source: branches/HeuristicLab.BottomUpTreeDistance/HeuristicLab.Problems.DataAnalysis.Symbolic/3.4/SimilarityCalculators/BottomUpSimilarityCalculator.cs @ 11225

Last change on this file since 11225 was 11225, checked in by bburlacu, 8 years ago

#2215: Fixed a couple of bugs in the BottomUpSimilarityCalculator:

  • the child sequences of matching nodes were not sorted in the same way (one was using StringComparison.Ordinal, the other the default)
  • when creating the mapping it is necessary to walk the nodes of the first tree in decreasing height order (not level-order as the author claims)
File size: 12.2 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.Drawing;
25using System.Globalization;
26using System.Linq;
27using System.Text;
28using HeuristicLab.Common;
29using HeuristicLab.Core;
30using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding;
31using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding.Views;
32using HeuristicLab.Optimization.Operators;
33using HeuristicLab.Persistence.Default.CompositeSerializers.Storable;
34
35namespace HeuristicLab.Problems.DataAnalysis.Symbolic {
36  [StorableClass]
37  [Item("BottomUpSimilarityCalculator", "A similarity calculator which uses the tree bottom-up distance as a similarity metric.")]
38  public class BottomUpSimilarityCalculator : SingleObjectiveSolutionSimilarityCalculator {
39    private readonly HashSet<string> commutativeSymbols = new HashSet<string> { "Addition", "Multiplication", "Average", "And", "Or", "Xor" };
40
41    public BottomUpSimilarityCalculator() { }
42
43    public override IDeepCloneable Clone(Cloner cloner) {
44      return new BottomUpSimilarityCalculator(this, cloner);
45    }
46
47    protected BottomUpSimilarityCalculator(BottomUpSimilarityCalculator original, Cloner cloner)
48      : base(original, cloner) {
49    }
50
51    public override double CalculateSolutionSimilarity(IScope leftSolution, IScope rightSolution) {
52      var t1 = leftSolution.Variables[SolutionVariableName].Value as ISymbolicExpressionTree;
53      var t2 = rightSolution.Variables[SolutionVariableName].Value as ISymbolicExpressionTree;
54
55      if (t1 == null || t2 == null)
56        throw new ArgumentException("Cannot calculate similarity when one of the arguments is null.");
57
58      var similarity = CalculateSolutionSimilarity(t1, t2);
59      if (similarity > 1.0)
60        throw new Exception("Similarity value cannot be greater than 1");
61
62      return similarity;
63    }
64
65    public double CalculateSolutionSimilarity(ISymbolicExpressionTree t1, ISymbolicExpressionTree t2) {
66      if (t1 == t2)
67        return 1;
68
69      var map = ComputeBottomUpMapping(t1.Root, t2.Root);
70      return 2.0 * map.Count / (t1.Length + t2.Length);
71    }
72
73    public Dictionary<ISymbolicExpressionTreeNode, ISymbolicExpressionTreeNode> ComputeBottomUpMapping(ISymbolicExpressionTreeNode n1, ISymbolicExpressionTreeNode n2) {
74      var compactedGraph = Compact(n1, n2);
75
76      var forwardMap = new Dictionary<ISymbolicExpressionTreeNode, ISymbolicExpressionTreeNode>(); // nodes of t1 => nodes of t2
77      var reverseMap = new Dictionary<ISymbolicExpressionTreeNode, ISymbolicExpressionTreeNode>(); // nodes of t2 => nodes of t1
78
79      // visit nodes in order of decreasing height to ensure correct mapping
80      foreach (var v in n1.IterateNodesPrefix().OrderByDescending(x => compactedGraph[x].Weight)) {
81        if (forwardMap.ContainsKey(v))
82          continue;
83        var kv = compactedGraph[v];
84        ISymbolicExpressionTreeNode w = null;
85        foreach (var t in n2.IterateNodesPrefix()) {
86          if (reverseMap.ContainsKey(t) || compactedGraph[t] != kv)
87            continue;
88          w = t;
89          break;
90        }
91        if (w == null) continue;
92
93        // 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)
94        // 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
95        var eV = IterateBreadthOrdered(v).GetEnumerator();
96        var eW = IterateBreadthOrdered(w).GetEnumerator();
97
98        while (eV.MoveNext() && eW.MoveNext()) {
99          var s = eV.Current;
