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source: trunk/sources/HeuristicLab.Analysis/3.3/MultidimensionalScaling/MultidimensionalScaling.cs @ 7259

Last change on this file since 7259 was 7259, checked in by swagner, 12 years ago

Updated year of copyrights to 2012 (#1716)

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1#region License Information
2/* HeuristicLab
3 * Copyright (C) 2002-2012 Heuristic and Evolutionary Algorithms Laboratory (HEAL)
4 *
5 * This file is part of HeuristicLab.
6 *
7 * HeuristicLab is free software: you can redistribute it and/or modify
8 * it under the terms of the GNU General Public License as published by
9 * the Free Software Foundation, either version 3 of the License, or
10 * (at your option) any later version.
11 *
12 * HeuristicLab is distributed in the hope that it will be useful,
13 * but WITHOUT ANY WARRANTY; without even the implied warranty of
14 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
15 * GNU General Public License for more details.
16 *
17 * You should have received a copy of the GNU General Public License
18 * along with HeuristicLab. If not, see <http://www.gnu.org/licenses/>.
19 */
20#endregion
21
22using System;
23using HeuristicLab.Data;
24
25namespace HeuristicLab.Analysis {
26  public static class MultidimensionalScaling {
27
28    /// <summary>
29    /// Performs the Kruskal-Shepard algorithm and applies a gradient descent method
30    /// to fit the coordinates such that the difference between the fit distances
31    /// and the dissimilarities becomes minimal.
32    /// </summary>
33    /// <remarks>
34    /// It will initialize the coordinates in a deterministic fashion such that all initial points are equally spaced on a circle.
35    /// </remarks>
36    /// <param name="dissimilarities">A symmetric NxN matrix that specifies the dissimilarities between each element i and j. Diagonal elements are ignored.</param>
37    ///
38    /// <returns>A Nx2 matrix where the first column represents the x- and the second column the y coordinates.</returns>
39    public static DoubleMatrix KruskalShepard(DoubleMatrix dissimilarities) {
40      if (dissimilarities == null) throw new ArgumentNullException("dissimilarities");
41      if (dissimilarities.Rows != dissimilarities.Columns) throw new ArgumentException("Dissimilarities must be a square matrix.", "dissimilarities");
42
43      int dimension = dissimilarities.Rows;
44      if (dimension == 1) return new DoubleMatrix(new double[,] { { 0, 0 } });
45      else if (dimension == 2) return new DoubleMatrix(new double[,] { { 0, 0 }, { 0, dissimilarities[0, 1] } });
46
47      DoubleMatrix coordinates = new DoubleMatrix(dimension, 2);
48      double rad = (2 * Math.PI) / coordinates.Rows;
49      for (int i = 0; i < dimension; i++) {
50        coordinates[i, 0] = 10 * Math.Cos(rad * i);
51        coordinates[i, 1] = 10 * Math.Sin(rad * i);
52      }
53
54      return KruskalShepard(dissimilarities, coordinates);
55    }
56
57    /// <summary>
58    /// Performs the Kruskal-Shepard algorithm and applies a gradient descent method
59    /// to fit the coordinates such that the difference between the fit distances
60    /// and the dissimilarities is minimal.
61    /// </summary>
62    /// <remarks>
63    /// It will use a pre-initialized x,y-coordinates matrix as a starting point of the gradient descent.
64    /// </remarks>
65    /// <param name="dissimilarities">A symmetric NxN matrix that specifies the dissimilarities between each element i and j. Diagonal elements are ignored.</param>
66    /// <param name="coordinates">The Nx2 matrix of initial coordinates.</param>
67    /// <param name="maximumIterations">The number of iterations for which the algorithm should run.
68    /// In every iteration it tries to find the best location for every item.</param>
69    /// <returns>A Nx2 matrix where the first column represents the x- and the second column the y coordinates.</returns>
70    public static DoubleMatrix KruskalShepard(DoubleMatrix dissimilarities, DoubleMatrix coordinates, int maximumIterations = 10) {
71      int dimension = dissimilarities.Rows;
72      if (dimension != dissimilarities.Columns || coordinates.Rows != dimension) throw new ArgumentException("The number of coordinates and the number of rows and columns in the dissimilarities matrix do not match.");
73
74      double epsg = 1e-7;
75      double epsf = 0;
76      double epsx = 0;
77      int maxits = 0;
78
79      alglib.minlmstate state;
80      alglib.minlmreport rep;
81      for (int iterations = 0; iterations < maximumIterations; iterations++) {
82        bool changed = false;
83        for (int i = 0; i < dimension; i++) {
84          double[] c = new double[] { coordinates[i, 0], coordinates[i, 1] };
85
