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source: branches/OaaS/HeuristicLab.Tests/HeuristicLab.Analysis-3.3/MultidimensionalScalingTest.cs @ 9204

Last change on this file since 9204 was 7915, checked in by mkommend, 12 years ago

#1777: Extracted unit tests into a separate solution.
File size: 6.2 KB
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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 System.Globalization;
24using HeuristicLab.Analysis;
25using HeuristicLab.Data;
26using Microsoft.VisualStudio.TestTools.UnitTesting;
27
28namespace HeuristicLab.Analysis_33.Tests {
29  [TestClass]
30  public class MultidimensionalScalingTest {
31    [TestMethod]
32    public void TestGoodnessOfFit() {
33      double stress;
34      DoubleMatrix distances3 = new DoubleMatrix(3, 3);
35      // Example 1: A right triangle
36      distances3[0, 1] = distances3[1, 0] = 3;
37      distances3[0, 2] = distances3[2, 0] = 4;
38      distances3[1, 2] = distances3[2, 1] = 5;
39      stress = MultidimensionalScaling.CalculateNormalizedStress(distances3,
40        MultidimensionalScaling.KruskalShepard(distances3));
41      Assert.IsTrue(stress < 0.1);
42      // Example 2: An arbitrary triangle
43      distances3[0, 1] = distances3[1, 0] = 8;
44      distances3[0, 2] = distances3[2, 0] = 6.4;
45      distances3[1, 2] = distances3[2, 1] = 5;
46      DoubleMatrix coords3 = MultidimensionalScaling.KruskalShepard(distances3);
47      Console.WriteLine("Coordinates: ");
48      Console.WriteLine("A = ({0}, {1}), B = ({2}, {3}), C = ({4}, {5})", coords3[0, 0], coords3[0, 1], coords3[1, 0], coords3[1, 1], coords3[2, 0], coords3[2, 1]);
49      stress = MultidimensionalScaling.CalculateNormalizedStress(distances3, coords3);
50      Console.WriteLine("Stress = " + stress.ToString(CultureInfo.InvariantCulture.NumberFormat));
51      Assert.IsTrue(stress < 0.1);
52      DoubleMatrix distances4 = new DoubleMatrix(4, 4);
53      // Example 3: A small square
54      distances4[0, 1] = distances4[1, 0] = 1;
55      distances4[0, 2] = distances4[2, 0] = Math.Sqrt(2);
56      distances4[0, 3] = distances4[3, 0] = 1;
57      distances4[1, 2] = distances4[2, 1] = 1;
58      distances4[1, 3] = distances4[3, 1] = Math.Sqrt(2);
59      distances4[2, 3] = distances4[3, 2] = 1;
60      stress = MultidimensionalScaling.CalculateNormalizedStress(distances4,
61        MultidimensionalScaling.KruskalShepard(distances4));
62      Assert.IsTrue(stress < 0.1);
63      // Example 4: A large square
64      distances4[0, 1] = distances4[1, 0] = 1000;
65      distances4[0, 2] = distances4[2, 0] = Math.Sqrt(2000000);
66      distances4[0, 3] = distances4[3, 0] = 1000;
67      distances4[1, 2] = distances4[2, 1] = 1000;
68      distances4[1, 3] = distances4[3, 1] = Math.Sqrt(2000000);
69      distances4[2, 3] = distances4[3, 2] = 1000;
70      stress = MultidimensionalScaling.CalculateNormalizedStress(distances4,
71        MultidimensionalScaling.KruskalShepard(distances4));
72      Assert.IsTrue(stress < 0.1);
