source: branches/2288_HeuristicLab.VariableInteractionNetworks/HeuristicLab.VariableInteractionNetworks/3.3/VariableInteractionNetwork.cs @ 16864

#region License Information
/* HeuristicLab
 * Copyright (C) 2002-2015 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
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 *
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 * 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
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#endregion

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics.Eventing.Reader;
using System.Linq;
using System.Text;
using HeuristicLab.Common;
using HeuristicLab.Core;
using HeuristicLab.Data;
using HeuristicLab.Persistence.Default.CompositeSerializers.Storable;
using HEAL.Attic;

namespace HeuristicLab.VariableInteractionNetworks {
  [Item("VariableInteractionNetwork", "A graph representation of variables and their relationships.")]
  [StorableType("CD0A2622-6872-4E61-BE01-E6AA9E41A60D")]
  public class VariableInteractionNetwork : DirectedGraph {

    /// <summary>
    /// Creates a simple network from a matrix of variable impacts (each row represents a target variable, each column represents an input variable)
    /// For each target variable not more than one row can be defined (no junction nodes are build, cf. FromNmseAndVariableImpacts(..) for building more complex networks).
    /// The network is acyclic. Values in the diagonal are ignored.
    /// The algorithm starts with an empty network and incrementally adds next most relevant input variable for each target variable up to a given threshold
    /// In each iteration cycles are broken by removing the weakest link.
    /// </summary>
    /// <param name="nmse">vector of NMSE values for each target variable</param>
    /// <param name="variableImpacts">Variable impacts (smaller is lower impact). Row names and columns names should be set</param>
    /// <param name="nmseThreshold">Threshold for NMSE values. Variables with a NMSE value larger than the threshold are considered as independent variables</param>
    /// <param name="varImpactThreshold">Threshold for variable impact values. Impacts with a value smaller than the threshold are considered as independent</param>
    /// <returns></returns>
    public static VariableInteractionNetwork CreateSimpleNetwork(double[] nmse, DoubleMatrix variableImpacts, double nmseThreshold = 0.2, double varImpactThreshold = 0.0) {
      if (variableImpacts.Rows != variableImpacts.Columns) throw new ArgumentException();
      var network = new VariableInteractionNetwork();
      var targets = new Dictionary<string, double>();
      string[] varNames = variableImpacts.RowNames.ToArray();
      if (nmse.Length != varNames.Length) throw new ArgumentException();

      for (int i = 0; i < varNames.Length; i++) {
        var name = varNames[i];
        var varVertex = new VariableNetworkNode() {Label = name, Weight = nmse[i]};
        network.AddVertex(varVertex);
        if (nmse[i] < nmseThreshold) {
          targets.Add(name, nmse[i]);
        }
      }

      // rel is updated (impacts which are represented in the network are set to zero)
      var rel = variableImpacts.CloneAsMatrix();
      // make sure the diagonal is not considered
      for (int i = 0; i < rel.GetLength(0); i++) rel[i, i] = double.NegativeInfinity;

      var addedArcs = AddArcs(network, rel, varNames, targets, varImpactThreshold);
      while (addedArcs.Any()) {
        var cycles = network.FindShortestCycles().ToList();
        while (cycles.Any()) {
          // delete weakest link
          var weakestArc = cycles.SelectMany(cycle => network.ArcsForCycle(cycle)).OrderBy(a => a.Weight).First();
          network.RemoveArc(weakestArc);

          cycles = network.FindShortestCycles().ToList();
        }

        addedArcs = AddArcs(network, rel, varNames, targets, varImpactThreshold);
      }

      return network;
    }

    private static List<IArc> AddArcs(VariableInteractionNetwork network, double[,] impacts, string[] varNames, Dictionary<string, double> targets, double threshold = 0.0) {
      var newArcs = new List<IArc>();
      for (int row = 0; row < impacts.GetLength(0); row++) {
        if (!targets.ContainsKey(varNames[row])) continue;

        var rowVector = Enumerable.Range(0, impacts.GetLength(0)).Select(col => impacts[row, col]).ToArray();
        var max = rowVector.Max();
        if (max > threshold) {
          var idxOfMax = Array.IndexOf<double>(rowVector, max);
          impacts[row, idxOfMax] = double.NegativeInfinity;
          var srcName = varNames[idxOfMax];
          var dstName = varNames[row];
          var srcVertex = network.Vertices.Single(v => v.Label == srcName);
          var dstVertex = network.Vertices.Single(v => v.Label == dstName);
          var arc = network.AddArc(srcVertex, dstVertex);
          arc.Weight = max;
          newArcs.Add(arc);
        }
      }

