/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with this
* work for additional information regarding copyright ownership. The ASF
* licenses this file to You under the Apache License, Version 2.0 (the
* "License"); you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
* License for the specific language governing permissions and limitations under
* the License.
*/
package org.apache.commons.math4.distribution.fitting;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import org.apache.commons.math4.distribution.MixtureMultivariateNormalDistribution;
import org.apache.commons.math4.distribution.MultivariateNormalDistribution;
import org.apache.commons.math4.distribution.fitting.MultivariateNormalMixtureExpectationMaximization;
import org.apache.commons.math4.exception.ConvergenceException;
import org.apache.commons.math4.exception.DimensionMismatchException;
import org.apache.commons.math4.exception.NotStrictlyPositiveException;
import org.apache.commons.math4.exception.NumberIsTooSmallException;
import org.apache.commons.math4.linear.Array2DRowRealMatrix;
import org.apache.commons.math4.linear.RealMatrix;
import org.apache.commons.math4.util.Pair;
import org.junit.Assert;
import org.junit.Test;
/**
* Test that demonstrates the use of
* {@link MultivariateNormalMixtureExpectationMaximization}.
*/
public class MultivariateNormalMixtureExpectationMaximizationTest {
@Test(expected = NotStrictlyPositiveException.class)
public void testNonEmptyData() {
// Should not accept empty data
new MultivariateNormalMixtureExpectationMaximization(new double[][] {});
}
@Test(expected = DimensionMismatchException.class)
public void testNonJaggedData() {
// Reject data with nonconstant numbers of columns
double[][] data = new double[][] {
{ 1, 2, 3 },
{ 4, 5, 6, 7 },
};
new MultivariateNormalMixtureExpectationMaximization(data);
}
@Test(expected = NumberIsTooSmallException.class)
public void testMultipleColumnsRequired() {
// Data should have at least 2 columns
double[][] data = new double[][] {
{ 1 }, { 2 }
};
new MultivariateNormalMixtureExpectationMaximization(data);
}
@Test(expected = NotStrictlyPositiveException.class)
public void testMaxIterationsPositive() {
// Maximum iterations for fit must be positive integer
double[][] data = getTestSamples();
MultivariateNormalMixtureExpectationMaximization fitter =
new MultivariateNormalMixtureExpectationMaximization(data);
MixtureMultivariateNormalDistribution
initialMix = MultivariateNormalMixtureExpectationMaximization.estimate(data, 2);
fitter.fit(initialMix, 0, 1E-5);
}
@Test(expected = NotStrictlyPositiveException.class)
public void testThresholdPositive() {
// Maximum iterations for fit must be positive
double[][] data = getTestSamples();
MultivariateNormalMixtureExpectationMaximization fitter =
new MultivariateNormalMixtureExpectationMaximization(
data);
MixtureMultivariateNormalDistribution
initialMix = MultivariateNormalMixtureExpectationMaximization.estimate(data, 2);
fitter.fit(initialMix, 1000, 0);
}
@Test(expected = ConvergenceException.class)
public void testConvergenceException() {
// ConvergenceException thrown if fit terminates before threshold met
double[][] data = getTestSamples();
MultivariateNormalMixtureExpectationMaximization fitter
= new MultivariateNormalMixtureExpectationMaximization(data);
MixtureMultivariateNormalDistribution
initialMix = MultivariateNormalMixtureExpectationMaximization.estimate(data, 2);
// 5 iterations not enough to meet convergence threshold
fitter.fit(initialMix, 5, 1E-5);
}
@Test(expected = DimensionMismatchException.class)
public void testIncompatibleIntialMixture() {
// Data has 3 columns
double[][] data = new double[][] {
{ 1, 2, 3 }, { 4, 5, 6 }, { 7, 8, 9 }
};
double[] weights = new double[] { 0.5, 0.5 };
// These distributions are compatible with 2-column data, not 3-column
// data
MultivariateNormalDistribution[] mvns = new MultivariateNormalDistribution[2];
mvns[0] = new MultivariateNormalDistribution(new double[] {
-0.0021722935000328823, 3.5432892936887908 },
new double[][] {
{ 4.537422569229048, 3.5266152281729304 },
{ 3.5266152281729304, 6.175448814169779 } });
mvns[1] = new MultivariateNormalDistribution(new double[] {
5.090902706507635, 8.68540656355283 }, new double[][] {
