source: branches/2457_ExpertSystem/HeuristicLab.Analysis/3.3/SelfOrganizingMaps/SOM.cs

#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.Common;
using HeuristicLab.Core;
using HeuristicLab.Data;
using HeuristicLab.Random;
using System;
using System.Linq;

namespace HeuristicLab.Analysis.SelfOrganizingMaps {
  public static class SOM {
    /// <summary>
    /// Performs a self-organizing map to a range of feature column-vectors organized in a matrix.
    /// </summary>
    /// <param name="features">The feature matrix containing the column-vectors.</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 features, 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 = features.Columns;
      var L = features.Rows;

      if (double.IsNaN(learningRate)) learningRate = 1.0 / Math.Sqrt(2.0 * L);
      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 scaledFeatures = Scale(features);
      var weights = Enumerable.Range(0, K).Select(k => Enumerable.Range(0, L).Select(_ => random.NextDouble()).ToArray()).ToArray();
      // normalize s.t. sum(alphas[k]) = 1
      for (var k = 0; k < K; k++) {
        var sum = weights[k].Sum();
        for (var i = 0; i < weights[k].Length; i++) weights[k][i] /= sum;
      }
      var oldWeights = weights.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(scaledFeatures, weights, i);

          for (var k = 0; k < K; k++) {
            for (var j = 0; j < L; j++) {
              weights[k][j] = oldWeights[k][j] + learningRate * neighborhood(iterations, iter, k, bmu) * (scaledFeatures[j, i] - oldWeights[k][j]);
            }
          }
        }
        for (var k = 0; k < K; k++) {
          for (var j = 0; j < L; j++) {
            oldWeights[k][j] = weights[k][j];
          }
        }
      }

      var result = new DoubleMatrix(N, 2);
      for (var i = 0; i < N; i++) {
        var bmu = GetBestMatchingUnit(scaledFeatures, weights, 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[][] weights, int i) {
      var bmu = -1;
      var minV = double.MaxValue;
      for (var k = 0; k < weights.Length; k++) {
        var d = 0.0;
        for (var r = 0; r < weights[k].Length; r++) {
          d += (D[r, i] - weights[k][r]) * (D[r, i] - weights[k][r]);
        }
        if (d < minV) {
          minV = d;
          bmu = k;
        }
      }
      return bmu;
    }

    private static DoubleMatrix Scale(DoubleMatrix features) {
      var scaledFeatures = new DoubleMatrix(features.Rows, features.Columns);
      for (var i = 0; i < features.Rows; i++) {
        var rowSum = 0.0;
        for (var j = 0; j < features.Columns; j++) rowSum += features[i, j];
        if (rowSum.IsAlmost(0.0)) rowSum = 1.0;
        for (var j = 0; j < features.Columns; j++) scaledFeatures[i, j] = features[i, j] / rowSum;
      }
      return scaledFeatures;
    }
  }
}