      return newArcs;
    }

    /// <summary>
    /// Creates a network from a matrix of variable impacts (each row represents a target variable, each column represents an input variable)
    /// The network is acyclic. Values in the diagonal are ignored.
    /// The algorithm starts with an empty network and incrementally adds next most relevant input variable for each target variable up to a given threshold
    /// In each iteration cycles are broken by removing the weakest link.
    /// </summary>
    /// <param name="nmse">vector of NMSE values for each target variable</param>
    /// <param name="variableImpacts">Variable impacts (smaller is lower impact). Row names and columns names should be set</param>
    /// <param name="nmseThreshold">Threshold for NMSE values. Variables with a NMSE value larger than the threshold are considered as independent variables</param>
    /// <param name="varImpactThreshold">Threshold for variable impact values. Impacts with a value smaller than the threshold are considered as independent</param>
    /// <returns></returns>
    public static VariableInteractionNetwork FromNmseAndVariableImpacts(double[] nmse, DoubleMatrix variableImpacts, double nmseThreshold = 0.2, double varImpactThreshold = 0.0) {
      if (variableImpacts.Rows != variableImpacts.Columns) throw new ArgumentException();
      var network = new VariableInteractionNetwork();

      Dictionary<string, IVertex> name2funVertex = new Dictionary<string, IVertex>(); // store vertexes representing the function for each target so we can easily add incoming arcs later on
      string[] varNames = variableImpacts.RowNames.ToArray();
      if (nmse.Length != varNames.Length) throw new ArgumentException();

      for (int i = 0; i < varNames.Length; i++) {
        var name = varNames[i];
        var varVertex = new VariableNetworkNode() { Label = name };
        network.AddVertex(varVertex);
        if (nmse[i] < nmseThreshold) {
          var functionVertex = new JunctionNetworkNode() { Label = "f_" + name };
          name2funVertex.Add(name, functionVertex);
          network.AddVertex(functionVertex);
          var predArc = network.AddArc(functionVertex, varVertex);
          predArc.Weight = double.PositiveInfinity; // never delete arcs from f_x -> x (representing output of a function)
        }
      }

      // rel is updated (impacts which are represented in the network are set to zero)
      var rel = variableImpacts.CloneAsMatrix();
      // make sure the diagonal is not considered
      for (int i = 0; i < rel.GetLength(0); i++) rel[i, i] = double.NegativeInfinity;

      var addedArcs = AddArcs(network, rel, varNames, name2funVertex, varImpactThreshold);
      while (addedArcs.Any()) {
        var cycles = network.FindShortestCycles().ToList();
        while (cycles.Any()) {
          // delete weakest link
          var weakestArc = cycles.SelectMany(cycle => network.ArcsForCycle(cycle)).OrderBy(a => a.Weight).First();
          network.RemoveArc(weakestArc);

          cycles = network.FindShortestCycles().ToList();
        }

        addedArcs = AddArcs(network, rel, varNames, name2funVertex, varImpactThreshold);
      }

      return network;
    }

    /// <summary>
    /// Produces a combined network from two networks. 
    /// The set of nodes of the new network is the union of the node sets of the two input networks.
    /// The set of edges of the new network is the union of the edge sets of the two input networks.
    /// Added and removed nodes and edges are marked so that it is possible to visualize the network difference using graphviz
    /// </summary>
    /// <returns></returns>
    public static VariableInteractionNetwork CalculateNetworkDiff(
      VariableInteractionNetwork from,
      VariableInteractionNetwork to) {
      var g = new VariableInteractionNetwork();

      // add nodes which are in both networks
      foreach (var node in from.Vertices.Intersect(to.Vertices, new VertexLabelComparer())) {
        g.AddVertex((IVertex)node.Clone());
      }
      // add nodes only in from network
      foreach (var node in from.Vertices.Except(to.Vertices, new VertexLabelComparer())) {
        var fromVertex = (IVertex)node.Clone();
        fromVertex.Label += " (removed)";
        g.AddVertex(fromVertex);
      }
      // add nodes only in to network
      foreach (var node in to.Vertices.Except(from.Vertices, new VertexLabelComparer())) {
        var fromVertex = (IVertex)node.Clone();
        fromVertex.Label += " (added)";
        g.AddVertex(fromVertex);
      }

