Changeset 14622


Ignore:
Timestamp:
01/31/17 12:56:50 (3 years ago)
Author:
gkronber
Message:

#2288: added a static method to create a network (as a DAG) from NMSE vector and variable impacts matrix as well as code for cycle detection and conversion of a network to graphviz and its adjacency matrix

Location:
branches/HeuristicLab.VariableInteractionNetworks
Files:
2 edited

Legend:

Unmodified
Added
Removed
  • branches/HeuristicLab.VariableInteractionNetworks

    • Property svn:ignore
      •  

        old new  
        11HeuristicLab.VariableInteractionNetworks.v12.suo
         2.vs
  • branches/HeuristicLab.VariableInteractionNetworks/HeuristicLab.VariableInteractionNetworks/3.3/VariableInteractionNetwork.cs

    r14275 r14622  
    2121
    2222using System;
     23using System.Collections;
     24using System.Collections.Generic;
     25using System.Linq;
     26using System.Text;
    2327using HeuristicLab.Common;
    2428using HeuristicLab.Core;
     29using HeuristicLab.Data;
    2530using HeuristicLab.Persistence.Default.CompositeSerializers.Storable;
    2631
     
    2934  [StorableClass]
    3035  public class VariableInteractionNetwork : DirectedGraph {
     36    /// <summary>
     37    /// Creates a network from a matrix of variable impacts (each row represents a target variable, each column represents an input variable)
     38    /// The network is acyclic. Values in the diagonal are ignored.
     39    /// The algorithm starts with an empty network and incrementally adds next most relevant input variable for each target variable up to a given threshold
     40    /// In each iteration cycles are broken by removing the weakest link.
     41    /// </summary>
     42    /// <param name="nmse">vector of NMSE values for each target variable</param>
     43    /// <param name="variableImpacts">Variable impacts (smaller is lower impact). Row names and columns names should be set</param>
     44    /// <param name="nmseThreshold">Threshold for NMSE values. Variables with a NMSE value larger than the threshold are considered as independent variables</param>
     45    /// <param name="varImpactThreshold">Threshold for variable impact values. Impacts with a value smaller than the threshold are considered as independent</param>
     46    /// <returns></returns>
     47    public static VariableInteractionNetwork FromNmseAndVariableImpacts(double[] nmse, DoubleMatrix variableImpacts, double nmseThreshold = 0.2, double varImpactThreshold = 0.0) {
     48      if(variableImpacts.Rows != variableImpacts.Columns) throw new ArgumentException();
     49      var network = new VariableInteractionNetwork();
     50
     51      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
     52      string[] varNames = variableImpacts.RowNames.ToArray();
     53      if(nmse.Length != varNames.Length) throw new ArgumentException();
     54
     55      for(int i = 0; i < varNames.Length; i++) {
     56        var name = varNames[i];
     57        var varVertex = new VariableNetworkNode() { Label = name };
     58        network.AddVertex(varVertex);
     59        if(nmse[i] < nmseThreshold) {
     60          var functionVertex = new JunctionNetworkNode() { Label = "f_" + name };
     61          name2funVertex.Add(name, functionVertex);
     62          network.AddVertex(functionVertex);
     63          var predArc = network.AddArc(functionVertex, varVertex);
     64          predArc.Weight = double.PositiveInfinity; // never delete arcs from f_x -> x (representing output of a function)
     65        }
     66      }
     67
     68      // rel is updated (impacts which are represented in the network are set to zero)
     69      var rel = variableImpacts.CloneAsMatrix();
     70      // make sure the diagonal is not considered
     71      for(int i = 0; i < rel.GetLength(0); i++) rel[i, i] = double.NegativeInfinity;
     72
     73      var addedArcs = AddArcs(network, rel, varNames, name2funVertex, varImpactThreshold);
     74      while(addedArcs.Any()) {
     75        var cycles = network.FindShortestCycles().ToList();
     76        while(cycles.Any()) {
     77          // delete weakest link
     78          var weakestArc = cycles.SelectMany(cycle => network.ArcsForCycle(cycle)).OrderBy(a => a.Weight).First();
     79          network.RemoveArc(weakestArc);
     80
     81          cycles = network.FindShortestCycles().ToList();
     82        }
     83
     84        addedArcs = AddArcs(network, rel, varNames, name2funVertex, varImpactThreshold);
     85      }
     86
     87      return network;
     88    }
     89
     90    private static List<IArc> AddArcs(VariableInteractionNetwork network, double[,] impacts, string[] varNames, Dictionary<string, IVertex> name2funVertex, double threshold = 0.0) {
     91      var newArcs = new List<IArc>();
     92      for(int row = 0; row < impacts.GetLength(0); row++) {
     93        if(!name2funVertex.ContainsKey(varNames[row])) continue; // this variable does not have an associated function (considered as independent)
     94
     95        var rowVector = Enumerable.Range(0, impacts.GetLength(0)).Select(col => impacts[row, col]).ToArray();
     96        var max = rowVector.Max();
     97        if(max > threshold) {
     98          var idxOfMax = Array.IndexOf<double>(rowVector, max);
     99          impacts[row, idxOfMax] = double.NegativeInfinity; // edge is not considered anymore
     100          var srcName = varNames[idxOfMax];
     101          var dstName = varNames[row];
     102          var vertex = network.Vertices.Single(v => v.Label == srcName);
     103          var arc = network.AddArc(vertex, name2funVertex[dstName]);
     104          arc.Weight = max;
     105          newArcs.Add(arc);
     106        }
     107      }
     108      return newArcs;
     109    }
     110
     111    [StorableConstructor]
     112    public VariableInteractionNetwork(bool deserializing) : base(deserializing) { }
     113
    31114    public VariableInteractionNetwork() { }
    32115
     
