source: branches/HeuristicLab.BottomUpTreeDistance/HeuristicLab.Problems.DataAnalysis.Symbolic/3.4/TreeMatching/SymbolicExpressionTreeBottomUpSimilarityCalculator.cs @ 11910

Last change on this file since 11910 was 11910, checked in by bburlacu, 7 years ago

#2215:

  • Unified the similarity and matching/equality classes under the same folder.
  • Renamed SymbolicExpressionTreeNodeSimilarityComparer to SymbolicExpressionTreeNodeEqualityComparer, renamed other classes to more descriptive names.
  • Removed unused classes (SymbolicDataAnalysisInternalDiversityAnalyzer.cs, SymbolicExpressionTreeMaxCommonSequenceCalculator.cs
  • Renamed tests and test files.
File size: 9.5 KB
Line 
1#region License Information
2/* HeuristicLab
3 * Copyright (C) 2002-2014 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.Diagnostics;
25using System.Globalization;
26using System.Linq;
27using HeuristicLab.Common;
28using HeuristicLab.Core;
29using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding;
30using HeuristicLab.Optimization.Operators;
31using HeuristicLab.Persistence.Default.CompositeSerializers.Storable;
32
33namespace HeuristicLab.Problems.DataAnalysis.Symbolic {
34  [StorableClass]
35  [Item("SymbolicExpressionTreeBottomUpSimilarityCalculator", "A similarity calculator which uses the tree bottom-up distance as a similarity metric.")]
36  public class SymbolicExpressionTreeBottomUpSimilarityCalculator : SingleObjectiveSolutionSimilarityCalculator {
37    private readonly HashSet<string> commutativeSymbols = new HashSet<string> { "Addition", "Multiplication", "Average", "And", "Or", "Xor" };
38    public bool MatchVariableWeights { get; set; }
39    public bool MatchConstantValues { get; set; }
40
41    public SymbolicExpressionTreeBottomUpSimilarityCalculator() { }
42
43    protected SymbolicExpressionTreeBottomUpSimilarityCalculator(SymbolicExpressionTreeBottomUpSimilarityCalculator original, Cloner cloner)
44      : base(original, cloner) {
45      MatchVariableWeights = original.MatchVariableWeights;
46      MatchConstantValues = original.MatchConstantValues;
47    }
48
49    public override IDeepCloneable Clone(Cloner cloner) {
50      return new SymbolicExpressionTreeBottomUpSimilarityCalculator(this, cloner);
51    }
52
53    public double CalculateSimilarity(ISymbolicExpressionTree t1, ISymbolicExpressionTree t2) {
54      if (t1 == t2)
55        return 1;
56
57      var map = ComputeBottomUpMapping(t1.Root, t2.Root);
58      return 2.0 * map.Count / (t1.Length + t2.Length);
59    }
60
61    public override double CalculateSolutionSimilarity(IScope leftSolution, IScope rightSolution) {
62      var t1 = leftSolution.Variables[SolutionVariableName].Value as ISymbolicExpressionTree;
63      var t2 = rightSolution.Variables[SolutionVariableName].Value as ISymbolicExpressionTree;
64
65      if (t1 == null || t2 == null)
66        throw new ArgumentException("Cannot calculate similarity when one of the arguments is null.");
67
68      var similarity = CalculateSimilarity(t1, t2);
69      if (similarity > 1.0)
70        throw new Exception("Similarity value cannot be greater than 1");
71
72      return similarity;
73    }
74
75    public Dictionary<ISymbolicExpressionTreeNode, ISymbolicExpressionTreeNode> ComputeBottomUpMapping(ISymbolicExpressionTreeNode n1, ISymbolicExpressionTreeNode n2) {
76      var comparer = new SymbolicExpressionTreeNodeComparer(); // use a node comparer because it's faster than calling node.ToString() (strings are expensive) and comparing strings
77      var compactedGraph = Compact(n1, n2);
78
79      var forwardMap = new Dictionary<ISymbolicExpressionTreeNode, ISymbolicExpressionTreeNode>(); // nodes of t1 => nodes of t2
80      var reverseMap = new Dictionary<ISymbolicExpressionTreeNode, ISymbolicExpressionTreeNode>(); // nodes of t2 => nodes of t1
81
82      // visit nodes in order of decreasing height to ensure correct mapping
83      var nodes1 = n1.IterateNodesPrefix().ToList();
84      var nodes2 = n2.IterateNodesPrefix().ToList();
85      for (int i = 0; i < nodes1.Count; ++i) {
86        var v = nodes1[i];
87        if (forwardMap.ContainsKey(v))
88          continue;
89        var kv = compactedGraph[v];
90        ISymbolicExpressionTreeNode w = null;
91        for (int j = 0; j < nodes2.Count; ++j) {
92          var t = nodes2[j];
93          if (reverseMap.ContainsKey(t) || compactedGraph[t] != kv)
94            continue;
95          w = t;
96          break;
97        }
98        if (w == null) continue;
99
100        // 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)
101        // 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
102        var vv = IterateBreadthOrdered(v, comparer).ToList();
103        var ww = IterateBreadthOrdered(w, comparer).ToList();
104        int len = Math.Min(vv.Count, ww.Count);
105        for (int j = 0; j < len; ++j) {
