1 | using System;
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2 | using HeuristicLab.Data;
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3 | using Microsoft.VisualStudio.TestTools.UnitTesting;
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4 |
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5 | namespace HeuristicLab.Analysis.Tests {
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6 | [TestClass]
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7 | public class MultidimensionalScalingTest {
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8 | [TestMethod]
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9 | public void TestGoodnessOfFit() {
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10 | double stress;
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11 | DoubleMatrix distances3 = new DoubleMatrix(3, 3);
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12 | // Example 1: A right triangle
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13 | distances3[0, 1] = distances3[1, 0] = 3;
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14 | distances3[0, 2] = distances3[2, 0] = 4;
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15 | distances3[1, 2] = distances3[2, 1] = 5;
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16 | stress = MultidimensionalScaling.CalculateNormalizedStress(distances3,
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17 | MultidimensionalScaling.KruskalShepard(distances3));
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18 | Assert.IsTrue(stress < 0.1);
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19 | // Example 2: An arbitrary triangle
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20 | distances3[0, 1] = distances3[1, 0] = 8;
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21 | distances3[0, 2] = distances3[2, 0] = 6.4;
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22 | distances3[1, 2] = distances3[2, 1] = 5;
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23 | stress = MultidimensionalScaling.CalculateNormalizedStress(distances3,
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24 | MultidimensionalScaling.KruskalShepard(distances3));
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25 | Assert.IsTrue(stress < 0.1);
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26 | DoubleMatrix distances4 = new DoubleMatrix(4, 4);
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27 | // Example 3: A small square
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28 | distances4[0, 1] = distances4[1, 0] = 1;
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29 | distances4[0, 2] = distances4[2, 0] = Math.Sqrt(2);
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30 | distances4[0, 3] = distances4[3, 0] = 1;
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31 | distances4[1, 2] = distances4[2, 1] = 1;
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32 | distances4[1, 3] = distances4[3, 1] = Math.Sqrt(2);
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33 | distances4[2, 3] = distances4[3, 2] = 1;
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34 | stress = MultidimensionalScaling.CalculateNormalizedStress(distances4,
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35 | MultidimensionalScaling.KruskalShepard(distances4));
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36 | Assert.IsTrue(stress < 0.1);
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37 | // Example 4: A large square
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38 | distances4[0, 1] = distances4[1, 0] = 1000;
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39 | distances4[0, 2] = distances4[2, 0] = Math.Sqrt(2000000);
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40 | distances4[0, 3] = distances4[3, 0] = 1000;
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41 | distances4[1, 2] = distances4[2, 1] = 1000;
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42 | distances4[1, 3] = distances4[3, 1] = Math.Sqrt(2000000);
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43 | distances4[2, 3] = distances4[3, 2] = 1000;
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44 | stress = MultidimensionalScaling.CalculateNormalizedStress(distances4,
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45 | MultidimensionalScaling.KruskalShepard(distances4));
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46 | Assert.IsTrue(stress < 0.1);
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47 | // Example 5: An arbitrary cloud of 8 points in a plane
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48 | DoubleMatrix distancesK = GetDistances(new double[,] { { 2, 1 }, { 5, 2 }, { 7, 1 }, { 4, 0 }, { 3, 3 }, { 4, 2 }, { 1, 8 }, { 6, 3 } });
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49 | stress = MultidimensionalScaling.CalculateNormalizedStress(distancesK,
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50 | MultidimensionalScaling.KruskalShepard(distancesK));
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51 | Assert.IsTrue(stress < 0.1);
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52 | // Example 6: A tetrahedron
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53 | distancesK = GetDistances(new double[,] { { 0, 0, 0 }, { 4, 0, 0 }, { 2, 3.4641, 0 }, { 2, 1.1547, 3.2660 } });
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54 | stress = MultidimensionalScaling.CalculateNormalizedStress(distancesK,
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55 | MultidimensionalScaling.KruskalShepard(distancesK));
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56 | Assert.IsTrue(stress < 0.1);
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57 | }
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58 |
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59 | internal DoubleMatrix GetDistances(double[,] coordinates) {
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60 | int dimension = coordinates.GetLength(0);
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61 | DoubleMatrix distances = new DoubleMatrix(dimension, dimension);
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62 | for (int i = 0; i < dimension - 1; i++)
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63 | for (int j = i + 1; j < dimension; j++) {
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64 | double sum = 0;
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65 | for (int k = 0; k < coordinates.GetLength(1); k++)
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66 | sum += (coordinates[i, k] - coordinates[j, k]) * (coordinates[i, k] - coordinates[j, k]);
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67 | distances[i, j] = distances[j, i] = Math.Sqrt(sum);
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68 | }
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69 | return distances;
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70 | }
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71 | }
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72 | }
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