1 | #region License Information
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2 | /* HeuristicLab
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3 | * Copyright (C) 2002-2014 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.Encodings.SymbolicExpressionTreeEncoding;
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28 | using HeuristicLab.Optimization.Operators;
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29 | using HeuristicLab.Persistence.Default.CompositeSerializers.Storable;
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30 |
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31 | namespace HeuristicLab.Problems.DataAnalysis.Symbolic {
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32 | [StorableClass]
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33 | [Item("BottomUpTreeSimilarityCalculator", "A similarity calculator which uses the tree bottom-up distance as a similarity metric.")]
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34 | public class BottomUpTreeSimilarityCalculator : SingleObjectiveSolutionSimilarityCalculator {
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35 | private readonly HashSet<string> commutativeSymbols;
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36 |
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37 | public BottomUpTreeSimilarityCalculator() {
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38 | commutativeSymbols = new HashSet<string>();
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39 | }
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40 |
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41 | public BottomUpTreeSimilarityCalculator(IEnumerable<string> commutativeSymbols) {
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42 | this.commutativeSymbols = new HashSet<string>(commutativeSymbols);
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43 | }
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44 |
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45 | public override IDeepCloneable Clone(Cloner cloner) {
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46 | return new BottomUpTreeSimilarityCalculator(this, cloner);
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47 | }
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48 |
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49 | protected BottomUpTreeSimilarityCalculator(BottomUpTreeSimilarityCalculator original, Cloner cloner)
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50 | : base(original, cloner) {
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51 | }
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52 |
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53 | public override double CalculateSolutionSimilarity(IScope leftSolution, IScope rightSolution) {
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54 | var t1 = leftSolution.Variables[SolutionVariableName].Value as ISymbolicExpressionTree;
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55 | var t2 = rightSolution.Variables[SolutionVariableName].Value as ISymbolicExpressionTree;
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56 |
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57 | if (t1 == null || t2 == null)
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58 | throw new ArgumentException("Cannot calculate similarity when one of the arguments is null.");
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59 |
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60 | var similarity = CalculateSolutionSimilarity(t1, t2);
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61 | if (similarity > 1.0)
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62 | throw new Exception("Similarity value cannot be greater than 1");
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63 |
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64 | return similarity;
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65 | }
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66 |
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67 | public bool AddCommutativeSymbol(string symbolName) {
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68 | return commutativeSymbols.Add(symbolName);
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69 | }
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70 |
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71 | public bool RemoveCommutativeSymbol(string symbolName) {
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72 | return commutativeSymbols.Remove(symbolName);
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73 | }
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74 |
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75 | public double CalculateSolutionSimilarity(ISymbolicExpressionTree t1, ISymbolicExpressionTree t2) {
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76 | if (t1 == t2)
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77 | return 1;
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78 |
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79 | var map = ComputeBottomUpMapping(t1.Root, t2.Root);
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80 | return 2.0 * map.Count / (t1.Length + t2.Length);
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81 | }
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82 |
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83 | public Dictionary<ISymbolicExpressionTreeNode, ISymbolicExpressionTreeNode> ComputeBottomUpMapping(ISymbolicExpressionTreeNode n1, ISymbolicExpressionTreeNode n2) {
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84 | var compactedGraph = Compact(n1, n2);
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85 |
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86 | var forwardMap = new Dictionary<ISymbolicExpressionTreeNode, ISymbolicExpressionTreeNode>(); // nodes of t1 => nodes of t2
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87 | var reverseMap = new Dictionary<ISymbolicExpressionTreeNode, ISymbolicExpressionTreeNode>(); // nodes of t2 => nodes of t1
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88 |
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89 | // visit nodes in order of decreasing height to ensure correct mapping
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90 | foreach (var v in n1.IterateNodesPrefix().OrderByDescending(x => compactedGraph[x].Depth)) {
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91 | if (forwardMap.ContainsKey(v))
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92 | continue;
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93 | var kv = compactedGraph[v];
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94 | ISymbolicExpressionTreeNode w = null;
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95 | foreach (var t in n2.IterateNodesPrefix()) {
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96 | if (reverseMap.ContainsKey(t) || compactedGraph[t] != kv)
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97 | continue;
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98 | w = t;
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99 | break;
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100 | }
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101 | if (w == null) continue;
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102 |
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103 | // at this point we know that v and w are isomorphic, however, the mapping cannot be done directly (as in the paper) because the trees are unordered (subtree order might differ)
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104 | // the solution is to sort subtrees by label using IterateBreadthOrdered (this will work because the subtrees are isomorphic!) and simultaneously iterate over the two subtrees
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105 | var eV = IterateBreadthOrdered(v).GetEnumerator();
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106 | var eW = IterateBreadthOrdered(w).GetEnumerator();
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107 |
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108 | while (eV.MoveNext() && eW.MoveNext()) {
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109 | var s = eV.Current;
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110 | var t = eW.Current;
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111 |
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112 | if (reverseMap.ContainsKey(t)) {
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113 | throw new Exception("A mapping to this node already exists.");
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114 | }
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115 |
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116 | forwardMap[s] = t;
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117 | reverseMap[t] = s;
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118 | }
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119 | }
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120 |
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121 | return forwardMap;
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122 | }
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123 |
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124 | /// <summary>