73      // Example 5: An arbitrary cloud of 8 points in a plane
74      DoubleMatrix distancesK = GetDistances(new double[,] { { 2, 1 }, { 5, 2 }, { 7, 1 }, { 4, 0 }, { 3, 3 }, { 4, 2 }, { 1, 8 }, { 6, 3 } });
75      stress = MultidimensionalScaling.CalculateNormalizedStress(distancesK,
76        MultidimensionalScaling.KruskalShepard(distancesK));
77      Assert.IsTrue(stress < 0.1);
78      // Example 6: A tetrahedron
79      distancesK = GetDistances(new double[,] { { 0, 0, 0 }, { 4, 0, 0 }, { 2, 3.4641, 0 }, { 2, 1.1547, 3.2660 } });
80      stress = MultidimensionalScaling.CalculateNormalizedStress(distancesK,
81        MultidimensionalScaling.KruskalShepard(distancesK));
82      Assert.IsTrue(stress < 0.1);
83      // Example 7: A matrix of perceived dissimilarities between 14 colors, published in the literature
84      distancesK = new DoubleMatrix(new double[,] {
85{ 0.00, 0.14, 0.58, 0.58, 0.82, 0.94, 0.93, 0.96, 0.98, 0.93, 0.91, 0.88, 0.87, 0.84 },
86{ 0.14, 0.00, 0.50, 0.56, 0.78, 0.91, 0.93, 0.93, 0.98, 0.96, 0.93, 0.89, 0.87, 0.86 },
87{ 0.58, 0.50, 0.00, 0.19, 0.53, 0.83, 0.90, 0.92, 0.98, 0.99, 0.98, 0.99, 0.95, 0.97 },
88{ 0.58, 0.56, 0.19, 0.00, 0.46, 0.75, 0.90, 0.91, 0.98, 0.99, 1.00, 0.99, 0.98, 0.96 },
89{ 0.82, 0.78, 0.53, 0.46, 0.00, 0.39, 0.69, 0.74, 0.93, 0.98, 0.98, 0.99, 0.98, 1.00 },
90{ 0.94, 0.91, 0.83, 0.75, 0.39, 0.00, 0.38, 0.55, 0.86, 0.92, 0.98, 0.98, 0.98, 0.99 },
91{ 0.93, 0.93, 0.90, 0.90, 0.69, 0.38, 0.00, 0.27, 0.78, 0.86, 0.95, 0.98, 0.98, 1.00 },
92{ 0.96, 0.93, 0.92, 0.91, 0.74, 0.55, 0.27, 0.00, 0.67, 0.81, 0.96, 0.97, 0.98, 0.98 },
93{ 0.98, 0.98, 0.98, 0.98, 0.93, 0.86, 0.78, 0.67, 0.00, 0.42, 0.63, 0.73, 0.80, 0.77 },
94{ 0.93, 0.96, 0.99, 0.99, 0.98, 0.92, 0.86, 0.81, 0.42, 0.00, 0.26, 0.50, 0.59, 0.72 },
95{ 0.91, 0.93, 0.98, 1.00, 0.98, 0.98, 0.95, 0.96, 0.63, 0.26, 0.00, 0.24, 0.38, 0.45 },
96{ 0.88, 0.89, 0.99, 0.99, 0.99, 0.98, 0.98, 0.97, 0.73, 0.50, 0.24, 0.00, 0.15, 0.32 },
97{ 0.87, 0.87, 0.95, 0.98, 0.98, 0.98, 0.98, 0.98, 0.80, 0.59, 0.38, 0.15, 0.00, 0.24 },
98{ 0.84, 0.86, 0.97, 0.96, 1.00, 0.99, 1.00, 0.98, 0.77, 0.72, 0.45, 0.32, 0.24, 0.00 }});
99      stress = MultidimensionalScaling.CalculateNormalizedStress(distancesK,
100        MultidimensionalScaling.KruskalShepard(distancesK));
101      Assert.IsTrue(stress < 0.1);
102    }
103
104    internal DoubleMatrix GetDistances(double[,] coordinates) {
105      int dimension = coordinates.GetLength(0);
106      DoubleMatrix distances = new DoubleMatrix(dimension, dimension);
107      for (int i = 0; i < dimension - 1; i++)
108        for (int j = i + 1; j < dimension; j++) {
109          double sum = 0;
110          for (int k = 0; k < coordinates.GetLength(1); k++)
111            sum += (coordinates[i, k] - coordinates[j, k]) * (coordinates[i, k] - coordinates[j, k]);
112          distances[i, j] = distances[j, i] = Math.Sqrt(sum);
113        }
114      return distances;
115    }
116  }
117}
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