106          var s = vv[j];
107          var t = ww[j];
108          Debug.Assert(!reverseMap.ContainsKey(t));
109
110          forwardMap[s] = t;
111          reverseMap[t] = s;
112        }
113      }
114
115      return forwardMap;
116    }
117
118    /// <summary>
119    /// Creates a compact representation of the two trees as a directed acyclic graph
120    /// </summary>
121    /// <param name="n1">The root of the first tree</param>
122    /// <param name="n2">The root of the second tree</param>
123    /// <returns>The compacted DAG representing the two trees</returns>
124    private Dictionary<ISymbolicExpressionTreeNode, GraphNode> Compact(ISymbolicExpressionTreeNode n1, ISymbolicExpressionTreeNode n2) {
125      var nodeMap = new Dictionary<ISymbolicExpressionTreeNode, GraphNode>(); // K
126      var labelMap = new Dictionary<string, GraphNode>(); // L
127      var childrenCount = new Dictionary<ISymbolicExpressionTreeNode, int>(); // Children
128
129      var nodes = n1.IterateNodesPostfix().Concat(n2.IterateNodesPostfix()); // the disjoint union F
130      var list = new List<GraphNode>();
131      var queue = new Queue<ISymbolicExpressionTreeNode>();
132
133      foreach (var n in nodes) {
134        if (n.SubtreeCount == 0) {
135          var label = Label(n);
136          if (!labelMap.ContainsKey(label)) {
137            var z = new GraphNode { SymbolicExpressionTreeNode = n, Label = label };
138            labelMap[z.Label] = z;
139          }
140          nodeMap[n] = labelMap[label];
141          queue.Enqueue(n);
142        } else {
143          childrenCount[n] = n.SubtreeCount;
144        }
145      }
146      while (queue.Any()) {
147        var n = queue.Dequeue();
148        if (n.SubtreeCount > 0) {
149          bool found = false;
150          var label = n.Symbol.Name;
151          var depth = n.GetDepth();
152
153          bool sort = n.SubtreeCount > 1 && commutativeSymbols.Contains(label);
154          var nSubtrees = n.Subtrees.Select(x => nodeMap[x]).ToList();
155          if (sort) nSubtrees.Sort((a, b) => string.CompareOrdinal(a.Label, b.Label));
156
157          for (int i = list.Count - 1; i >= 0; --i) {
158            var w = list[i];
159            if (!(n.SubtreeCount == w.SubtreeCount && label == w.Label && depth == w.Depth))
160              continue;
161
162            // sort V and W when the symbol is commutative because we are dealing with unordered trees
163            var m = w.SymbolicExpressionTreeNode;
164            var mSubtrees = m.Subtrees.Select(x => nodeMap[x]).ToList();
165            if (sort) mSubtrees.Sort((a, b) => string.CompareOrdinal(a.Label, b.Label));
166
167            found = nSubtrees.SequenceEqual(mSubtrees);
168            if (found) {
169              nodeMap[n] = w;
170              break;
171            }
172          }
173
174          if (!found) {
175            var w = new GraphNode { SymbolicExpressionTreeNode = n, Label = label, Depth = depth };
176            list.Add(w);
177            nodeMap[n] = w;
178          }
179        }
180
181        if (n == n1 || n == n2)
182          continue;
183
184        var p = n.Parent;
185        if (p == null)
186          continue;
187
188        childrenCount[p]--;
189
190        if (childrenCount[p] == 0)
191          queue.Enqueue(p);
192      }
193
194      return nodeMap;
195    }
196
197    private IEnumerable<ISymbolicExpressionTreeNode> IterateBreadthOrdered(ISymbolicExpressionTreeNode node, ISymbolicExpressionTreeNodeComparer comparer) {
198      var list = new List<ISymbolicExpressionTreeNode> { node };
199      int i = 0;
200      while (i < list.Count) {
201        var n = list[i];
202        if (n.SubtreeCount > 0) {
203          var subtrees = commutativeSymbols.Contains(node.Symbol.Name) ? n.Subtrees.OrderBy(x => x, comparer) : n.Subtrees;
204          list.AddRange(subtrees);
205        }
206        i++;
207      }
208      return list;
209    }
210
211    private string Label(ISymbolicExpressionTreeNode node) {
212      if (node.SubtreeCount > 0)
213        return node.Symbol.Name;
214
215      var constant = node as ConstantTreeNode;
216      if (constant != null)
217        return MatchConstantValues ? constant.Value.ToString(CultureInfo.InvariantCulture) : constant.Symbol.Name;
218      var variable = node as VariableTreeNode;
219      if (variable != null) {
220        return MatchVariableWeights ? variable.Weight + variable.VariableName : variable.VariableName;
221      }
222
223      return node.ToString();
224    }
225
226    private class GraphNode {
227      public ISymbolicExpressionTreeNode SymbolicExpressionTreeNode;
228      public string Label;
229      public int Depth;
230      public int SubtreeCount { get { return SymbolicExpressionTreeNode.SubtreeCount; } }
231    }
232  }
233}
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