source: branches/2707_HeuristicLab.VRPEnhancements/HeuristicLab.Problems.VehicleRouting/3.4/Encodings/Potvin/Creators/Cluster.cs

#region License Information
/* HeuristicLab
 * Copyright (C) 2002-2019 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 HeuristicLab.Core;
using HeuristicLab.Encodings.PermutationEncoding;

namespace HeuristicLab.Problems.VehicleRouting.Encodings.Potvin {

  public class KMeansAlgorithm<TData> where TData : class {

    private class ClusterInfo {
      public TData Mean;
      public double Variance;
      public int Size;
    }

    private readonly Func<List<TData>, TData> meanCalculator;
    private readonly Func<TData, TData, double> distanceCalculator;

    public KMeansAlgorithm(Func<List<TData>, TData> meanCalculator, Func<TData, TData, double> distanceCalculator) {
      this.meanCalculator = meanCalculator;
      this.distanceCalculator = distanceCalculator;
    }

    public List<List<int>> Run(List<TData> data, int k, double changeThreshold, IRandom random) {
      int numClusters = Math.Min(k, data.Count);

      var assignments = new int[data.Count];
      for (int i = 0; i < assignments.Length; i++)
        assignments[i] = -1; // unassigned

      // (1) initialize each cluster with a random element as mean
      var clusters = new ClusterInfo[numClusters];
      var initIndices = new Permutation(PermutationTypes.Absolute, data.Count, random);
      for (int c = 0; c < numClusters; c++) {
        assignments[initIndices[c]] = c;
        clusters[c] = new ClusterInfo {
          Mean = data[initIndices[c]],
          Size = 1
        };
      }

      // (2) repeat clustering until change rate is below the threshold
      double changeRate;
      do {
        int changes = Iterate(data, assignments, clusters);
        changeRate = (double)changes / data.Count;
      } while (changeRate > changeThreshold);

      // (3) return non-empty clusters
      var clustersData = new List<List<int>>(numClusters);
      for (int c = 0; c < numClusters; c++)
        clustersData.Add(new List<int>());
      for (int i = 0; i < assignments.Length; i++)
        clustersData[assignments[i]].Add(i);
      clustersData.RemoveAll(c => c.Count == 0);
      return clustersData;
    }

    private int Iterate(List<TData> data, int[] assignments, ClusterInfo[] clusters) {
      int changes = 0;

      var newAssignments = new int[data.Count];
      assignments.CopyTo(newAssignments, 0);

      // assign elements to currently most suited cluster
      for (int i = 0; i < data.Count; i++) {
        int bestCluster = 0;
        double bestImpact = CalculateImpact(data[i], clusters[0]);
        for (int c = 1; c < clusters.Length; c++) {
          double impact = CalculateImpact(data[i], clusters[c]);
          if (impact < bestImpact) {
            bestImpact = impact;
            bestCluster = c;
          }
        }
        newAssignments[i] = bestCluster;
        if (newAssignments[i] != assignments[i])
          changes++;
      }

      // update clusters
      var clustersData = new List<List<TData>>(clusters.Length);
      for (int c = 0; c < clusters.Length; c++)
        clustersData.Add(new List<TData>());
      for (int i = 0; i < data.Count; i++) {
        assignments[i] = newAssignments[i];
        clustersData[assignments[i]].Add(data[i]);
      }
      for (int c = 0; c < clusters.Length; c++) {
        var clusterData = clustersData[c];
        if (clusterData.Count == 0)
          continue;

        clusters[c].Mean = meanCalculator(clusterData);

        clusters[c].Variance = 0;
        foreach (var e in clusterData)
          clusters[c].Variance += Math.Pow(distanceCalculator(e, clusters[c].Mean), 2);
        clusters[c].Variance /= clusterData.Count;

        clusters[c].Size = clusterData.Count;
      }

      return changes;
    }

    private double CalculateImpact(TData datum, ClusterInfo cluster) {
      double newVariance = (cluster.Variance * cluster.Size + Math.Pow(distanceCalculator(datum, cluster.Mean), 2)) / (cluster.Size + 1);
      return newVariance - cluster.Variance;
    }
  }
}