      // add edges which are in both networks
      foreach (var arc in from.Arcs.Intersect(to.Arcs, new ArcComparer())) {
        g.AddArc(
          g.Vertices.Single(v => arc.Source.Label == v.Label),
          g.Vertices.Single(v => arc.Target.Label == v.Label)
        );
      }
      // add edges only in from network
      foreach (var arc in from.Arcs.Except(to.Arcs, new ArcComparer())) {
        var fromVertex =
          g.Vertices.Single(v => v.Label == arc.Source.Label || v.Label == arc.Source.Label + " (removed)");
        var toVertex =
          g.Vertices.Single(v => v.Label == arc.Target.Label || v.Label == arc.Target.Label + " (removed)");
        var newArc = g.AddArc(
          fromVertex,
          toVertex
        );
        newArc.Label += " (removed)";
      }
      // add arcs only in to network
      foreach (var arc in to.Arcs.Except(from.Arcs, new ArcComparer())) {
        var fromVertex =
          g.Vertices.Single(v => v.Label == arc.Source.Label || v.Label == arc.Source.Label + " (added)");
        var toVertex =
          g.Vertices.Single(v => v.Label == arc.Target.Label || v.Label == arc.Target.Label + " (added)");
        var newArc = g.AddArc(
          fromVertex,
          toVertex
        );
        newArc.Label += " (added)";
      }
      return g;
    }


    private static List<IArc> AddArcs(VariableInteractionNetwork network, double[,] impacts, string[] varNames, Dictionary<string, IVertex> name2funVertex, double threshold = 0.0) {
      var newArcs = new List<IArc>();
      for (int row = 0; row < impacts.GetLength(0); row++) {
        if (!name2funVertex.ContainsKey(varNames[row])) continue; // this variable does not have an associated function (considered as independent)

        var rowVector = Enumerable.Range(0, impacts.GetLength(0)).Select(col => impacts[row, col]).ToArray();
        var max = rowVector.Max();
        if (max > threshold) {
          var idxOfMax = Array.IndexOf<double>(rowVector, max);
          impacts[row, idxOfMax] = double.NegativeInfinity; // edge is not considered anymore
          var srcName = varNames[idxOfMax];
          var dstName = varNames[row];
          var vertex = network.Vertices.Single(v => v.Label == srcName);
          var arc = network.AddArc(vertex, name2funVertex[dstName]);
          arc.Weight = max;
          newArcs.Add(arc);
        }
      }
      return newArcs;
    }

    [StorableConstructor]
    public VariableInteractionNetwork(StorableConstructorFlag _) : base(_) { }

    public VariableInteractionNetwork() { }

    protected VariableInteractionNetwork(VariableInteractionNetwork original, Cloner cloner) : base(original, cloner) { }

    public override IDeepCloneable Clone(Cloner cloner) {
      return new VariableInteractionNetwork(this, cloner);
    }
    private IList<IArc> ArcsForCycle(IList<IVertex> cycle) {
      var res = new List<IArc>();
      foreach (var t in cycle.Zip(cycle.Skip(1), Tuple.Create)) {
        var src = t.Item1;
        var dst = t.Item2;
        var arc = Arcs.Single(a => a.Source == src && a.Target == dst);
        res.Add(arc);
      }
      return res;
    }


    // finds the shortest cycles in the graph and returns all sub-graphs containing only the nodes / edges within the cycle
    public IEnumerable<IList<IVertex>> FindShortestCycles() {
      foreach (var startVariable in base.Vertices.OfType<VariableNetworkNode>()) {
        foreach (var cycle in FindShortestCycles(startVariable))
          yield return cycle;
      }
    }

    private IEnumerable<IList<IVertex>> FindShortestCycles(VariableNetworkNode startVariable) {
      var q = new Queue<List<IVertex>>(); // queue of paths
      var path = new List<IVertex>();
      var cycles = new List<List<IVertex>>();
      var maxPathLength = base.Vertices.Count();

      path.Add(startVariable);
      q.Enqueue(new List<IVertex>(path));

      FindShortestCycles(q, maxPathLength, cycles);
      return cycles;
    }

    // TODO efficiency
    private void FindShortestCycles(Queue<List<IVertex>> queue, int maxPathLength, List<List<IVertex>> cycles) {
      while (queue.Any()) {
        var path = queue.Dequeue();
        if (path.Count > 1 && path.First() == path.Last()) {
          cycles.Add(new List<IVertex>(path)); // found a cycle
        } else if (path.Count >= maxPathLength) {
          continue;
        } else {
          var lastVert = path.Last();
          var neighbours = base.Arcs.Where(a => a.Source == lastVert).Select(a => a.Target);
          foreach (var neighbour in neighbours) {
            queue.Enqueue(new List<IVertex>(path.Concat(new IVertex[] { neighbour })));
          }
        }
      }
    }

    public DoubleMatrix GetWeightsMatrix() {
      var names = Vertices.OfType<VariableNetworkNode>()
        .Select(v => v.Label)
        .OrderBy(s => s, new NaturalStringComparer()).ToArray();
      var w = new double[names.Length, names.Length];

      var name2idx = new Dictionary<string, int>();
      for (int i = 0; i < names.Length; i++) {
        name2idx.Add(names[i], i);
      }

