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source: branches/QAP/HeuristicLab.Problems.QuadraticAssignment.Views/3.3/MultidimensionalScaling.cs @ 5641

Last change on this file since 5641 was 5641, checked in by abeham, 12 years ago

#1330

  • worked on visualization (and MDS)
File size: 6.6 KB
Line 
1#region License Information
2/* HeuristicLab
3 * Copyright (C) 2002-2011 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.Problems.QuadraticAssignment {
26  public static class MultidimensionalScaling {
27
28    public static DoubleMatrix Classic(DoubleMatrix distances, out double error) {
29      if (distances == null) throw new ArgumentNullException("distances");
30      if (distances.Rows != distances.Columns) throw new ArgumentException("Distance matrix must be a square matrix.", "distances");
31      error = 0.0;
32
33      int dimension = distances.Rows;
34      if (dimension == 1) return new DoubleMatrix(new double[,] { { 0, 0 } });
35      else if (dimension == 2) return new DoubleMatrix(new double[,] { { 0, distances[0, 1] } });
36
37      double[,] A = new double[dimension + 1, dimension + 1];
38      for (int i = 1; i < dimension; i++) {
39        for (int j = i + 1; j < dimension + 1; j++) {
40          A[i, j] = -0.5 * distances[i - 1, j - 1] * distances[i - 1, j - 1];
41          A[j, i] = A[i, j];
42          A[0, 0] += A[i, j] / (dimension * dimension);
43          double avg = A[i, j] / (double)dimension;
44          A[0, j] += avg;
45          A[0, i] += avg;
46          A[i, 0] += avg;
47          A[j, 0] += avg;
48        }
49      }
50      double[,] B = new double[dimension, dimension];
51      for (int i = 0; i < dimension - 1; i++) {
52        for (int j = i + 1; j < dimension; j++) {
53          B[i, j] = A[i + 1, j + 1] - A[0, j + 1] - A[i + 1, 0] + A[0, 0];
54        }
55      }
56      double[] eigenvalues;
57      double[,] eigenvectors;
58      alglib.smatrixevd(B, dimension, 1, true, out eigenvalues, out eigenvectors);
59
60      DoubleMatrix coordinates = new DoubleMatrix(dimension, 2);
61      for (int i = 0; i < dimension; i++) {
62        for (int j = 0; j < dimension; j++) {
63          coordinates[i, 0] += eigenvectors[eigenvectors.GetLength(0) - 1, j]
64                             * distances[i, j];
65          coordinates[i, 1] += eigenvectors[eigenvectors.GetLength(0) - 2, j]
66                             * distances[i, j];
67        }
68      }
69
70      return coordinates;
71    }
72
73    /// <summary>
74    /// Performs the Kruskal-Shepard algorithm and applies a gradient descent method
75    /// to fit the coordinates such that the difference between the fit distances
76    /// and the actual distances is minimal.
77    /// </summary>
78    /// <param name="distances">A symmetric NxN matrix that specifies the distances between each element i and j. Diagonal elements are ignored.</param>
79    /// <param name="error">Returns the error between the fit distances and the actual distances.</param>
80    /// <returns>A Nx2 matrix where the first column represents the x- and the second column the y coordinates.</returns>
81    public static DoubleMatrix Metric(DoubleMatrix distances, out double error) {
82      if (distances == null) throw new ArgumentNullException("distances");
83      if (distances.Rows != distances.Columns) throw new ArgumentException("Distance matrix must be a square matrix.", "distances");
84      error = 0.0;
85
86      int dimension = distances.Rows;
87      if (dimension == 1) return new DoubleMatrix(new double[,] { { 0, 0 } });
88      else if (dimension == 2) return new DoubleMatrix(new double[,] { { 0, distances[0, 1] } });
89
90      DoubleMatrix coordinates = new DoubleMatrix(dimension, 2);
91      double rad = (2 * Math.PI) / coordinates.Rows;
92      for (int i = 0; i < dimension; i++) {
93        coordinates[i, 0] = 10 * Math.Cos(rad * i);
94        coordinates[i, 1] = 10 * Math.Sin(rad * i);
95      }
96      double epsg = 0.0000000001;
97      double epsf = 0;
98      double epsx = 0;
99      int maxits = 1000;
100      alglib.mincgstate state = null;
101      alglib.mincgreport rep;
102
103      for (int iterations = 0; iterations < 200; iterations++) {
104        for (int i = 0; i < dimension; i++) {
105          double[] c = new double[] { coordinates[i, 0], coordinates[i, 1] };
106
107          if (iterations == 0 && i == 0) {
108            alglib.mincgcreate(c, out state);
109            alglib.mincgsetcond(state, epsg, epsf, epsx, maxits);
110          } else {
111            alglib.mincgrestartfrom(state, c);
112          }
113          alglib.mincgoptimize(state, func, null, new Info(coordinates, distances, i));
114          alglib.mincgresults(state, out c, out rep);
115
116          coordinates[i, 0] = c[0];
117          coordinates[i, 1] = c[1];
118        }
119      }
120      error = 0;
121      for (int i = 0; i < dimension - 1; i++) {
122        for (int j = i + 1; j < dimension; j++) {
123          if (distances[i, j] != 0) {
124            double dx = coordinates[i, 0] - coordinates[j, 0];
125            double dy = coordinates[i, 1] - coordinates[j, 1];
126            double d = Math.Sqrt(dx * dx + dy * dy);
127            error += ((distances[i, j] - d) * (distances[i, j] - d)) / (distances[i, j] * distances[i, j]);
128          }
129        }
130      }
131      return coordinates;
132    }
133
134    public static void func(double[] x, ref double func, double[] grad, object obj) {
135      func = 0; grad[0] = 0; grad[1] = 0;
136      Info info = (obj as Info);
137      for (int i = 0; i < x.Length; i++) {
138        if (i != info.Row) {
139          double d = (x[0] - info.Coordinates[i, 0])
140                   * (x[0] - info.Coordinates[i, 0])
141                   + (x[1] - info.Coordinates[i, 1])
142                   * (x[1] - info.Coordinates[i, 1]);
143          func += (d - info.Distances[info.Row, i]) * (d - info.Distances[info.Row, i]);
144          grad[0] += 2 * x[0] - 2 * info.Coordinates[i, 0];
145          grad[1] += 2 * x[1] - 2 * info.Coordinates[i, 1];
146        }
147      }
148    }
149
150    private class Info {
151      public DoubleMatrix Coordinates { get; set; }
152      public DoubleMatrix Distances { get; set; }
153      public int Row { get; set; }
154
155      public Info(DoubleMatrix c, DoubleMatrix d, int r) {
156        Coordinates = c;
157        Distances = d;
158        Row = r;
159      }
160    }
161  }
162}
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