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source: branches/HeuristicLab.BottomUpTreeDistance/HeuristicLab.Problems.DataAnalysis.Symbolic/3.4/SimilarityCalculators/BottomUpSimilarityCalculator.cs @ 11486

Last change on this file since 11486 was 11486, checked in by bburlacu, 8 years ago

#2215: Renamed BottomUpTreeSimilarityCalculator to BottomUpSimilarityCalculator, improved performance by 10% by using the SymbolicExpressionTreeNodeComparer for ordering nodes (instead of string.Compare on node.ToString()). Updated the rest of the files accordingly.

File size: 9.2 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("BottomUpSimilarityCalculator", "A similarity calculator which uses the tree bottom-up distance as a similarity metric.")]
36  public class BottomUpSimilarityCalculator : 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 BottomUpSimilarityCalculator() { }
42
43    protected BottomUpSimilarityCalculator(BottomUpSimilarityCalculator original, Cloner cloner)
44      : base(original, cloner) {
45    }
46
47    public override IDeepCloneable Clone(Cloner cloner) {
48      return new BottomUpSimilarityCalculator(this, cloner);
49    }
50
51    public double CalculateSimilarity(ISymbolicExpressionTree t1, ISymbolicExpressionTree t2) {
52      if (t1 == t2)
53        return 1;
54
55      var map = ComputeBottomUpMapping(t1.Root, t2.Root);
56      return 2.0 * map.Count / (t1.Length + t2.Length);
57    }
58
59    public override double CalculateSolutionSimilarity(IScope leftSolution, IScope rightSolution) {
60      var t1 = leftSolution.Variables[SolutionVariableName].Value as ISymbolicExpressionTree;
61      var t2 = rightSolution.Variables[SolutionVariableName].Value as ISymbolicExpressionTree;
62
63      if (t1 == null || t2 == null)
64        throw new ArgumentException("Cannot calculate similarity when one of the arguments is null.");
65
66      var similarity = CalculateSimilarity(t1, t2);
67      if (similarity > 1.0)
68        throw new Exception("Similarity value cannot be greater than 1");
69
70      return similarity;
71    }
72
73    public Dictionary<ISymbolicExpressionTreeNode, ISymbolicExpressionTreeNode> ComputeBottomUpMapping(ISymbolicExpressionTreeNode n1, ISymbolicExpressionTreeNode n2) {
74      var comparer = new SymbolicExpressionTreeNodeComparer(); // use a node comparer because it's faster than calling node.ToString() (strings are expensive) and comparing strings
75      var compactedGraph = Compact(n1, n2);
76
77      var forwardMap = new Dictionary<ISymbolicExpressionTreeNode, ISymbolicExpressionTreeNode>(); // nodes of t1 => nodes of t2
78      var reverseMap = new Dictionary<ISymbolicExpressionTreeNode, ISymbolicExpressionTreeNode>(); // nodes of t2 => nodes of t1
79
80      // visit nodes in order of decreasing height to ensure correct mapping
81      foreach (var v in n1.IterateNodesPrefix().OrderByDescending(x => compactedGraph[x].Depth)) {
82        if (forwardMap.ContainsKey(v))
83          continue;
84        var kv = compactedGraph[v];
85        ISymbolicExpressionTreeNode w = null;
86        foreach (var t in n2.IterateNodesPrefix()) {
87          if (reverseMap.ContainsKey(t) || compactedGraph[t] != kv)
88            continue;
89          w = t;
90          break;
91        }
92        if (w == null) continue;
93
94        // 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)
95        // 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
96        var eV = IterateBreadthOrdered(v, comparer).GetEnumerator();
97        var eW = IterateBreadthOrdered(w, comparer).GetEnumerator();
98
99        while (eV.MoveNext() && eW.MoveNext()) {
100          var s = eV.Current;
101          var t = eW.Current;
102
103          Debug.Assert(!reverseMap.ContainsKey(t));
104
105          forwardMap[s] = t;
106          reverseMap[t] = s;
107        }
108      }
109
110      return forwardMap;
111    }
112
113    /// <summary>
114    /// Creates a compact representation of the two trees as a directed acyclic graph
115    /// </summary>
116    /// <param name="n1">The root of the first tree</param>
117    /// <param name="n2">The root of the second tree</param>
118    /// <returns>The compacted DAG representing the two trees</returns>
