1 | #region License Information |
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2 | /* HeuristicLab |
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3 | * Copyright (C) 2002-2018 Heuristic and Evolutionary Algorithms Laboratory (HEAL) |
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4 | * and the BEACON Center for the Study of Evolution in Action. |
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5 | * |
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6 | * This file is part of HeuristicLab. |
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7 | * |
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8 | * HeuristicLab is free software: you can redistribute it and/or modify |
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9 | * it under the terms of the GNU General Public License as published by |
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10 | * the Free Software Foundation, either version 3 of the License, or |
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11 | * (at your option) any later version. |
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12 | * |
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13 | * HeuristicLab is distributed in the hope that it will be useful, |
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14 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
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15 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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16 | * GNU General Public License for more details. |
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17 | * |
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18 | * You should have received a copy of the GNU General Public License |
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19 | * along with HeuristicLab. If not, see <http://www.gnu.org/licenses/>. |
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20 | */ |
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21 | #endregion |
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22 | |
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23 | using System; |
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24 | using System.Collections.Generic; |
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25 | using System.Linq; |
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26 | using HeuristicLab.Common; |
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27 | using HeuristicLab.Core; |
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28 | using HeuristicLab.Encodings.BinaryVectorEncoding; |
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29 | using HeuristicLab.Persistence.Default.CompositeSerializers.Storable; |
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30 | using HeuristicLab.Random; |
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31 | |
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32 | namespace HeuristicLab.Algorithms.ParameterlessPopulationPyramid { |
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33 | // This code is based off the publication |
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34 | // B. W. Goldman and W. F. Punch, "Parameter-less Population Pyramid," GECCO, pp. 785–792, 2014 |
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35 | // and the original source code in C++11 available from: https://github.com/brianwgoldman/Parameter-less_Population_Pyramid |
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36 | [StorableClass] |
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37 | public class LinkageTree : DeepCloneable { |
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38 | [Storable] |
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39 | private readonly int[][][] occurances; |
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40 | [Storable] |
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41 | private readonly List<int>[] clusters; |
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42 | [Storable] |
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43 | private List<int> clusterOrdering; |
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44 | [Storable] |
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45 | private readonly int length; |
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46 | [Storable] |
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47 | private readonly IRandom rand; |
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48 | [Storable] |
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49 | private bool rebuildRequired = false; |
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50 | |
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51 | |
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52 | [StorableConstructor] |
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53 | protected LinkageTree(bool deserializing) : base() { } |
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54 | |
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55 | |
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56 | protected LinkageTree(LinkageTree original, Cloner cloner) : base(original, cloner) { |
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57 | occurances = new int[original.occurances.Length][][]; |
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58 | //mkommend: first entry is not used, cf. ctor line 83 |
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59 | for (int i = 1; i < original.occurances.Length; i++) { |
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60 | occurances[i] = new int[original.occurances[i].Length][]; |
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61 | for (int j = 0; j < original.occurances[i].Length; j++) |
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62 | occurances[i][j] = original.occurances[i][j].ToArray(); |
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63 | } |
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64 | |
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65 | clusters = original.clusters.Select(c => c.ToList()).ToArray(); |
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66 | clusterOrdering = new List<int>(original.clusterOrdering); |
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67 | length = original.length; |
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68 | rand = cloner.Clone(original.rand); |
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69 | rebuildRequired = original.rebuildRequired; |
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70 | } |
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71 | |
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72 | |
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73 | public override IDeepCloneable Clone(Cloner cloner) { |
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74 | return new LinkageTree(this, cloner); |
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75 | } |
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76 | |
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77 | public LinkageTree(int length, IRandom rand) { |
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78 | this.length = length; |
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79 | this.rand = rand; |
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80 | occurances = new int[length][][]; |
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81 | |
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82 | // Create a lower triangular matrix without the diagonal |
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83 | for (int i = 1; i < length; i++) { |
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84 | occurances[i] = new int[i][]; |
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85 | for (int j = 0; j < i; j++) { |
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86 | occurances[i][j] = new int[4]; |
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87 | } |
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88 | } |
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89 | clusters = new List<int>[2 * length - 1]; |
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90 | for (int i = 0; i < clusters.Length; i++) { |
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91 | clusters[i] = new List<int>(); |
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92 | } |
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93 | clusterOrdering = new List<int>(); |
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94 | |
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95 | // first "length" clusters just contain a single gene |
