source: branches/2457_ExpertSystem/HeuristicLab.Analysis/3.3/SelfOrganizingMaps/RelationalSOM.cs @ 15831

#region License Information
/* HeuristicLab
 * Copyright (C) 2002-2016 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 HeuristicLab.Core;
using HeuristicLab.Data;
using HeuristicLab.Random;
using System;
using System.Linq;

namespace HeuristicLab.Analysis.SelfOrganizingMaps {
  public static class RelationalSOM {
    /// <summary>
    /// This is the online algorithm described in
    /// Olteanu, M. and Villa-Vialaneix, N. 2015.
    /// On-line relational and multiple relational SOM.
    /// Neurocomputing 147, pp. 15-30.
    /// </summary>
    /// <param name="dissimilarities">The full NxN matrix containing all dissimilarities between N points.</param>
    /// <param name="random">The random number generator to use.</param>
    /// <param name="somSize">The length of a side of the SOM grid (there are somSize * somSize neurons).</param>
    /// <param name="iterations">The amount of iterations to perform in learning.</param>
    /// <param name="learningRate">The initial learning rate.</param>
    /// <param name="learningRadius">The initial learning radius.</param>
    /// <param name="jittering">If the final coordinates should be jittered slightly within the grid.</param>
    /// <returns>A matrix of coordinates having N rows and 2 columns.</returns>
    public static DoubleMatrix Map(DoubleMatrix dissimilarities, IRandom random = null, int somSize = 5, int iterations = 100, double learningRate = double.NaN, double learningRadius = 5.0, bool jittering = true) {
      if (random == null) random = new MersenneTwister();
      var K = somSize * somSize;
      var N = dissimilarities.Rows;
      if (double.IsNaN(learningRate)) learningRate = 1.0 / Math.Sqrt(2.0 * N);
      var fixedLearningRate = learningRate / 10.0;
      var varLearningRate = 9.0 * fixedLearningRate;
      Func<int, int> getX = (neuron) => neuron % somSize;
      Func<int, int> getY = (neuron) => neuron / somSize;
      Func<int, int, int, int, double> neighborhood = (maxIter, iter, k, bmu) => {
        var sigma = learningRadius * ((maxIter - iter) / (double)maxIter) + 0.0001;
        var xK = getX(k);
        var yK = getY(k);
        var xW = getX(bmu);
        var yW = getY(bmu);
        var d = (xK - xW) * (xK - xW) + (yK - yW) * (yK - yW);
        return Math.Exp(-d / (2.0 * sigma * sigma));
      };
      var alphas = Enumerable.Range(0, K).Select(k => Enumerable.Range(0, N).Select(_ => random.NextDouble()).ToArray()).ToArray();
      // normalize s.t. sum(alphas[k]) = 1
      for (var k = 0; k < K; k++) {
        var sum = alphas[k].Sum();
        for (var i = 0; i < alphas[k].Length; i++) alphas[k][i] /= sum;
      }
      var oldAlphas = alphas.Select(x => (double[])x.Clone()).ToArray();

      for (var iter = 0; iter < iterations; iter++) {
        learningRate = varLearningRate * ((iterations - iter) / (double)iterations) + fixedLearningRate;
        var pointShuffle = Enumerable.Range(0, N).Shuffle(random).ToArray();
        for (var p = 0; p < N; p++) {
          var i = pointShuffle[p];
          var bmu = GetBestMatchingUnit(dissimilarities, alphas, i);

          for (var k = 0; k < K; k++) {
            for (var j = 0; j < N; j++) {
              alphas[k][j] = oldAlphas[k][j] + learningRate * neighborhood(iterations, iter, k, bmu) * ((i == j ? 1.0 : 0.0) - oldAlphas[k][j]);
            }
          }
        }
        for (var k = 0; k < K; k++) {
          for (var j = 0; j < N; j++) {
            oldAlphas[k][j] = alphas[k][j];
          }
        }
      }

      var result = new DoubleMatrix(N, 2);
      for (var i = 0; i < N; i++) {
        var bmu = GetBestMatchingUnit(dissimilarities, alphas, i);
        if (!jittering) {
          result[i, 0] = getX(bmu);
          result[i, 1] = getY(bmu);
        } else {
          result[i, 0] = getX(bmu) + random.NextDouble() * 0.8;
          result[i, 1] = getY(bmu) + random.NextDouble() * 0.8;
        }
      }
      return result;
    }

    private static int GetBestMatchingUnit(DoubleMatrix D, double[][] alphas, int i) {
      var bmu = -1;
      var minV = double.MaxValue;
      for (var k = 0; k < alphas.Length; k++) {
        var Daki = 0.0;
        var akDak = 0.0;
        for (var r = 0; r < D.Rows; r++) {
          var Dakr = 0.0;
          for (var s = 0; s < D.Rows; s++) {
            Dakr += D[r, s] * alphas[k][s];
          }
          if (r == i) Daki = Dakr;
          akDak += alphas[k][r] * Dakr;
        }
        var v = Daki - 0.5 * akDak;
        if (v < minV) {
          bmu = k;
          minV = v;
        }
      }
      return bmu;
    }
  }
}