#region License Information /* HeuristicLab * Copyright (C) 2002-2019 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 . */ #endregion using System; using System.Globalization; using HeuristicLab.Data; using Microsoft.VisualStudio.TestTools.UnitTesting; namespace HeuristicLab.Analysis.Tests { [TestClass] public class MultidimensionalScalingTest { [TestMethod] [TestCategory("Algorithms.DataAnalysis")] [TestProperty("Time", "short")] public void TestGoodnessOfFit() { double stress; DoubleMatrix distances3 = new DoubleMatrix(3, 3); // Example 1: A right triangle distances3[0, 1] = distances3[1, 0] = 3; distances3[0, 2] = distances3[2, 0] = 4; distances3[1, 2] = distances3[2, 1] = 5; stress = MultidimensionalScaling.CalculateNormalizedStress(distances3, MultidimensionalScaling.KruskalShepard(distances3)); Assert.IsTrue(stress < 0.1); // Example 2: An arbitrary triangle distances3[0, 1] = distances3[1, 0] = 8; distances3[0, 2] = distances3[2, 0] = 6.4; distances3[1, 2] = distances3[2, 1] = 5; DoubleMatrix coords3 = MultidimensionalScaling.KruskalShepard(distances3); Console.WriteLine("Coordinates: "); 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]); stress = MultidimensionalScaling.CalculateNormalizedStress(distances3, coords3); Console.WriteLine("Stress = " + stress.ToString(CultureInfo.InvariantCulture.NumberFormat)); Assert.IsTrue(stress < 0.1); DoubleMatrix distances4 = new DoubleMatrix(4, 4); // Example 3: A small square distances4[0, 1] = distances4[1, 0] = 1; distances4[0, 2] = distances4[2, 0] = Math.Sqrt(2); distances4[0, 3] = distances4[3, 0] = 1; distances4[1, 2] = distances4[2, 1] = 1; distances4[1, 3] = distances4[3, 1] = Math.Sqrt(2); distances4[2, 3] = distances4[3, 2] = 1; stress = MultidimensionalScaling.CalculateNormalizedStress(distances4, MultidimensionalScaling.KruskalShepard(distances4)); Assert.IsTrue(stress < 0.1); // Example 4: A large square distances4[0, 1] = distances4[1, 0] = 1000; distances4[0, 2] = distances4[2, 0] = Math.Sqrt(2000000); distances4[0, 3] = distances4[3, 0] = 1000; distances4[1, 2] = distances4[2, 1] = 1000; distances4[1, 3] = distances4[3, 1] = Math.Sqrt(2000000); distances4[2, 3] = distances4[3, 2] = 1000; stress = MultidimensionalScaling.CalculateNormalizedStress(distances4, MultidimensionalScaling.KruskalShepard(distances4)); Assert.IsTrue(stress < 0.1); // Example 5: An arbitrary cloud of 8 points in a plane DoubleMatrix distancesK = GetDistances(new double[,] { { 2, 1 }, { 5, 2 }, { 7, 1 }, { 4, 0 }, { 3, 3 }, { 4, 2 }, { 1, 8 }, { 6, 3 } }); stress = MultidimensionalScaling.CalculateNormalizedStress(distancesK, MultidimensionalScaling.KruskalShepard(distancesK)); Assert.IsTrue(stress < 0.1); // Example 6: A tetrahedron distancesK = GetDistances(new double[,] { { 0, 0, 0 }, { 4, 0, 0 }, { 2, 3.4641, 0 }, { 2, 1.1547, 3.2660 } }); stress = MultidimensionalScaling.CalculateNormalizedStress(distancesK, MultidimensionalScaling.KruskalShepard(distancesK)); Assert.IsTrue(stress < 0.1); // Example 7: A matrix of perceived dissimilarities between 14 colors, published in the literature distancesK = new DoubleMatrix(new double[,] { { 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 }, { 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 }, { 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 }, { 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 }, { 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 }, { 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 }, { 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 }, { 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 }, { 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 }, { 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 }, { 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 }, { 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 }, { 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 }, { 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 }}); stress = MultidimensionalScaling.CalculateNormalizedStress(distancesK, MultidimensionalScaling.KruskalShepard(distancesK)); Assert.IsTrue(stress < 0.1); } internal DoubleMatrix GetDistances(double[,] coordinates) { int dimension = coordinates.GetLength(0); DoubleMatrix distances = new DoubleMatrix(dimension, dimension); for (int i = 0; i < dimension - 1; i++) for (int j = i + 1; j < dimension; j++) { double sum = 0; for (int k = 0; k < coordinates.GetLength(1); k++) sum += (coordinates[i, k] - coordinates[j, k]) * (coordinates[i, k] - coordinates[j, k]); distances[i, j] = distances[j, i] = Math.Sqrt(sum); } return distances; } } }