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96 | for (int i = 0; i < length; i++) { |
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97 | clusters[i].Add(i); |
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98 | } |
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99 | } |
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100 | |
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101 | public void Add(BinaryVector solution) { |
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102 | if (solution.Length != length) throw new ArgumentException("The individual has not the correct length."); |
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103 | for (int i = 1; i < solution.Length; i++) { |
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104 | for (int j = 0; j < i; j++) { |
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105 | // Updates the entry of the 4 long array based on the two bits |
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106 | |
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107 | var pattern = (Convert.ToByte(solution[j]) << 1) + Convert.ToByte(solution[i]); |
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108 | occurances[i][j][pattern]++; |
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109 | } |
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110 | } |
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111 | rebuildRequired = true; |
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112 | } |
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113 | |
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114 | // While "total" always has an integer value, it is a double to reduce |
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115 | // how often type casts are needed to prevent integer divison |
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116 | // In the GECCO paper, calculates Equation 2 |
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117 | private static double NegativeEntropy(int[] counts, double total) { |
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118 | double sum = 0; |
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119 | for (int i = 0; i < counts.Length; i++) { |
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120 | if (counts[i] != 0) { |
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121 | sum += ((counts[i] / total) * Math.Log(counts[i] / total)); |
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122 | } |
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123 | } |
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124 | return sum; |
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125 | } |
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126 | |
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127 | // Uses the frequency table to calcuate the entropy distance between two indices. |
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128 | // In the GECCO paper, calculates Equation 1 |
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129 | private double EntropyDistance(int i, int j) { |
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130 | int[] bits = new int[4]; |
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131 | // This ensures you are using the lower triangular part of "occurances" |
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132 | if (i < j) { |
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133 | int temp = i; |
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134 | i = j; |
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135 | j = temp; |
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136 | } |
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137 | var entry = occurances[i][j]; |
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138 | // extracts the occurrences of the individual bits |
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139 | bits[0] = entry[0] + entry[2]; // i zero |
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140 | bits[1] = entry[1] + entry[3]; // i one |
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141 | bits[2] = entry[0] + entry[1]; // j zero |
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142 | bits[3] = entry[2] + entry[3]; // j one |
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143 | double total = bits[0] + bits[1]; |
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144 | // entropy of the two bits on their own |
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145 | double separate = NegativeEntropy(bits, total); |
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146 | // entropy of the two bits as a single unit |
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147 | double together = NegativeEntropy(entry, total); |
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148 | // If together there is 0 entropy, the distance is zero |
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149 | if (together.IsAlmost(0)) { |
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150 | return 0.0; |
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151 | } |
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152 | return 2 - (separate / together); |
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153 | } |
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154 | |
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155 | |
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156 | |
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157 | // Performs O(N^2) clustering based on the method described in: |
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158 | // "Optimal implementations of UPGMA and other common clustering algorithms" |
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159 | // by I. Gronau and S. Moran |
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160 | // In the GECCO paper, Figure 2 is a simplified version of this algorithm. |
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161 | private void Rebuild() { |
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162 | double[][] distances = null; |
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163 | if (distances == null) { |
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164 | distances = new double[clusters.Length * 2 - 1][]; |
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165 | for (int i = 0; i < distances.Length; i++) |
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166 | distances[i] = new double[clusters.Length * 2 - 1]; |
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167 | } |
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168 | |
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169 | |
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170 | // Keep track of which clusters have not been merged |
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171 | var topLevel = new List<int>(length); |
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172 | for (int i = 0; i < length; i++) |
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173 | topLevel.Add(i); |
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174 | |
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175 | bool[] useful = new bool[clusters.Length]; |
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176 | for (int i = 0; i < useful.Length; i++) |
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177 | useful[i] = true; |
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178 | |
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179 | // Store the distances between all clusters |
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180 | for (int i = 1; i < length; i++) { |
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181 | for (int j = 0; j < i; j++) { |
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182 | distances[i][j] = EntropyDistance(clusters[i][0], clusters[j][0]); |
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183 | // make it symmetric |
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184 | distances[j][i] = distances[i][j]; |
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185 | } |
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186 | } |
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187 | // Each iteration we add some amount to the path, and remove the last |
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188 | // two elements. This keeps track of how much of usable is in the path. |
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189 | int end_of_path = 0; |
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190 | |
