source: branches/HeuristicLab.VariableInteractionNetworks/HeuristicLab.VariableInteractionNetworks/3.3/VariableInteractionNetwork.cs @ 14622

#region License Information
/* HeuristicLab
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 *
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 * GNU General Public License for more details.
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#endregion

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using HeuristicLab.Common;
using HeuristicLab.Core;
using HeuristicLab.Data;
using HeuristicLab.Persistence.Default.CompositeSerializers.Storable;

namespace HeuristicLab.VariableInteractionNetworks {
  [Item("VariableInteractionNetwork", "A graph representation of variables and their relationships.")]
  [StorableClass]
  public class VariableInteractionNetwork : DirectedGraph {
    /// <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;
    }

    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(bool deserializing) : base(deserializing) { }

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

  [Item("VariableNetworkNode", "A graph vertex which represents a symbolic regression variable.")]
  [StorableClass]
  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.")]
  [StorableClass]
  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; }
  }
}