      foreach (var arc in Arcs) {
        // only consider arcs going into a junction node
        var target = arc.Target as JunctionNetworkNode;
        if (target != null) {
          var srcVarName = arc.Source.Label;
          // each function node must have exactly one outgoing arc
          var dstVarName = arc.Target.OutArcs.Single().Target.Label;

          w[name2idx[dstVarName], name2idx[srcVarName]] = arc.Weight;
        }
      }


      return new DoubleMatrix(w, names, names);
    }

    public DoubleMatrix GetSimpleWeightsMatrix() {
      var names = Vertices.OfType<VariableNetworkNode>()
        .Select(v => v.Label)
        .OrderBy(s => s, new NaturalStringComparer()).ToArray();
      var w = new double[names.Length, names.Length];

      var name2idx = new Dictionary<string, int>();
      for (int i = 0; i < names.Length; i++) {
        name2idx.Add(names[i], i);
      }

      foreach (var arc in Arcs) {
        if (arc.Target != null) {
          var srcVarName = arc.Source.Label;
          var dstVarName = arc.Target.Label;          
          w[name2idx[dstVarName], name2idx[srcVarName]] = arc.Weight;
        }
      }

      return new DoubleMatrix(w, names, names);
    }

    public string ToGraphVizString() {
      Func<string, string> NodeAndEdgeColor = (str) =>
      {
        if (string.IsNullOrEmpty(str)) return "black";
        else if (str.Contains("removed")) return "red";
        else if (str.Contains("added")) return "green";
        else return "black";
      };

      var sb = new StringBuilder();
      sb.AppendLine("digraph {");
      sb.AppendLine("rankdir=LR");
      foreach (var v in Vertices.OfType<VariableNetworkNode>()) {
        sb.AppendFormat("\"{0}\" [shape=oval, color={1}]", v.Label, NodeAndEdgeColor(v.Label)).AppendLine();
      }
      foreach (var v in Vertices.OfType<JunctionNetworkNode>()) {
        sb.AppendFormat("\"{0}\" [shape=box, color={1}]", v.Label, NodeAndEdgeColor(v.Label)).AppendLine();
      }
      foreach (var arc in Arcs) {
        sb.AppendFormat("\"{0}\"->\"{1}\" [color=\"{3}\"]", arc.Source.Label, arc.Target.Label, arc.Label, NodeAndEdgeColor(arc.Label)).AppendLine();
      }
      sb.AppendLine("}");
      return sb.ToString();
    }
  }

  public class VertexLabelComparer : IEqualityComparer<IVertex> {
    public bool Equals(IVertex x, IVertex y) {
      if (x == null && y == null) return true;
      if (x != null && y != null) {
        return x.Label == y.Label;
      } else return false;
    }

    public int GetHashCode(IVertex obj) {
      return obj.Label.GetHashCode();
    }
  }

  public class ArcComparer : IEqualityComparer<IArc> {
    public bool Equals(IArc x, IArc y) {
      if (x == null && y == null) return true;
      if (x != null && y != null) {
        return x.Source.Label == y.Source.Label && x.Target.Label == y.Target.Label;
      } else return false;
    }

    public int GetHashCode(IArc obj) {
      return obj.Source.Label.GetHashCode() ^ obj.Target.Label.GetHashCode();
    }
  }

  [Item("VariableNetworkNode", "A graph vertex which represents a symbolic regression variable.")]
  [StorableType("95E27B45-DD4B-4C32-AC5E-40A4714EA6F7")]
  public class VariableNetworkNode : Vertex<IDeepCloneable>, INetworkNode {
    public VariableNetworkNode() {
      Id = Guid.NewGuid().ToString();
    }

    public VariableNetworkNode(VariableNetworkNode original, Cloner cloner) : base(original, cloner) {
      Id = original.Id;
      Description = original.Description;
    }

    public override IDeepCloneable Clone(Cloner cloner) {
      return new VariableNetworkNode(this, cloner);
    }

    public string Id { get; }
    public string Description { get; set; }
  }

  [Item("FunctionNetworkNode", "A graph vertex representing a junction node.")]
  [StorableType("8D4E55AC-EBF8-49BA-8361-FC51EF3BE990")]
  public class JunctionNetworkNode : Vertex<IDeepCloneable>, INetworkNode {
    public JunctionNetworkNode() {
      Id = Guid.NewGuid().ToString();
    }

    public JunctionNetworkNode(JunctionNetworkNode original, Cloner cloner) : base(original, cloner) {
      Id = original.Id;
      Description = original.Description;
    }

    public override IDeepCloneable Clone(Cloner cloner) {
      return new JunctionNetworkNode(this, cloner);
    }

    public string Id { get; }
    public string Description { get; set; }
  }
}