100          var t = eW.Current;
101
102          if (reverseMap.ContainsKey(t)) {
103            throw new Exception("A mapping to this node already exists.");
104          }
105
106          forwardMap[s] = t;
107          reverseMap[t] = s;
108        }
109      }
110
111      return forwardMap;
112    }
113
114    /// <summary>
115    /// Creates a compact representation of the two trees as a directed acyclic graph
116    /// </summary>
117    /// <param name="t1">The first tree</param>
118    /// <param name="t2">The second tree</param>
119    /// <returns>The compacted DAG representing the two trees</returns>
120    private Dictionary<ISymbolicExpressionTreeNode, IVertex> Compact(ISymbolicExpressionTreeNode n1, ISymbolicExpressionTreeNode n2) {
121      var nodesToVertices = new Dictionary<ISymbolicExpressionTreeNode, IVertex>(); // K
122      var labelsToVertices = new Dictionary<string, IVertex>(); // L
123      var childrenCount = new Dictionary<ISymbolicExpressionTreeNode, int>(); // Children
124      var vertices = new List<IVertex>(); // G
125
126      var nodes = n1.IterateNodesPostfix().Concat(n2.IterateNodesPostfix()); // the disjoint union F
127      var queue = new Queue<ISymbolicExpressionTreeNode>();
128
129      foreach (var n in nodes) {
130        if (n.SubtreeCount == 0) {
131          var label = n.ToString();
132          if (!labelsToVertices.ContainsKey(label)) {
133            var z = new Vertex { Content = n, Label = label };
134            labelsToVertices[z.Label] = z;
135            vertices.Add(z);
136          }
137          nodesToVertices[n] = labelsToVertices[label];
138          queue.Enqueue(n);
139        } else {
140          childrenCount[n] = n.SubtreeCount;
141        }
142      }
143
144      while (queue.Any()) {
145        var v = queue.Dequeue();
146
147        if (v.SubtreeCount > 0) {
148          var label = v.Symbol.Name;
149          bool found = false;
150          var height = v.GetDepth();
151
152          bool sort = commutativeSymbols.Contains(label);
153          var vSubtrees = v.Subtrees.Select(x => nodesToVertices[x]).ToList();
154          if (sort) vSubtrees.Sort((a, b) => String.Compare(a.Label, b.Label, StringComparison.Ordinal));
155
156          // for all nodes w in G in reverse order
157          for (int i = vertices.Count - 1; i >= 0; --i) {
158            var w = vertices[i];
159            var n = (ISymbolicExpressionTreeNode)w.Content;
160            if (v.SubtreeCount != n.SubtreeCount || label != w.Label || height != (int)w.Weight)
161              continue;
162
163            // sort V and W when the symbol is commutative because we are dealing with unordered trees
164            var wSubtrees = n.Subtrees.Select(x => nodesToVertices[x]).ToList();
165            if (sort) wSubtrees.Sort((a, b) => String.Compare(a.Label, b.Label, StringComparison.Ordinal));
166
167            if (vSubtrees.SequenceEqual(wSubtrees)) {
168              nodesToVertices[v] = w;
169              found = true;
170              break;
171            }
172          } // 32: end for
173
174          if (!found) {
175            var w = new Vertex { Content = v, Label = label, Weight = height };
176            vertices.Add(w);
177            nodesToVertices[v] = w;
178
179            foreach (var u in v.Subtrees) {
180              AddArc(w, nodesToVertices[u]);
181            } // 40: end for
182          } // 41: end if
183        } // 42: end if
184
185        var p = v.Parent;
186        if (p == null)
187          continue;
188
189        childrenCount[p]--;
190
191        if (childrenCount[p] == 0)
192          queue.Enqueue(p);
193      }
194
195      return nodesToVertices;
196    }
197
198    private IEnumerable<ISymbolicExpressionTreeNode> IterateBreadthOrdered(ISymbolicExpressionTreeNode node) {
199      var list = new List<ISymbolicExpressionTreeNode> { node };
200      int i = 0;
201      while (i < list.Count) {
202        var n = list[i];
203        if (n.SubtreeCount > 0) {
204          var subtrees = commutativeSymbols.Contains(node.Symbol.Name) ? n.Subtrees.OrderBy(s => s.ToString()) : n.Subtrees;
205          list.AddRange(subtrees);
206        }