86          try {
87            alglib.minlmcreatevj(dimension - 1, c, out state);
88            alglib.minlmsetcond(state, epsg, epsf, epsx, maxits);
89            alglib.minlmoptimize(state, StressFitness, StressJacobian, null, new Info(coordinates, dissimilarities, i));
90            alglib.minlmresults(state, out c, out rep);
91          } catch (alglib.alglibexception) { }
92          if (!double.IsNaN(c[0]) && !double.IsNaN(c[1])) {
93            changed = changed || (coordinates[i, 0] != c[0]) || (coordinates[i, 1] != c[1]);
94            coordinates[i, 0] = c[0];
95            coordinates[i, 1] = c[1];
96          }
97        }
98        if (!changed) break;
99      }
100      return coordinates;
101    }
102
103    private static void StressFitness(double[] x, double[] fi, object obj) {
104      Info info = (obj as Info);
105      for (int i = 0; i < info.Coordinates.Rows; i++) {
106        double f = Stress(x, info.Dissimilarities[info.Row, i], info.Coordinates[i, 0], info.Coordinates[i, 1]);
107        if (i < info.Row) fi[i] = f;
108        else if (i > info.Row) fi[i - 1] = f;
109      }
110    }
111
112    private static void StressJacobian(double[] x, double[] fi, double[,] jac, object obj) {
113      Info info = (obj as Info);
114      int idx = 0;
115      for (int i = 0; i < info.Coordinates.Rows; i++) {
116        if (i != info.Row) {
117          double c = info.Dissimilarities[info.Row, i];
118          double a = info.Coordinates[i, 0];
119          double b = info.Coordinates[i, 1];
120          double f = Stress(x, c, a, b);
121          fi[idx] = f;
122          jac[idx, 0] = 2 * (x[0] - a) * (Math.Sqrt((a - x[0]) * (a - x[0]) + (b - x[1]) * (b - x[1])) - c) / Math.Sqrt((a - x[0]) * (a - x[0]) + (b - x[1]) * (b - x[1]));
123          jac[idx, 1] = 2 * (x[1] - b) * (Math.Sqrt((a - x[0]) * (a - x[0]) + (b - x[1]) * (b - x[1])) - c) / Math.Sqrt((a - x[0]) * (a - x[0]) + (b - x[1]) * (b - x[1]));
124          idx++;
125        }
126      }
127    }
128
129    private static double Stress(double[] x, double distance, double xCoord, double yCoord) {
130      return Stress(x[0], x[1], distance, xCoord, yCoord);
131    }
132
133    private static double Stress(double x, double y, double distance, double otherX, double otherY) {
134      double d = Math.Sqrt((x - otherX) * (x - otherX)
135                         + (y - otherY) * (y - otherY));
136      return (d - distance) * (d - distance);
137    }
138
139    /// <summary>
140    /// This method computes the normalized raw-stress value according to Groenen and van de Velden 2004. "Multidimensional Scaling". Technical report EI 2004-15.
141    /// </summary>
142    /// <remarks>
143    /// Throws an ArgumentException when the <paramref name="dissimilarities"/> matrix is not symmetric.
144    /// </remarks>
145    ///
146    /// <param name="dissimilarities">The matrix with the dissimilarities.</param>
147    /// <param name="coordinates">The actual location of the points.</param>
148    /// <returns>The normalized raw-stress value that describes the goodness-of-fit between the distances in the points and the size of the dissimilarities. If the value is &lt; 0.1 the fit is generally considered good. If between 0.1 and 0.2 it is considered acceptable, but the usefulness of the scaling with higher values is doubtful.</returns>
149    public static double CalculateNormalizedStress(DoubleMatrix dissimilarities, DoubleMatrix coordinates) {
150      int dimension = dissimilarities.Rows;
151      if (dimension != dissimilarities.Columns || dimension != coordinates.Rows) throw new ArgumentException("The number of coordinates and the number of rows and columns in the dissimilarities matrix do not match.");
152      double stress = 0, normalization = 0;
153      for (int i = 0; i < dimension - 1; i++) {
154        for (int j = i + 1; j < dimension; j++) {
155          if (dissimilarities[i, j] != dissimilarities[j, i]) throw new ArgumentException("Dissimilarities is not a symmetric matrix.", "dissimilarities");
156          if (dissimilarities[i, j] != 0) {
157            stress += Stress(coordinates[i, 0], coordinates[i, 1], dissimilarities[i, j], coordinates[j, 0], coordinates[j, 1]);
158            normalization += (dissimilarities[i, j] * dissimilarities[i, j]);
159          }
160        }
161      }
162      return stress / normalization;
163    }
164
165    private class Info {
166      public DoubleMatrix Coordinates { get; set; }
167      public DoubleMatrix Dissimilarities { get; set; }
168      public int Row { get; set; }
169
170      public Info(DoubleMatrix c, DoubleMatrix d, int r) {
171        Coordinates = c;
172        Dissimilarities = d;
173        Row = r;
174      }
175    }
176  }
177}
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