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source: trunk/sources/HeuristicLab.Problems.DataAnalysis/3.4/Implementation/Classification/ThresholdCalculators/NormalDistributionCutPointsThresholdCalculator.cs @ 8680

Last change on this file since 8680 was 8680, checked in by gkronber, 10 years ago

#1925 : minor code improvements

File size: 9.2 KB
Line 
1#region License Information
2/* HeuristicLab
3 * Copyright (C) 2002-2012 Heuristic and Evolutionary Algorithms Laboratory (HEAL)
4 *
5 * This file is part of HeuristicLab.
6 *
7 * HeuristicLab is free software: you can redistribute it and/or modify
8 * it under the terms of the GNU General Public License as published by
9 * the Free Software Foundation, either version 3 of the License, or
10 * (at your option) any later version.
11 *
12 * HeuristicLab is distributed in the hope that it will be useful,
13 * but WITHOUT ANY WARRANTY; without even the implied warranty of
14 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
15 * GNU General Public License for more details.
16 *
17 * You should have received a copy of the GNU General Public License
18 * along with HeuristicLab. If not, see <http://www.gnu.org/licenses/>.
19 */
20#endregion
21
22using System;
23using System.Collections.Generic;
24using System.Linq;
25using HeuristicLab.Common;
26using HeuristicLab.Core;
27using HeuristicLab.Persistence.Default.CompositeSerializers.Storable;
28
29namespace HeuristicLab.Problems.DataAnalysis {
30  /// <summary>
31  /// Represents a threshold calculator that calculates thresholds as the cutting points between the estimated class distributions (assuming normally distributed class values).
32  /// </summary>
33  [StorableClass]
34  [Item("NormalDistributionCutPointsThresholdCalculator", "Represents a threshold calculator that calculates thresholds as the cutting points between the estimated class distributions (assuming normally distributed class values).")]
35  public class NormalDistributionCutPointsThresholdCalculator : ThresholdCalculator {
36
37    [StorableConstructor]
38    protected NormalDistributionCutPointsThresholdCalculator(bool deserializing) : base(deserializing) { }
39    protected NormalDistributionCutPointsThresholdCalculator(NormalDistributionCutPointsThresholdCalculator original, Cloner cloner)
40      : base(original, cloner) {
41    }
42    public NormalDistributionCutPointsThresholdCalculator()
43      : base() {
44    }
45
46    public override IDeepCloneable Clone(Cloner cloner) {
47      return new NormalDistributionCutPointsThresholdCalculator(this, cloner);
48    }
49
50    public override void Calculate(IClassificationProblemData problemData, IEnumerable<double> estimatedValues, IEnumerable<double> targetClassValues, out double[] classValues, out double[] thresholds) {
51      NormalDistributionCutPointsThresholdCalculator.CalculateThresholds(problemData, estimatedValues, targetClassValues, out classValues, out thresholds);
52    }
53
54    public static void CalculateThresholds(IClassificationProblemData problemData, IEnumerable<double> estimatedValues, IEnumerable<double> targetClassValues, out double[] classValues, out double[] thresholds) {
55      var estimatedTargetValues = Enumerable.Zip(estimatedValues, targetClassValues, (e, t) => new { EstimatedValue = e, TargetValue = t }).ToList();
56      double estimatedValuesRange = estimatedValues.Range();
57
58      Dictionary<double, double> classMean = new Dictionary<double, double>();
59      Dictionary<double, double> classStdDev = new Dictionary<double, double>();
60      // calculate moments per class
61      foreach (var group in estimatedTargetValues.GroupBy(p => p.TargetValue)) {
62        IEnumerable<double> estimatedClassValues = group.Select(x => x.EstimatedValue);
63        double classValue = group.Key;
64        double mean, variance;
65        OnlineCalculatorError meanErrorState, varianceErrorState;
66        OnlineMeanAndVarianceCalculator.Calculate(estimatedClassValues, out mean, out variance, out meanErrorState, out varianceErrorState);
67
68        if (meanErrorState == OnlineCalculatorError.None && varianceErrorState == OnlineCalculatorError.None) {
69          classMean[classValue] = mean;
70          classStdDev[classValue] = Math.Sqrt(variance);
71        }
72      }
73      double[] originalClasses = classMean.Keys.OrderBy(x => x).ToArray();
74      int nClasses = originalClasses.Length;
75      List<double> thresholdList = new List<double>();
76      for (int i = 0; i < nClasses - 1; i++) {
77        for (int j = i + 1; j < nClasses; j++) {
78          double x1, x2;
79          double class0 = originalClasses[i];
80          double class1 = originalClasses[j];
81          // calculate all thresholds
82          CalculateCutPoints(classMean[class0], classStdDev[class0], classMean[class1], classStdDev[class1], out x1, out x2);
83
84          // if the two cut points are too close (for instance because the stdDev=0)
85          // then move them by 0.1% of the range of estimated values
86          if (x1.IsAlmost(x2)) {