    35118    public override IDeepCloneable Clone(Cloner cloner) {
    36119      return new VariableInteractionNetwork(this, cloner);
     120    }
     121    private IList<IArc> ArcsForCycle(IList<IVertex> cycle) {
     122      var res = new List<IArc>();
     123      foreach(var t in cycle.Zip(cycle.Skip(1), Tuple.Create)) {
     124        var src = t.Item1;
     125        var dst = t.Item2;
     126        var arc = Arcs.Single(a => a.Source == src && a.Target == dst);
     127        res.Add(arc);
     128      }
     129      return res;
     130    }
     131
     132
     133    // finds the shortest cycles in the graph and returns all sub-graphs containing only the nodes / edges within the cycle
     134    public IEnumerable<IList<IVertex>> FindShortestCycles() {
     135      foreach(var startVariable in base.Vertices.OfType<VariableNetworkNode>()) {
     136        foreach(var cycle in FindShortestCycles(startVariable))
     137          yield return cycle;
     138      }
     139    }
     140
     141    private IEnumerable<IList<IVertex>> FindShortestCycles(VariableNetworkNode startVariable) {
     142      var q = new Queue<List<IVertex>>(); // queue of paths
     143      var path = new List<IVertex>();
     144      var cycles = new List<List<IVertex>>();
     145      var maxPathLength = base.Vertices.Count();
     146
     147      path.Add(startVariable);
     148      q.Enqueue(new List<IVertex>(path));
     149
     150      FindShortestCycles(q, maxPathLength, cycles);
     151      return cycles;
     152    }
     153
     154    // TODO efficiency
     155    private void FindShortestCycles(Queue<List<IVertex>> queue, int maxPathLength, List<List<IVertex>> cycles) {
     156      while(queue.Any()) {
     157        var path = queue.Dequeue();
     158        if(path.Count > 1 && path.First() == path.Last()) {
     159          cycles.Add(new List<IVertex>(path)); // found a cycle
     160        } else if(path.Count >= maxPathLength) {
     161          continue;
     162        } else {
     163          var lastVert = path.Last();
     164          var neighbours = base.Arcs.Where(a => a.Source == lastVert).Select(a => a.Target);
     165          foreach(var neighbour in neighbours) {
     166            queue.Enqueue(new List<IVertex>(path.Concat(new IVertex[] { neighbour })));
     167          }
     168        }
     169      }
     170    }
     171
     172    public DoubleMatrix GetWeightsMatrix() {
     173      var names = Vertices.OfType<VariableNetworkNode>()
     174        .Select(v => v.Label)
     175        .OrderBy(s => s, new NaturalStringComparer()).ToArray();
     176      var w = new double[names.Length, names.Length];
     177
     178      var name2idx = new Dictionary<string, int>();
     179      for(int i = 0; i < names.Length; i++) {
     180        name2idx.Add(names[i], i);
     181      }
     182
     183      foreach(var arc in Arcs) {
     184        // only consider arcs going into a junction node
     185        var target = arc.Target as JunctionNetworkNode;
     186        if(target != null)
     187        {
     188          var srcVarName = arc.Source.Label;
     189          // each function node must have exactly one outgoing arc
     190          var dstVarName = arc.Target.OutArcs.Single().Target.Label;
     191
     192          w[name2idx[dstVarName], name2idx[srcVarName]] = arc.Weight;
     193        }
     194      }
     195
     196
     197      return new DoubleMatrix(w, names, names);
     198    }
     199
     200    public string ToGraphVizString() {
     201      var sb = new StringBuilder();
     202      sb.AppendLine("digraph {");
     203      sb.AppendLine("rankdir=LR");
     204      foreach(var v in Vertices.OfType<VariableNetworkNode>()) {
     205        sb.AppendFormat("\"{0}\" [shape=oval]", v.Label).AppendLine();
     206      }
     207      foreach(var v in Vertices.OfType<JunctionNetworkNode>()) {
     208        sb.AppendFormat("\"{0}\" [shape=box]", v.Label).AppendLine();
     209      }
     210      foreach(var arc in Arcs) {
     211        sb.AppendFormat("\"{0}\"->\"{1}\"", arc.Source.Label, arc.Target.Label).AppendLine();
     212      }
     213      sb.AppendLine("}");
     214      return sb.ToString();
    37215    }
    38216  }
Note: See TracChangeset for help on using the changeset viewer.