source: branches/HeuristicLab.EvolutionaryTracking/HeuristicLab.Problems.DataAnalysis.Symbolic/3.4/SymbolicDataAnalysisExpressionTreeSimilarity.cs @ 13042

#region License Information
/* HeuristicLab
 * Copyright (C) 2002-2012 Heuristic and Evolutionary Algorithms Laboratory (HEAL)
 *
 * This file is part of HeuristicLab.
 *
 * HeuristicLab is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * HeuristicLab is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with HeuristicLab. If not, see <http://www.gnu.org/licenses/>.
 */
#endregion

using System;
using System.Collections.Generic;
using System.Linq;
using HeuristicLab.Common;
using HeuristicLab.Core;
using HeuristicLab.Data;
using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding;
using HeuristicLab.Operators;
using HeuristicLab.Parameters;
using HeuristicLab.Persistence.Default.CompositeSerializers.Storable;

namespace HeuristicLab.Problems.DataAnalysis.Symbolic {
  [StorableClass]
  public class SymbolicDataAnalysisExpressionTreeSimilarityCalculator : SingleSuccessorOperator {
    private const string SymbolicExpressionTreeParameterName = "SymbolicExpressionTree";
    private const string CurrentSymbolicExpressionTreeParameterName = "CurrentSymbolicExpressionTree";
    private const string SimilarityValuesParmeterName = "Similarity";
    // comparer parameters
    private const string MatchVariablesParameterName = "MatchVariableNames";
    private const string MatchVariableWeightsParameterName = "MatchVariableWeights";
    private const string MatchConstantValuesParameterName = "MatchConstantValues";

    public IScopeTreeLookupParameter<ISymbolicExpressionTree> SymbolicExpressionTreeParameter {
      get { return (IScopeTreeLookupParameter<ISymbolicExpressionTree>)Parameters[SymbolicExpressionTreeParameterName]; }
    }
    public IValueParameter<ISymbolicExpressionTree> CurrentSymbolicExpressionTreeParameter {
      get { return (IValueParameter<ISymbolicExpressionTree>)Parameters[CurrentSymbolicExpressionTreeParameterName]; }
    }
    public ILookupParameter<BoolValue> MatchVariableNamesParameter {
      get { return (ILookupParameter<BoolValue>)Parameters[MatchVariablesParameterName]; }
    }
    public ILookupParameter<BoolValue> MatchVariableWeightsParameter {
      get { return (ILookupParameter<BoolValue>)Parameters[MatchVariableWeightsParameterName]; }
    }
    public ILookupParameter<BoolValue> MatchConstantValuesParameter {
      get { return (ILookupParameter<BoolValue>)Parameters[MatchConstantValuesParameterName]; }
    }
    public ILookupParameter<DoubleValue> SimilarityParameter {
      get { return (ILookupParameter<DoubleValue>)Parameters[SimilarityValuesParmeterName]; }
    }

    public ISymbolicExpressionTree CurrentSymbolicExpressionTree {
      get { return CurrentSymbolicExpressionTreeParameter.Value; }
      set { CurrentSymbolicExpressionTreeParameter.Value = value; }
    }

    public SymbolicExpressionTreeNodeSimilarityComparer SimilarityComparer { get; set; }

    public Dictionary<ISymbolicExpressionTree, SymbolicDataAnalysisExpressionTreeSimilarity.GeneticItem[]> GeneticItems;

    public int MaximumTreeDepth { get; set; }

    protected SymbolicDataAnalysisExpressionTreeSimilarityCalculator(SymbolicDataAnalysisExpressionTreeSimilarityCalculator original, Cloner cloner) : base(original, cloner) { }
    public override IDeepCloneable Clone(Cloner cloner) { return new SymbolicDataAnalysisExpressionTreeSimilarityCalculator(this, cloner); }
    [StorableConstructor]
    protected SymbolicDataAnalysisExpressionTreeSimilarityCalculator(bool deserializing) : base(deserializing) { }

    public SymbolicDataAnalysisExpressionTreeSimilarityCalculator()
      : base() {
      Parameters.Add(new ScopeTreeLookupParameter<ISymbolicExpressionTree>(SymbolicExpressionTreeParameterName, "The symbolic expression trees to analyze."));
      Parameters.Add(new ValueParameter<ISymbolicExpressionTree>(CurrentSymbolicExpressionTreeParameterName, ""));
      Parameters.Add(new LookupParameter<BoolValue>(MatchVariablesParameterName, "Specify if the symbolic expression tree comparer should match variable names."));
      Parameters.Add(new LookupParameter<BoolValue>(MatchVariableWeightsParameterName, "Specify if the symbolic expression tree comparer should match variable weights."));
      Parameters.Add(new LookupParameter<BoolValue>(MatchConstantValuesParameterName, "Specify if the symbolic expression tree comparer should match constant values."));
      Parameters.Add(new LookupParameter<DoubleValue>(SimilarityValuesParmeterName, ""));
    }