87            x1 -= 0.001 * estimatedValuesRange;
88            x2 += 0.001 * estimatedValuesRange;
89          }
90          if (!double.IsInfinity(x1) && !thresholdList.Any(x => x.IsAlmost(x1))) thresholdList.Add(x1);
91          if (!double.IsInfinity(x2) && !thresholdList.Any(x => x.IsAlmost(x2))) thresholdList.Add(x2);
92        }
93      }
94      thresholdList.Sort();
95
96      // add small value and large value for the calculation of most influential class in each thresholded section
97      thresholdList.Insert(0, estimatedValues.Min() - 1);
98      thresholdList.Add(estimatedValues.Max() + 1);
99
100      // determine class values for each partition separated by a threshold by calculating the density of all class distributions
101      // all points in the partition are classified as the class with the maximal density in the parition
102      List<double> classValuesList = new List<double>();
103      if (thresholdList.Count == 2) {
104        // this happens if there are no thresholds (distributions for all classes are exactly the same)
105        // -> all samples should be classified as the first class
106        classValuesList.Add(originalClasses[0]);
107      } else {
108        // at least one reasonable threshold ...
109        // find the most likely class for the points between thresholds m
110        for (int i = 0; i < thresholdList.Count - 1; i++) {
111
112          // determine class with maximal density mass between the thresholds
113          double maxDensity = LogNormalDensityMass(thresholdList[i], thresholdList[i + 1], classMean[originalClasses[0]], classStdDev[originalClasses[0]]);
114          double maxDensityClassValue = originalClasses[0];
115          foreach (var classValue in originalClasses.Skip(1)) {
116            double density = LogNormalDensityMass(thresholdList[i], thresholdList[i + 1], classMean[classValue], classStdDev[classValue]);
117            if (density > maxDensity) {
118              maxDensity = density;
119              maxDensityClassValue = classValue;
120            }
121          }
122          classValuesList.Add(maxDensityClassValue);
123        }
124      }
125
126      // only keep thresholds at which the class changes
127      // class B overrides threshold s. So only thresholds r and t are relevant and have to be kept
128      //
129      //      A    B  C
130      //       /\  /\/\       
131      //      / r\/ /\t\       
132      //     /   /\/  \ \     
133      //    /   / /\s  \ \     
134      //  -/---/-/ -\---\-\----
135
136      List<double> filteredThresholds = new List<double>();
137      List<double> filteredClassValues = new List<double>();
138      filteredThresholds.Add(double.NegativeInfinity); // the smallest possible threshold for the first class
139      filteredClassValues.Add(classValuesList[0]);
140      // do not include the last threshold which was just needed for the previous step
141      for (int i = 0; i < classValuesList.Count - 1; i++) {
142        if (!classValuesList[i].IsAlmost(classValuesList[i + 1])) {
143          filteredThresholds.Add(thresholdList[i + 1]);
144          filteredClassValues.Add(classValuesList[i + 1]);
145        }
146      }
147      thresholds = filteredThresholds.ToArray();
148      classValues = filteredClassValues.ToArray();
149    }
150
151    private static double LogNormalDensityMass(double lower, double upper, double mu, double sigma) {
152      if (sigma.IsAlmost(0.0)) {
153        if (lower < mu && mu < upper) return double.PositiveInfinity; // log(1)
154        else return double.NegativeInfinity; // log(0)
155      }
156
157      Func<double, double> f = (x) =>
158        x * -0.5 * Math.Log(2.0 * Math.PI * sigma * sigma) - Math.Pow(x - mu, 3) / (3 * 2.0 * sigma * sigma);
159
160      if (double.IsNegativeInfinity(lower)) return f(upper);
161      else return f(upper) - f(lower);
162    }
163
164    private static void CalculateCutPoints(double m1, double s1, double m2, double s2, out double x1, out double x2) {
165      if (s1.IsAlmost(s2)) {
166        if (m1.IsAlmost(m2)) {
167          x1 = double.NegativeInfinity;
168          x2 = double.NegativeInfinity;
169        } else {
170          x1 = (m1 + m2) / 2;
171          x2 = double.NegativeInfinity;
172        }
173      } else if (s1.IsAlmost(0.0)) {
174        x1 = m1;
175        x2 = m1;
176      } else if (s2.IsAlmost(0.0)) {
177        x1 = m2;
178        x2 = m2;
179      } else {
180        if (s2 < s1) {
181          // make sure s2 is the larger std.dev.
182          CalculateCutPoints(m2, s2, m1, s1, out x1, out x2);
183        } else {
184          double a = (s1 + s2) * (s1 - s2);
185          double g = Math.Sqrt(s1 * s1 * s2 * s2 * ((m1 - m2) * (m1 - m2) + 2.0 * (s1 * s1 + s2 * s2) * Math.Log(s2 / s1)));
186          double m1s2 = m1 * s2 * s2;
187          double m2s1 = m2 * s1 * s1;
188          x1 = -(-m2s1 + m1s2 + g) / a;
189          x2 = (m2s1 - m1s2 + g) / a;
190        }
191      }
192    }
193  }
194}
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