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125 | /// Creates a compact representation of the two trees as a directed acyclic graph
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126 | /// </summary>
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127 | /// <param name="n1">The root of the first tree</param>
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128 | /// <param name="n2">The root of the second tree</param>
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129 | /// <returns>The compacted DAG representing the two trees</returns>
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130 | private Dictionary<ISymbolicExpressionTreeNode, GraphNode> Compact(ISymbolicExpressionTreeNode n1, ISymbolicExpressionTreeNode n2) {
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131 | var nodeMap = new Dictionary<ISymbolicExpressionTreeNode, GraphNode>(); // K
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132 | var labelMap = new Dictionary<string, GraphNode>(); // L
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133 | var childrenCount = new Dictionary<ISymbolicExpressionTreeNode, int>(); // Children
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134 |
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135 | var nodes = n1.IterateNodesPostfix().Concat(n2.IterateNodesPostfix()); // the disjoint union F
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136 | var list = new List<GraphNode>();
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137 | var queue = new Queue<ISymbolicExpressionTreeNode>();
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138 |
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139 | foreach (var n in nodes) {
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140 | if (n.SubtreeCount == 0) {
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141 | var label = n.ToString();
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142 | if (!labelMap.ContainsKey(label)) {
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143 | var z = new GraphNode { SymbolicExpressionTreeNode = n, Label = label };
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144 | labelMap[z.Label] = z;
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145 | list.Add(z);
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146 | }
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147 | nodeMap[n] = labelMap[label];
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148 | queue.Enqueue(n);
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149 | } else {
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150 | childrenCount[n] = n.SubtreeCount;
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151 | }
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152 | }
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153 | while (queue.Any()) {
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154 | var n = queue.Dequeue();
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155 |
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156 | if (n.SubtreeCount > 0) {
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157 | var label = n.Symbol.Name;
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158 | bool found = false;
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159 | var depth = n.GetDepth();
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160 |
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161 | bool sort = commutativeSymbols.Contains(label);
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162 | var nNodes = n.Subtrees.Select(x => nodeMap[x]).ToList();
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163 | if (sort) nNodes.Sort((a, b) => String.Compare(a.Label, b.Label, StringComparison.Ordinal));
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164 |
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165 | for (int i = list.Count - 1; i >= 0; --i) {
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166 | var w = list[i];
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167 |
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168 | if (!(n.SubtreeCount == w.ChildrenCount && label == w.Label && depth == w.Depth))
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169 | continue;
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170 |
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171 | // sort V and W when the symbol is commutative because we are dealing with unordered trees
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172 | var m = w.SymbolicExpressionTreeNode;
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173 | var mNodes = m.Subtrees.Select(x => nodeMap[x]).ToList();
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174 | if (sort) mNodes.Sort((a, b) => String.Compare(a.Label, b.Label, StringComparison.Ordinal));
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175 |
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176 | if (nNodes.SequenceEqual(mNodes)) {
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177 | nodeMap[n] = w;
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178 | found = true;
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179 | break;
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180 | }
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181 | }
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182 |
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183 | if (!found) {
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184 | var w = new GraphNode { SymbolicExpressionTreeNode = n, Label = label, Depth = depth, ChildrenCount = n.SubtreeCount };
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185 | list.Add(w);
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186 | nodeMap[n] = w;
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187 | }
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188 | }
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189 |
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190 | var p = n.Parent;
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191 | if (p == null)
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192 | continue;
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193 |
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194 | childrenCount[p]--;
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195 |
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196 | if (childrenCount[p] == 0)
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197 | queue.Enqueue(p);
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198 | }
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199 |
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200 | return nodeMap;
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201 | }
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202 |
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203 | /// <summary>
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204 | /// This method iterates the nodes of a subtree in breadth order while also sorting the subtrees of commutative symbols based on their label.
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205 | /// This is necessary in order for the mapping to be realized correctly.
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206 | /// </summary>
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207 | /// <param name="node">The root of the subtree</param>
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208 | /// <returns>A list of nodes in breadth order (with children of commutative symbols sorted by label)</returns>
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209 | private IEnumerable<ISymbolicExpressionTreeNode> IterateBreadthOrdered(ISymbolicExpressionTreeNode node) {
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210 | var list = new List<ISymbolicExpressionTreeNode> { node };
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211 | int i = 0;
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212 | while (i < list.Count) {
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213 | var n = list[i];
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214 | if (n.SubtreeCount > 0) {
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215 | var subtrees = commutativeSymbols.Contains(node.Symbol.Name) ? n.Subtrees.OrderBy(x => x.ToString(), StringComparer.Ordinal) : n.Subtrees;
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216 | list.AddRange(subtrees);
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217 | }
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218 | i++;
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219 | }
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220 | return list;
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221 | }
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222 |
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223 | private class GraphNode {
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224 | public ISymbolicExpressionTreeNode SymbolicExpressionTreeNode;
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225 | public string Label;
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226 | public int Depth;
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227 | public int ChildrenCount;
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228 | }
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229 | }
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230 | }
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