    public override IOperation Apply() {
      var trees = SymbolicExpressionTreeParameter.ActualValue;

      double similarity = 0.0;
      var current = CurrentSymbolicExpressionTree;

      bool found = false;
      foreach (var tree in trees) {
        if (tree == current) {
          found = true;
          continue;
        }

        if (found) {
          similarity += SymbolicDataAnalysisExpressionTreeSimilarity.MaxCommonSubtreeSimilarity(current, tree, SimilarityComparer);
          //          similarity += SymbolicDataAnalysisExpressionTreeSimilarity.GeneticItemSimilarity(GeneticItems[current], GeneticItems[tree], MaximumTreeDepth);
        }
      }

      lock (SimilarityParameter.ActualValue) {
        SimilarityParameter.ActualValue.Value += similarity;
      }
      return base.Apply();
    }
  }

  public static class SymbolicDataAnalysisExpressionTreeSimilarity {
    public static double CalculateSimilarity(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b, SymbolicExpressionTreeNodeSimilarityComparer comp) {
      return 2.0 * SymbolicExpressionTreeMatching.Match(a, b, comp) / (a.GetLength() + b.GetLength());
    }

    public static double MaxCommonSubtreeSimilarity(ISymbolicExpressionTree a, ISymbolicExpressionTree b, SymbolicExpressionTreeNodeSimilarityComparer comparer) {
      double max = 0;
      var rootA = a.Root.GetSubtree(0).GetSubtree(0);
      var rootB = b.Root.GetSubtree(0).GetSubtree(0);
      foreach (var aa in rootA.IterateNodesBreadth()) {
        int lenA = aa.GetLength();
        if (lenA <= max) continue;
        foreach (var bb in rootB.IterateNodesBreadth()) {
          int lenB = bb.GetLength();
          if (lenB <= max) continue;
          int matches = SymbolicExpressionTreeMatching.Match(aa, bb, comparer);
          if (max < matches) max = matches;
        }
      }
      return 2.0 * max / (rootA.GetLength() + rootB.GetLength());
    }

    public static double GeneticItemSimilarity(ISymbolicExpressionTree a, ISymbolicExpressionTree b, int maximumTreeHeight, bool preventMultipleContribution = true) {
      const int minLevelDelta = 1;
      const int maxLevelDelta = 4;

      var itemsA = a.GetGeneticItems(minLevelDelta, maxLevelDelta).ToArray();
      var itemsB = b.GetGeneticItems(minLevelDelta, maxLevelDelta).ToArray();

      return GeneticItemSimilarity(itemsA, itemsB, maximumTreeHeight);
    }

    public static double GeneticItemSimilarity(GeneticItem[] itemsA, GeneticItem[] itemsB, int maximumTreeHeight, bool preventMultipleContribution = true) {
      double similarity = 0.0;
      if (itemsA.Length == 0 || itemsB.Length == 0) return similarity;

      var flagsB = new bool[itemsB.Length];

      for (int i = 0; i != itemsA.Length; ++i) {
        double simMax = 0.0;
        int index = -1;
        for (int j = 0; j != itemsB.Length; ++j) {
          if (flagsB[j]) continue;
          double sim = StructuralSimilarity(itemsA[i], itemsB[j], maximumTreeHeight);
          if (sim > simMax) {
            simMax = sim;
            index = j;
          }
          if (preventMultipleContribution && index > -1) {
            flagsB[index] = true;
          }
        }
        similarity += simMax;
      }
      return similarity / itemsA.Length;
    }

    public static double AdditiveSimilarity(ISymbolicExpressionTree a, ISymbolicExpressionTree b, SymbolicExpressionTreeNodeSimilarityComparer comparer) {
      var nA = a.Root.GetSubtree(0).GetSubtree(0);
      var nB = b.Root.GetSubtree(0).GetSubtree(0);

      var nodesA = nA.IterateNodesBreadth().ToArray();
      var nodesB = nB.IterateNodesBreadth().ToArray();

      var similarities = nodesA.SelectMany(ia => nodesB, (ia, ib) => CalculateSimilarity(ia, ib, comparer)).Where(s => !s.IsAlmost(0.0)).ToList();

      double average = similarities.Count > 0 ? similarities.Average() : 0;
      if (average > 1.0) throw new Exception("Similarity average should be less than 1.0");
      if (average < 0.0) throw new Exception("Similarity average should be greater than 0.0");
      return average;
    }

    private static double StructuralSimilarity(GeneticItem g1, GeneticItem g2, int heightMax) {
      if (!(SameType(g1.Ascendant, g2.Ascendant) && SameType(g1.Descendant, g2.Descendant))) return 0.0;

      double s1 = 1.0 - Math.Abs(g1.LevelDelta - g2.LevelDelta) / heightMax;
      double s2 = g1.Index == g2.Index ? 1.0 : 0.0;
      double s3 = g1.ParamA.Variant.Name.Equals(g2.ParamA.Variant.Name) ? 1.0 : 0.0;
      double s4 = g1.ParamB.Variant.Name.Equals(g2.ParamB.Variant.Name) ? 1.0 : 0.0;

      double deltaCa = Math.Abs(g1.ParamA.Coeff - g2.ParamA.Coeff);
      double deltaCb = Math.Abs(g1.ParamB.Coeff - g2.ParamB.Coeff);
      double s5 = 0.0;
      double s6 = 0.0;
      // no time offsets so we hardcode s7 = s8 = 0.0
      double s7 = 0.0;
      double s8 = 0.0;
      // variable indexes
      double s9 = 0.0;
      double s10 = 0.0;