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191 | // build all clusters of size greater than 1 |
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192 | for (int index = length; index < clusters.Length; index++) { |
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193 | // Shuffle everything not yet in the path |
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194 | topLevel.ShuffleInPlace(rand, end_of_path, topLevel.Count - 1); |
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195 | |
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196 | // if nothing in the path, just add a random usable node |
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197 | if (end_of_path == 0) { |
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198 | end_of_path = 1; |
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199 | } |
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200 | while (end_of_path < topLevel.Count) { |
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201 | // last node in the path |
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202 | int final = topLevel[end_of_path - 1]; |
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203 | |
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204 | // best_index stores the location of the best thing in the top level |
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205 | int best_index = end_of_path; |
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206 | double min_dist = distances[final][topLevel[best_index]]; |
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207 | // check all options which might be closer to "final" than "topLevel[best_index]" |
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208 | for (int option = end_of_path + 1; option < topLevel.Count; option++) { |
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209 | if (distances[final][topLevel[option]] < min_dist) { |
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210 | min_dist = distances[final][topLevel[option]]; |
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211 | best_index = option; |
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212 | } |
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213 | } |
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214 | // If the current last two in the path are minimally distant |
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215 | if (end_of_path > 1 && min_dist >= distances[final][topLevel[end_of_path - 2]]) { |
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216 | break; |
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217 | } |
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218 | |
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219 | // move the best to the end of the path |
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220 | topLevel.Swap(end_of_path, best_index); |
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221 | end_of_path++; |
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222 | } |
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223 | // Last two elements in the path are the clusters to join |
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224 | int first = topLevel[end_of_path - 2]; |
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225 | int second = topLevel[end_of_path - 1]; |
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226 | |
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227 | // Only keep a cluster if the distance between the joining clusters is > zero |
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228 | bool keep = !distances[first][second].IsAlmost(0.0); |
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229 | useful[first] = keep; |
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230 | useful[second] = keep; |
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231 | |
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232 | // create the new cluster |
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233 | clusters[index] = clusters[first].Concat(clusters[second]).ToList(); |
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234 | // Calculate distances from all clusters to the newly created cluster |
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235 | int i = 0; |
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236 | int end = topLevel.Count - 1; |
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237 | while (i <= end) { |
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238 | int x = topLevel[i]; |
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239 | // Moves 'first' and 'second' to after "end" in topLevel |
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240 | if (x == first || x == second) { |
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241 | topLevel.Swap(i, end); |
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242 | end--; |
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243 | continue; |
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244 | } |
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245 | // Use the previous distances to calculate the joined distance |
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246 | double first_distance = distances[first][x]; |
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247 | first_distance *= clusters[first].Count; |
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248 | double second_distance = distances[second][x]; |
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249 | second_distance *= clusters[second].Count; |
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250 | distances[x][index] = ((first_distance + second_distance) |
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251 | / (clusters[first].Count + clusters[second].Count)); |
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252 | // make it symmetric |
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253 | distances[index][x] = distances[x][index]; |
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254 | i++; |
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255 | } |
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256 | |
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257 | // Remove first and second from the path |
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258 | end_of_path -= 2; |
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259 | topLevel.RemoveAt(topLevel.Count - 1); |
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260 | topLevel[topLevel.Count - 1] = index; |
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261 | } |
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262 | // Extract the useful clusters |
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263 | clusterOrdering.Clear(); |
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264 | // Add all useful clusters. The last one is never useful. |
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265 | for (int i = 0; i < useful.Length - 1; i++) { |
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266 | if (useful[i]) clusterOrdering.Add(i); |
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267 | } |
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268 | |
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269 | // Shuffle before sort to ensure ties are broken randomly |
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270 | clusterOrdering.ShuffleInPlace(rand); |
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271 | clusterOrdering = clusterOrdering.OrderBy(i => clusters[i].Count).ToList(); |
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272 | } |
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273 | |
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274 | public IEnumerable<List<int>> Clusters { |
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275 | get { |
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276 | // Just in time rebuilding |
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277 | if (rebuildRequired) Rebuild(); |
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278 | foreach (var index in clusterOrdering) { |
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279 | // Send out the clusters in the desired order |
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280 | yield return clusters[index]; |
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281 | } |
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282 | } |
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283 | } |
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284 | } |
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285 | } |
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