207        i++;
208      }
209      return list;
210    }
211
212    private static IArc AddArc(IVertex source, IVertex target) {
213      var arc = new Arc(source, target);
214      source.AddForwardArc(arc);
215      target.AddReverseArc(arc);
216      return arc;
217    }
218
219    // debugging
220    private static string FormatMapping(ISymbolicExpressionTree t1, ISymbolicExpressionTree t2, Dictionary<ISymbolicExpressionTreeNode, ISymbolicExpressionTreeNode> map) {
221      var symbolNameMap = new Dictionary<string, string>
222    {
223      {"ProgramRootSymbol", "Prog"},
224      {"StartSymbol","RPB"},
225      {"Multiplication", "$\\times$"},
226      {"Division", "$\\div$"},
227      {"Addition", "$+$"},
228      {"Subtraction", "$-$"},
229      {"Exponential", "$\\exp$"},
230      {"Logarithm", "$\\log$"}
231    };
232
233      var sb = new StringBuilder();
234      var nodeIds = new Dictionary<ISymbolicExpressionTreeNode, string>();
235      int offset = 0;
236      var layoutEngine = new ReingoldTilfordLayoutEngine<ISymbolicExpressionTreeNode>(x => x.Subtrees);
237      var nodeCoordinates = layoutEngine.CalculateLayout(t1.Root).ToDictionary(n => n.Content, n => new PointF(n.X, n.Y));
238
239      double ws = 0.5;
240      double hs = 0.5;
241
242      var nl = Environment.NewLine;
243      sb.Append("\\documentclass[class=minimal,border=0pt]{standalone}" + nl +
244                 "\\usepackage{tikz}" + nl +
245                 "\\begin{document}" + nl +
246                 "\\begin{tikzpicture}" + nl +
247                 "\\def\\ws{1}" + nl +
248                 "\\def\\hs{0.7}" + nl +
249                 "\\def\\offs{" + offset + "}" + nl);
250
251      foreach (var node in t1.IterateNodesBreadth()) {
252        var id = Guid.NewGuid().ToString();
253        nodeIds[node] = id;
254        var coord = nodeCoordinates[node];
255        var nodeName = symbolNameMap.ContainsKey(node.Symbol.Name) ? symbolNameMap[node.Symbol.Name] : node.ToString();
256        sb.AppendLine(string.Format(CultureInfo.InvariantCulture, "\\node ({0}) at (\\ws*{1} + \\offs,\\hs*{2}) {{{3}}};", nodeIds[node], ws * coord.X, -hs * coord.Y, EscapeLatexString(nodeName)));
257      }
258
259      foreach (ISymbolicExpressionTreeNode t in t1.IterateNodesBreadth()) {
260        var n = t;
261        foreach (var s in t.Subtrees) {
262          sb.AppendLine(string.Format(CultureInfo.InvariantCulture, "\\draw ({0}) -- ({1});", nodeIds[n], nodeIds[s]));
263        }
264      }
265
266      nodeCoordinates = layoutEngine.CalculateLayout(t2.Root).ToDictionary(n => n.Content, n => new PointF(n.X, n.Y));
267
268      offset = 20;
269      sb.Append("\\def\\offs{" + offset + "}" + nl);
270      foreach (var node in t2.IterateNodesBreadth()) {
271        var id = Guid.NewGuid().ToString();
272        nodeIds[node] = id;
273        var coord = nodeCoordinates[node];
274        var nodeName = symbolNameMap.ContainsKey(node.Symbol.Name) ? symbolNameMap[node.Symbol.Name] : node.ToString();
275        sb.AppendLine(string.Format(CultureInfo.InvariantCulture, "\\node ({0}) at (\\ws*{1} + \\offs,\\hs*{2}) {{{3}}};", nodeIds[node], ws * coord.X, -hs * coord.Y, EscapeLatexString(nodeName)));
276      }
277
278      foreach (ISymbolicExpressionTreeNode t in t2.IterateNodesBreadth()) {
279        var n = t;
280        foreach (var s in t.Subtrees) {
281          sb.AppendLine(string.Format(CultureInfo.InvariantCulture, "\\draw ({0}) -- ({1});", nodeIds[n], nodeIds[s]));
282        }
283      }
284
285      foreach (var p in map) {
286        var id1 = nodeIds[p.Key];
287        var id2 = nodeIds[p.Value];
288
289        sb.Append(string.Format(CultureInfo.InvariantCulture, "\\path[draw,->,color=gray] ({0}) edge[bend left,dashed] ({1});" + Environment.NewLine, id1, id2));
290      }
291      sb.Append("\\end{tikzpicture}" + nl +
292                "\\end{document}" + nl);
293      return sb.ToString();
294    }
295
296    private static string EscapeLatexString(string s) {
297      return s.Replace("\\", "\\\\").Replace("{", "\\{").Replace("}", "\\}").Replace("_", "\\_");
298    }
299  }
300}
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