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.Random;
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27 |
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28 | namespace HeuristicLab.Problems.Instances.DataAnalysis {
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29 | public class FeatureSelection : ArtificialRegressionDataDescriptor {
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30 | private int trainingSamples;
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31 | private const int TestSamples = 5000;
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32 |
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33 | private int numberOfFeatures;
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34 | private double selectionProbability;
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35 | private double noiseRatio;
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36 |
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37 | public override string Name { get { return string.Format("FeatSel-{0}-{1:0%}-{2:0%}", numberOfFeatures, selectionProbability, noiseRatio); } }
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38 | public override string Description {
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39 | get {
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40 | return "This problem is specifically designed to test feature selection." + Environment.NewLine
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41 | + "In this instance the number of rows for training (" + trainingSamples +
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42 | ") is only slightly larger than the number of columns (" + numberOfFeatures +
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43 | ") and only a subset of the columns must be selected for the predictive model." + Environment.NewLine
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44 | +
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45 | "The target variable is calculated as a noisy linear combination of randomly selected features: y = w * S + n." +
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46 | Environment.NewLine
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47 | +
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48 | "Where is the S is a N x d matrix containing the selected columns from N x k the matrix of all features X" +
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49 | Environment.NewLine
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50 | + "For each feature the probability that it is selected is " + selectionProbability + "%" +
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51 | Environment.NewLine
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52 | + "X(i,j) ~ N(0, 1) iid, w(i) ~ U(0, 10) iid, n ~ N(0, sigma(w*S) * SQRT(" + noiseRatio + "))" +
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53 | Environment.NewLine
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54 | + "The noise level is " + noiseRatio + " * sigma, thus an optimal model has R² = " +
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55 | Math.Round(1 - noiseRatio, 2) + " (or equivalently: NMSE = " + noiseRatio + ")" + Environment.NewLine
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56 | + "N = " + (trainingSamples + TestSamples) + " (" + trainingSamples + " training, " + TestSamples +
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57 | " test)" + Environment.NewLine
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58 | + "k = " + numberOfFeatures;
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59 | ;
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60 | }
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61 | }
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62 |
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63 | public FeatureSelection(int numberOfFeatures, double selectionProbability, double noiseRatio) {
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64 | this.numberOfFeatures = numberOfFeatures;
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65 | this.trainingSamples = (int)Math.Round(numberOfFeatures * 1.2); // 20% more rows than columns
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66 | this.selectionProbability = selectionProbability;
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67 | this.noiseRatio = noiseRatio;
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68 | }
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69 |
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70 | protected override string TargetVariable { get { return "Y"; } }
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71 |
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72 | protected override string[] VariableNames {
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73 | get { return AllowedInputVariables.Concat(new string[] { "Y" }).ToArray(); }
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74 | }
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75 |
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76 | protected override string[] AllowedInputVariables {
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77 | get {
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78 | return Enumerable.Range(1, numberOfFeatures)
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79 | .Select(i => string.Format("X{0:000}", i))
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80 | .ToArray();
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81 | }
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82 | }
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83 | protected override int TrainingPartitionStart { get { return 0; } }
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84 | protected override int TrainingPartitionEnd { get { return trainingSamples; } }
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85 | protected override int TestPartitionStart { get { return trainingSamples; } }
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86 | protected override int TestPartitionEnd { get { return trainingSamples + TestSamples; } }
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87 |
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88 | protected override List<List<double>> GenerateValues() {
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89 | List<List<double>> data = new List<List<double>>();
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90 | for (int i = 0; i < AllowedInputVariables.Count(); i++) {
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91 | data.Add(ValueGenerator.GenerateNormalDistributedValues(TestPartitionEnd, 0, 1).ToList());
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92 | }
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93 |
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94 | var random = new MersenneTwister();
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95 | var selectedFeatures =
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96 | Enumerable.Range(0, AllowedInputVariables.Count())
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97 | .Where(_ => random.NextDouble() < selectionProbability)
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98 | .ToArray();
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99 | var w = ValueGenerator.GenerateUniformDistributedValues(selectedFeatures.Length, 0, 10)
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100 | .ToArray();
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101 | var target = new List<double>();
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102 | for (int i = 0; i < data[0].Count; i++) {
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103 | var s = selectedFeatures
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104 | .Select(index => data[index][i])
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105 | .ToArray();
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106 | target.Add(ScalarProd(s, w));
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107 | }
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108 | var targetSigma = target.StandardDeviation();
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109 | var noisePrng = new NormalDistributedRandom(random, 0, targetSigma * Math.Sqrt(noiseRatio));
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110 |
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111 | data.Add(target.Select(t => t + noisePrng.NextDouble()).ToList());
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112 |
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113 | return data;
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114 | }
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115 |
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116 | private double ScalarProd(double[] s, double[] w) {
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117 | if (s.Length != w.Length) throw new ArgumentException();
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118 | return s.Zip(w, (a, b) => a * b).Sum();
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119 | }
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120 | }
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121 | }
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