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package de.lmu.ifi.dbs.elki.math.statistics.dependence;
/*
This file is part of ELKI:
Environment for Developing KDD-Applications Supported by Index-Structures
Copyright (C) 2015
Ludwig-Maximilians-Universität München
Lehr- und Forschungseinheit für Datenbanksysteme
ELKI Development Team
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU Affero General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program 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 Affero General Public License for more details.
You should have received a copy of the GNU Affero General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
import static org.junit.Assert.assertEquals;
import java.util.Arrays;
import java.util.Random;
import org.junit.Test;
import de.lmu.ifi.dbs.elki.JUnit4Test;
import de.lmu.ifi.dbs.elki.math.MathUtil;
import de.lmu.ifi.dbs.elki.utilities.datastructures.arraylike.ArrayLikeUtil;
/**
* Validate correlation by comparing to manual computation.
*
* @author Erich Schubert
* @since 0.7.0
*/
public class MutualInformationEquiwidthDependenceMeasureTest implements JUnit4Test {
double[][] data = { //
{ 1, 2, 3, 4 }, //
{ 1, 3, 5, 7 }, //
{ 4, 3, 2, 1 }, //
{ 1, 4, 2, 3 }, //
{ 1, 0, 0, 1 }, //
{ 0, 1, 1, 1 }, //
};
// Due to ties in last example, quantization yields:
// X [1, 0] 1
// Y [1, 2] 3
// M [2, 2] 4
final static double HH = (.5 * Math.log(4. / 3) + .25 * Math.log(2.) + .25 * Math.log(2. / 3)) * MathUtil.ONE_BY_LOG2;
// Diagonal: [1, 3]
final static double H4 = (.75 * Math.log(4. / 3) + .25 * Math.log(4.)) * MathUtil.ONE_BY_LOG2;
double[][] manual = { //
{ 1. }, //
{ 1., 1. }, //
{ 1., 1., 1. }, //
{ 0., 0., 0., 1. }, //
{ 0., 0., 0., 0., 1 }, //
{ HH, HH, HH, HH, HH, H4 }, //
};
@Test
public void testMI() {
DependenceMeasure mi = MutualInformationEquiwidthDependenceMeasure.STATIC;
// Single computations
for(int i = 0; i < data.length; i++) {
for(int j = 0; j <= i; j++) {
double co = mi.dependence(data[i], data[j]);
assertEquals("MI does not match for " + i + "," + j, manual[i][j], co, 1e-7);
}
}
// Bulk computation
double[] mat = mi.dependence(ArrayLikeUtil.DOUBLEARRAYADAPTER, Arrays.asList(data));
for(int i = 0, c = 0; i < data.length; i++) {
for(int j = 0; j < i; j++) {
double co = mat[c++];
assertEquals("MI does not match for " + i + "," + j, manual[i][j], co, 1e-7);
}
}
}
@Test
public void testUniform() {
int len = 10000;
DependenceMeasure mi = MutualInformationEquiwidthDependenceMeasure.STATIC;
double[] data1 = new double[len], data2 = new double[len];
Random r = new Random(0);
for(int i = 0; i < len; i++) {
data1[i] = r.nextDouble();
data2[i] = r.nextDouble();
}
// These values are only regression tests...
// Our implementation will use 100 bins, and rescale via
// log2(100.) = 6.6438561897747244!
assertEquals("Self-MI1", 0.999, mi.dependence(data1, data1), 1e-3);
assertEquals("Self-MI2", 0.999, mi.dependence(data2, data2), 1e-3);
assertEquals("MI", 0.1235388559, mi.dependence(data1, data2), 1e-8);
}
}
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