119    private Dictionary<ISymbolicExpressionTreeNode, GraphNode> Compact(ISymbolicExpressionTreeNode n1, ISymbolicExpressionTreeNode n2) {
120      var nodeMap = new Dictionary<ISymbolicExpressionTreeNode, GraphNode>(); // K
121      var labelMap = new Dictionary<string, GraphNode>(); // L
122      var childrenCount = new Dictionary<ISymbolicExpressionTreeNode, int>(); // Children
123
124      var nodes = n1.IterateNodesPostfix().Concat(n2.IterateNodesPostfix()); // the disjoint union F
125      var list = new List<GraphNode>(); // preallocate size to avoid list resizing as it has a performance hit
126      var queue = new Queue<ISymbolicExpressionTreeNode>();
127
128      foreach (var n in nodes) {
129        if (n.SubtreeCount == 0) {
130          var label = Label(n);
131          if (!labelMap.ContainsKey(label)) {
132            var z = new GraphNode { SymbolicExpressionTreeNode = n, Label = label };
133            labelMap[z.Label] = z;
134            list.Add(z);
135          }
136          nodeMap[n] = labelMap[label];
137          queue.Enqueue(n);
138        } else {
139          childrenCount[n] = n.SubtreeCount;
140        }
141      }
142      while (queue.Any()) {
143        var n = queue.Dequeue();
144
145        if (n.SubtreeCount > 0) {
146          var label = n.Symbol.Name;
147          bool found = false;
148          var depth = n.GetDepth();
149
150          bool sort = commutativeSymbols.Contains(label);
151          var nNodes = n.Subtrees.Select(x => nodeMap[x]).ToList();
152          if (sort) nNodes.Sort((a, b) => string.CompareOrdinal(a.Label, b.Label));
153
154          for (int i = list.Count - 1; i >= 0; --i) {
155            var w = list[i];
156
157            if (!(n.SubtreeCount == w.ChildrenCount && label == w.Label && depth == w.Depth))
158              continue;
159
160            // sort V and W when the symbol is commutative because we are dealing with unordered trees
161            var m = w.SymbolicExpressionTreeNode;
162            var mNodes = m.Subtrees.Select(x => nodeMap[x]).ToList();
163            if (sort) mNodes.Sort((a, b) => string.CompareOrdinal(a.Label, b.Label));
164
165            if (nNodes.SequenceEqual(mNodes)) {
166              nodeMap[n] = w;
167              found = true;
168              break;
169            }
170          }
171
172          if (!found) {
173            var w = new GraphNode { SymbolicExpressionTreeNode = n, Label = label, Depth = depth };
174            list.Add(w);
175            nodeMap[n] = w;
176          }
177        }
178
179        if (n == n1 || n == n2)
180          continue;
181
182        var p = n.Parent;
183        if (p == null)
184          continue;
185
186        childrenCount[p]--;
187
188        if (childrenCount[p] == 0)
189          queue.Enqueue(p);
190      }
191
192      return nodeMap;
193    }
194
195    private IEnumerable<ISymbolicExpressionTreeNode> IterateBreadthOrdered(ISymbolicExpressionTreeNode node, ISymbolicExpressionTreeNodeComparer comparer) {
196      var list = new List<ISymbolicExpressionTreeNode> { node };
197      int i = 0;
198      while (i < list.Count) {
199        var n = list[i];
200        if (n.SubtreeCount > 0) {
201          var subtrees = commutativeSymbols.Contains(node.Symbol.Name) ? n.Subtrees.OrderBy(x => x, comparer) : n.Subtrees;
202          list.AddRange(subtrees);
203        }
204        i++;
205      }
206      return list;
207    }
208
209    private string Label(ISymbolicExpressionTreeNode node) {
210      if (node.SubtreeCount > 0)
211        return node.Symbol.Name;
212
213      var constant = node as ConstantTreeNode;
214      if (constant != null)
215        return MatchConstantValues ? constant.Value.ToString(CultureInfo.InvariantCulture) : constant.Symbol.Name;
216      var variable = node as VariableTreeNode;
217      if (variable != null) {
218        return MatchVariableWeights ? variable.Weight + variable.VariableName : variable.VariableName;
219      }
220
221      return node.ToString();
222    }
223
224    private class GraphNode {
225      public ISymbolicExpressionTreeNode SymbolicExpressionTreeNode;
226      public string Label;
227      public int Depth;
228      public int ChildrenCount { get { return SymbolicExpressionTreeNode.SubtreeCount; } }
229    }
230  }
231}
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