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71 | }
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72 | }
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73 | double[] originalClasses = classMean.Keys.OrderBy(x => x).ToArray();
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74 | int nClasses = originalClasses.Length;
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75 | List<double> thresholdList = new List<double>();
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76 | for (int i = 0; i < nClasses - 1; i++) {
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77 | for (int j = i + 1; j < nClasses; j++) {
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78 | double x1, x2;
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79 | double class0 = originalClasses[i];
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80 | double class1 = originalClasses[j];
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81 | // calculate all thresholds
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82 | CalculateCutPoints(classMean[class0], classStdDev[class0], classMean[class1], classStdDev[class1], out x1, out x2);
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83 |
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84 | // if the two cut points are too close (for instance because the stdDev=0)
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85 | // then move them by 0.1% of the range of estimated values
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86 | if (x1.IsAlmost(x2)) {
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87 | x1 -= 0.001 * estimatedValuesRange;
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88 | x2 += 0.001 * estimatedValuesRange;
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89 | }
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90 | if (!double.IsInfinity(x1) && !thresholdList.Any(x => x.IsAlmost(x1))) thresholdList.Add(x1);
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91 | if (!double.IsInfinity(x2) && !thresholdList.Any(x => x.IsAlmost(x2))) thresholdList.Add(x2);
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92 | }
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93 | }
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94 | thresholdList.Sort();
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95 |
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96 | // add small value and large value for the calculation of most influential class in each thresholded section
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97 | thresholdList.Insert(0, estimatedValues.Min() - 1);
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98 | thresholdList.Add(estimatedValues.Max() + 1);
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99 |
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100 | // determine class values for each partition separated by a threshold by calculating the density of all class distributions
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101 | // all points in the partition are classified as the class with the maximal density in the parition
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102 | List<double> classValuesList = new List<double>();
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103 | if (thresholdList.Count == 2) {
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104 | // this happens if there are no thresholds (distributions for all classes are exactly the same)
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105 | // -> all samples should be classified as the first class
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106 | classValuesList.Add(originalClasses[0]);
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107 | } else {
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108 | // at least one reasonable threshold ...
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109 | // find the most likely class for the points between thresholds m
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110 | for (int i = 0; i < thresholdList.Count - 1; i++) {
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111 |
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112 | // determine class with maximal density mass between the thresholds
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113 | double maxDensity = LogNormalDensityMass(thresholdList[i], thresholdList[i + 1], classMean[originalClasses[0]], classStdDev[originalClasses[0]]);
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114 | double maxDensityClassValue = originalClasses[0];
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115 | foreach (var classValue in originalClasses.Skip(1)) {
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116 | double density = LogNormalDensityMass(thresholdList[i], thresholdList[i + 1], classMean[classValue], classStdDev[classValue]);
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117 | if (density > maxDensity) {
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118 | maxDensity = density;
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119 | maxDensityClassValue = classValue;
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120 | }
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121 | }
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122 | classValuesList.Add(maxDensityClassValue);
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123 | }
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124 | }
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125 |
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126 | // only keep thresholds at which the class changes
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127 | // class B overrides threshold s. So only thresholds r and t are relevant and have to be kept
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128 | //
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129 | // A B C
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130 | // /\ /\/\
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131 | // / r\/ /\t\
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132 | // / /\/ \ \
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133 | // / / /\s \ \
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134 | // -/---/-/ -\---\-\----
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135 |
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136 | List<double> filteredThresholds = new List<double>();
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137 | List<double> filteredClassValues = new List<double>();
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138 | filteredThresholds.Add(double.NegativeInfinity); // the smallest possible threshold for the first class
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139 | filteredClassValues.Add(classValuesList[0]);
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140 | // do not include the last threshold which was just needed for the previous step
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141 | for (int i = 0; i < classValuesList.Count - 1; i++) {
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142 | if (!classValuesList[i].IsAlmost(classValuesList[i + 1])) {
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143 | filteredThresholds.Add(thresholdList[i + 1]);
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144 | filteredClassValues.Add(classValuesList[i + 1]);
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145 | }
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146 | }
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147 | thresholds = filteredThresholds.ToArray();
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148 | classValues = filteredClassValues.ToArray();
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149 | }
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150 |
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151 | private static double LogNormalDensityMass(double lower, double upper, double mu, double sigma) {
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152 | if (sigma.IsAlmost(0.0)) {
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153 | if (lower < mu && mu < upper) return double.PositiveInfinity; // log(1)
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154 | else return double.NegativeInfinity; // log(0)
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155 | }
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156 |
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157 | Func<double, double> f = (x) =>
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158 | x * -0.5 * Math.Log(2.0 * Math.PI * sigma * sigma) - Math.Pow(x - mu, 3) / (3 * 2.0 * sigma * sigma);
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159 |
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160 | if (double.IsNegativeInfinity(lower)) return f(upper);
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161 | else return f(upper) - f(lower);
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162 | }
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163 |
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164 | private static double LogNormalDensity(double x, double mu, double sigma) {
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165 | if (sigma.IsAlmost(0.0)) {
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166 | if (x.IsAlmost(mu)) return 0.0; // log(1);
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167 | else return double.NegativeInfinity;
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168 | }
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169 |
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170 | return -0.5 * Math.Log(2.0 * Math.PI * sigma * sigma) - Math.Pow(x - mu, 2) / (2.0 * sigma * sigma);
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171 | }
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172 |
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173 | private static void CalculateCutPoints(double m1, double s1, double m2, double s2, out double x1, out double x2) {
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174 | if (s1.IsAlmost(s2)) {
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175 | if (m1.IsAlmost(m2)) {
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176 | x1 = double.NegativeInfinity;
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177 | x2 = double.NegativeInfinity;
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178 | } else {
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179 | x1 = (m1 + m2) / 2;
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180 | x2 = double.NegativeInfinity;
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181 | }
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182 | } else if (s1.IsAlmost(0.0)) {
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183 | x1 = m1;
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184 | x2 = m1;
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185 | } else if (s2.IsAlmost(0.0)) {
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186 | x1 = m2;
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187 | x2 = m2;
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188 | } else {
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189 | if (s2 < s1) {
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190 | // make sure s2 is the larger std.dev.
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191 | CalculateCutPoints(m2, s2, m1, s1, out x1, out x2);
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192 | } else {
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193 | // scale s1 and s2 for numeric stability
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194 | //s2 = s2 / s1;
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195 | //s1 = 1.0;
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196 | double a = (s1 + s2) * (s1 - s2);
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197 | double g = Math.Sqrt(s1 * s1 * s2 * s2 * ((m1 - m2) * (m1 - m2) + 2.0 * (s1 * s1 + s2 * s2) * Math.Log(s2 / s1)));
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198 | double m1s2 = m1 * s2 * s2;
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199 | double m2s1 = m2 * s1 * s1;
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200 | x1 = -(-m2s1 + m1s2 + g) / a;
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201 | x2 = (m2s1 - m1s2 + g) / a;
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202 | }
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203 | }
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204 | }
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205 | }
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206 | }
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