{ 2.886778573963039, 1.5257474543463154 },
{ 1.5257474543463154, 3.3794567673616918 } });
// Create components and mixture
List<Pair<Double, MultivariateNormalDistribution>> components =
new ArrayList<>();
components.add(new Pair<>(
weights[0], mvns[0]));
components.add(new Pair<>(
weights[1], mvns[1]));
MixtureMultivariateNormalDistribution badInitialMix
= new MixtureMultivariateNormalDistribution(components);
MultivariateNormalMixtureExpectationMaximization fitter
= new MultivariateNormalMixtureExpectationMaximization(data);
fitter.fit(badInitialMix);
}
@Test
public void testInitialMixture() {
// Testing initial mixture estimated from data
final double[] correctWeights = new double[] { 0.5, 0.5 };
final double[][] correctMeans = new double[][] {
{-0.0021722935000328823, 3.5432892936887908},
{5.090902706507635, 8.68540656355283},
};
final RealMatrix[] correctCovMats = new Array2DRowRealMatrix[2];
correctCovMats[0] = new Array2DRowRealMatrix(new double[][] {
{ 4.537422569229048, 3.5266152281729304 },
{ 3.5266152281729304, 6.175448814169779 } });
correctCovMats[1] = new Array2DRowRealMatrix( new double[][] {
{ 2.886778573963039, 1.5257474543463154 },
{ 1.5257474543463154, 3.3794567673616918 } });
final MultivariateNormalDistribution[] correctMVNs = new
MultivariateNormalDistribution[2];
correctMVNs[0] = new MultivariateNormalDistribution(correctMeans[0],
correctCovMats[0].getData());
correctMVNs[1] = new MultivariateNormalDistribution(correctMeans[1],
correctCovMats[1].getData());
final MixtureMultivariateNormalDistribution initialMix
= MultivariateNormalMixtureExpectationMaximization.estimate(getTestSamples(), 2);
int i = 0;
for (Pair<Double, MultivariateNormalDistribution> component : initialMix
.getComponents()) {
Assert.assertEquals(correctWeights[i], component.getFirst(),
Math.ulp(1d));
final double[] means = component.getValue().getMeans();
Assert.assertTrue(Arrays.equals(correctMeans[i], means));
final RealMatrix covMat = component.getValue().getCovariances();
Assert.assertEquals(correctCovMats[i], covMat);
i++;
}
}
@Test
public void testFit() {
// Test that the loglikelihood, weights, and models are determined and
// fitted correctly
final double[][] data = getTestSamples();
final double correctLogLikelihood = -4.292431006791994;
final double[] correctWeights = new double[] { 0.2962324189652912, 0.7037675810347089 };
final double[][] correctMeans = new double[][]{
{-1.4213112715121132, 1.6924690505757753},
{4.213612224374709, 7.975621325853645}
};
final RealMatrix[] correctCovMats = new Array2DRowRealMatrix[2];
correctCovMats[0] = new Array2DRowRealMatrix(new double[][] {
{ 1.739356907285747, -0.5867644251487614 },
{ -0.5867644251487614, 1.0232932029324642 } }
);
correctCovMats[1] = new Array2DRowRealMatrix(new double[][] {
{ 4.245384898007161, 2.5797798966382155 },
{ 2.5797798966382155, 3.9200272522448367 } });
final MultivariateNormalDistribution[] correctMVNs = new MultivariateNormalDistribution[2];
correctMVNs[0] = new MultivariateNormalDistribution(correctMeans[0], correctCovMats[0].getData());
correctMVNs[1] = new MultivariateNormalDistribution(correctMeans[1], correctCovMats[1].getData());
MultivariateNormalMixtureExpectationMaximization fitter
= new MultivariateNormalMixtureExpectationMaximization(data);
MixtureMultivariateNormalDistribution initialMix
= MultivariateNormalMixtureExpectationMaximization.estimate(data, 2);
fitter.fit(initialMix);
MixtureMultivariateNormalDistribution fittedMix = fitter.getFittedModel();
List<Pair<Double, MultivariateNormalDistribution>> components = fittedMix.getComponents();
Assert.assertEquals(correctLogLikelihood,
fitter.getLogLikelihood(),
Math.ulp(1d));
int i = 0;
for (Pair<Double, MultivariateNormalDistribution> component : components) {
final double weight = component.getFirst();
final MultivariateNormalDistribution mvn = component.getSecond();
final double[] mean = mvn.getMeans();
final RealMatrix covMat = mvn.getCovariances();
Assert.assertEquals(correctWeights[i], weight, Math.ulp(1d));
Assert.assertTrue(Arrays.equals(correctMeans[i], mean));
Assert.assertEquals(correctCovMats[i], covMat);
i++;
}
}
private double[][] getTestSamples() {
// generated using R Mixtools rmvnorm with mean vectors [-1.5, 2] and
// [4, 8.2]