      // same type with g2.Ascendant so we only do one check
      if (g1.Ascendant is VariableTreeNode) {
        s5 = deltaCa / (((Variable)g1.Ascendant.Symbol).WeightManipulatorSigma * 4);
        s9 = g1.ParamA.VariableIndex.Equals(g2.ParamA.VariableIndex) ? 1.0 : 0.0;
      }
      if (g1.Descendant is VariableTreeNode) {
        s6 = deltaCb / (((Variable)g1.Descendant.Symbol).WeightManipulatorSigma * 4);
        s10 = g1.ParamB.VariableIndex.Equals(g2.ParamB.VariableIndex) ? 1.0 : 0.0;
      }

      double similarity = 1.0;

      double[] constributors = new double[10] { s1, s2, s3, s4, s5, s6, s7, s8, s9, s10 }; // s1...s10
      double[] coefficients = new double[10] { 0.8, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2 }; // c1...c10

      for (int i = 0; i != 10; ++i) {
        similarity *= (1 - (1 - constributors[i]) * coefficients[i]);
      }
      return double.IsNaN(similarity) ? 0 : similarity;
    }

    // genetic items for computing tree similarity (S. Winkler)
    public class GeneticItem {
      public ISymbolicExpressionTreeNode Ascendant;
      public ISymbolicExpressionTreeNode Descendant;
      public int LevelDelta;
      public int Index;
      public double[] Coefficients; // c_i = 0.2, i=1,...,10, d_1 = 0.8
      // parameters for the Ascendant and Descendant
      public GeneticItemParameters ParamA;
      public GeneticItemParameters ParamB;
    }

    public class GeneticItemParameters {
      public Symbol Variant; // the variant of functions
      public double Coeff; // the coefficient of terminals
      public int TimeOffset; // the time offset of terminals
      public int VariableIndex; // the variable index (of terminals)
    }
    // get genetic items
    public static List<GeneticItem> GetGeneticItems(this ISymbolicExpressionTree tree, int minLevelDelta, int maxLevelDelta) {
      return GetGeneticItems(tree.Root.GetSubtree(0).GetSubtree(0), minLevelDelta, maxLevelDelta).ToList();
    }

    private static double Coefficient(this ISymbolicExpressionTreeNode node) {
      var variable = node as VariableTreeNode;
      if (variable != null)
        return variable.Weight;
      var constant = node as ConstantTreeNode;
      if (constant != null)
        return constant.Value;
      return 0.0;
    }

    private static int VariableIndex(this ISymbolicExpressionTreeNode node) {
      var variable = node as VariableTreeNode;
      if (variable != null)
        return variable.Symbol.AllVariableNames.ToList().IndexOf(variable.VariableName);
      return -1;
    }

    private static IEnumerable<GeneticItem> GetGeneticItems(ISymbolicExpressionTreeNode node, int minimumLevelDelta, int maximumLevelDelta) {
      var descendants = node.IterateNodesBreadth().Skip(1).ToArray();
      for (int i = 0; i != descendants.Length; ++i) {
        var descendant = descendants[i];
        var levelDelta = node.GetBranchLevel(descendant);
        if (!(minimumLevelDelta <= levelDelta && levelDelta <= maximumLevelDelta)) continue;
        var p = descendant;
        while (p.Parent != node && p.Parent != null)
          p = p.Parent;
        if (p.Parent == null) throw new Exception("The child is not a descendant of node");
        var geneticItem = new GeneticItem {
          Ascendant = node, Descendant = descendant, LevelDelta = levelDelta, Index = node.IndexOfSubtree(p),
          ParamA = new GeneticItemParameters {
            Coeff = node.Coefficient(), TimeOffset = 0, VariableIndex = node.VariableIndex(), Variant = (Symbol)node.Symbol
          },
          ParamB = new GeneticItemParameters {
            Coeff = descendant.Coefficient(), TimeOffset = 0, VariableIndex = descendant.VariableIndex(), Variant = (Symbol)descendant.Symbol
          }
        };
        yield return geneticItem;
      }
    }

    // returns true if both nodes are variables, or both are constants, or both are functions
    private static bool SameType(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
      if (a is VariableTreeNode) {
        return b is VariableTreeNode;
      }
      if (a is ConstantTreeNode) {
        return b is ConstantTreeNode;
      }
      return true;
    }
  }
}