return new double[][] { { 7.358553610469948, 11.31260831446758 },
{ 7.175770420124739, 8.988812210204454 },
{ 4.324151905768422, 6.837727899051482 },
{ 2.157832219173036, 6.317444585521968 },
{ -1.890157421896651, 1.74271202875498 },
{ 0.8922409354455803, 1.999119343923781 },
{ 3.396949764787055, 6.813170372579068 },
{ -2.057498232686068, -0.002522983830852255 },
{ 6.359932157365045, 8.343600029975851 },
{ 3.353102234276168, 7.087541882898689 },
{ -1.763877221595639, 0.9688890460330644 },
{ 6.151457185125111, 9.075011757431174 },
{ 4.281597398048899, 5.953270070976117 },
{ 3.549576703974894, 8.616038155992861 },
{ 6.004706732349854, 8.959423391087469 },
{ 2.802915014676262, 6.285676742173564 },
{ -0.6029879029880616, 1.083332958357485 },
{ 3.631827105398369, 6.743428504049444 },
{ 6.161125014007315, 9.60920569689001 },
{ -1.049582894255342, 0.2020017892080281 },
{ 3.910573022688315, 8.19609909534937 },
{ 8.180454017634863, 7.861055769719962 },
{ 1.488945440439716, 8.02699903761247 },
{ 4.813750847823778, 12.34416881332515 },
{ 0.0443208501259158, 5.901148093240691 },
{ 4.416417235068346, 4.465243084006094 },
{ 4.0002433603072, 6.721937850166174 },
{ 3.190113818788205, 10.51648348411058 },
{ 4.493600914967883, 7.938224231022314 },
{ -3.675669533266189, 4.472845076673303 },
{ 6.648645511703989, 12.03544085965724 },
{ -1.330031331404445, 1.33931042964811 },
{ -3.812111460708707, 2.50534195568356 },
{ 5.669339356648331, 6.214488981177026 },
{ 1.006596727153816, 1.51165463112716 },
{ 5.039466365033024, 7.476532610478689 },
{ 4.349091929968925, 7.446356406259756 },
{ -1.220289665119069, 3.403926955951437 },
{ 5.553003979122395, 6.886518211202239 },
{ 2.274487732222856, 7.009541508533196 },
{ 4.147567059965864, 7.34025244349202 },
{ 4.083882618965819, 6.362852861075623 },
{ 2.203122344647599, 7.260295257904624 },
{ -2.147497550770442, 1.262293431529498 },
{ 2.473700950426512, 6.558900135505638 },
{ 8.267081298847554, 12.10214104577748 },
{ 6.91977329776865, 9.91998488301285 },
{ 0.1680479852730894, 6.28286034168897 },
{ -1.268578659195158, 2.326711221485755 },
{ 1.829966451374701, 6.254187605304518 },
{ 5.648849025754848, 9.330002040750291 },
{ -2.302874793257666, 3.585545172776065 },
{ -2.629218791709046, 2.156215538500288 },
{ 4.036618140700114, 10.2962785719958 },
{ 0.4616386422783874, 0.6782756325806778 },
{ -0.3447896073408363, 0.4999834691645118 },
{ -0.475281453118318, 1.931470384180492 },
{ 2.382509690609731, 6.071782429815853 },
{ -3.203934441889096, 2.572079552602468 },
{ 8.465636032165087, 13.96462998683518 },
{ 2.36755660870416, 5.7844595007273 },
{ 0.5935496528993371, 1.374615871358943 },
{ -2.467481505748694, 2.097224634713005 },
{ 4.27867444328542, 10.24772361238549 },
{ -2.013791907543137, 2.013799426047639 },
{ 6.424588084404173, 9.185334939684516 },
{ -0.8448238876802175, 0.5447382022282812 },
{ 1.342955703473923, 8.645456317633556 },
{ 3.108712208751979, 8.512156853800064 },
{ 4.343205178315472, 8.056869549234374 },
{ -2.971767642212396, 3.201180146824761 },
{ 2.583820931523672, 5.459873414473854 },
{ 4.209139115268925, 8.171098193546225 },
{ 0.4064909057902746, 1.454390775518743 },
{ 3.068642411145223, 6.959485153620035 },
{ 6.085968972900461, 7.391429799500965 },
{ -1.342265795764202, 1.454550012997143 },
{ 6.249773274516883, 6.290269880772023 },
{ 4.986225847822566, 7.75266344868907 },
{ 7.642443254378944, 10.19914817500263 },
{ 6.438181159163673, 8.464396764810347 },
{ 2.520859761025108, 7.68222425260111 },
{ 2.883699944257541, 6.777960331348503 },
{ 2.788004550956599, 6.634735386652733 },
{ 3.331661231995638, 5.794191300046592 },
{ 3.526172276645504, 6.710802266815884 },
{ 3.188298528138741, 10.34495528210205 },
{ 0.7345539486114623, 5.807604004180681 },
{ 1.165044595880125, 7.830121829295257 },
{ 7.146962523500671, 11.62995162065415 },
{ 7.813872137162087, 10.62827008714735 },
{ 3.118099164870063, 8.286003148186371 },
{ -1.708739286262571, 1.561026755374264 },
{ 1.786163047580084, 4.172394388214604 },
{ 3.718506403232386, 7.807752990130349 },
{ 6.167414046828899, 10.01104941031293 },
{ -1.063477247689196, 1.61176085846339 },
{ -3.396739609433642, 0.7127911050002151 },
{ 2.438885945896797, 7.353011138689225 },
{ -0.2073204144780931, 0.850771146627012 }, };
}
}