1 /*
2 * Licensed to the Hipparchus project under one or more
3 * contributor license agreements. See the NOTICE file distributed with
4 * this work for additional information regarding copyright ownership.
5 * The Hipparchus project licenses this file to You under the Apache License,
6 * Version 2.0 (the "License"); you may not use this file except in compliance
7 * with the License. You may obtain a copy of the License at
8 *
9 * https://www.apache.org/licenses/LICENSE-2.0
10 *
11 * Unless required by applicable law or agreed to in writing, software
12 * distributed under the License is distributed on an "AS IS" BASIS,
13 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14 * See the License for the specific language governing permissions and
15 * limitations under the License.
16 */
17 package org.hipparchus.stat.projection;
18
19 import org.hipparchus.exception.MathIllegalStateException;
20 import org.hipparchus.stat.LocalizedStatFormats;
21 import org.junit.Assert;
22 import org.junit.Test;
23
24 public class PCATest {
25
26 // example from:
27 // https://towardsdatascience.com/the-mathematics-behind-principal-component-analysis-fff2d7f4b643
28 // https://stattrek.com/matrix-algebra/covariance-matrix
29 private static final double[][] SCORES = {
30 {90, 60, 90},
31 {90, 90, 30},
32 {60, 60, 60},
33 {60, 60, 90},
34 {30, 30, 30},
35 };
36
37 public static final double[] EXPECTED_MEAN = {66, 60, 60};
38 public static final double[] EXPECTED_VARIANCE = {1137.587441, 786.387983, 56.024575};
39
40 private static final double[][] EXPECTED_COMPONENTS = {
41 { 0.6558023, 0.385999 },
42 { 0.4291978, 0.516366 },
43 { 0.6210577, -0.7644414 }
44 };
45
46 /**
47 * This is the expected value (give or take sign) when centering (covariance)
48 * but no scaling is applied. In general, components with the same values but
49 * differing sign are
50 * <a href="https://stats.stackexchange.com/questions/30348/is-it-acceptable-to-reverse-a-sign-of-a-principal-component-score">equivalent</a>.
51 *
52 * The result has been cross-checked with
53 * <a href="https://scikit-learn.org/stable/modules/generated/sklearn.decomposition.PCA.html">sklearn.decomposition.PCA</a>
54 * <a href="https://javadoc.io/static/nz.ac.waikato.cms.weka/weka-dev/3.9.4/weka/attributeSelection/PrincipalComponents.html>weka.attributeSelection.PrincipalComponents</a>
55 * (with the <code>centerData</code> option set to <code>true</code>)
56 * <a href="https://github.com/datumbox/datumbox-framework/blob/develop/datumbox-framework-core/src/main/java/com/datumbox/framework/core/machinelearning/featureselection/PCA.java">com.datumbox.framework.core.machinelearning.featureselection.PCA</a>
57 * (but for whatever reason datumbox does the transform on the unnormalized original data rather than normalized data - normalizing manually achieves the result below)
58 * <a href="https://www.javadoc.io/doc/com.github.haifengl/smile-core/latest/smile/feature/extraction/PCA.html">smile.feature.extraction.PCA</a>
59 * (using the PCA.fit method)
60 * <a href="https://au.mathworks.com/help/stats/pca.html">pca from matlab</a>
61 */
62 private static final double[][] EXPECTED_COV = {
63 { 34.3709848, -13.6692708 },
64 { 9.9834573, 47.6882055 },
65 { -3.9348135, -2.3159927 },
66 { 14.6969171, -25.2492347 },
67 { -55.1165457, -6.4537072 },
68 };
69
70 /**
71 * This is the expected value give or take sign when centering and scaling (correlation).
72 *
73 * The result has been cross-checked with
74 * <a href="https://javadoc.io/static/nz.ac.waikato.cms.weka/weka-dev/3.9.4/weka/attributeSelection/PrincipalComponents.html></a>
75 * <a href="https://au.mathworks.com/help/stats/pca.html">pca from matlab</a>
76 * (using the 'VariableWeights','variance' option)
77 */
78 private static final double[][] EXPECTED_COR = {
79 { 0.9118256, -0.942809 },
80 { 1.3832302, 1.4142136 },
81 { -0.1690309, 0.0 },
82 { 0.0666714, -0.942809 },
83 { -2.1926964, 0.4714045 },
84 };
85
86 /**
87 * This is the expected value give or take sign when centering and scaling (correlation)
88 * is applied with no bias adjustment. In general, bias adjustment is more accurate but
89 * alters most PCA machine learning models by an insignificant amount so is often not accounted for.
90 *
91 * The result has been cross-checked with
92 * <a href="https://scikit-learn.org/stable/modules/generated/sklearn.decomposition.PCA.html">sklearn.decomposition.PCA</a>
93 * (but with prior preprocessing using <a href="https://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.StandardScaler.html">sklearn.preprocessing.StandardScaler</a>)
94 * <a href="https://www.javadoc.io/doc/com.github.haifengl/smile-core/latest/smile/feature/extraction/PCA.html">smile.feature.extraction.PCA</a>
95 * (using the PCA.cor method)
96 */
97 public static final double[][] EXPECTED_COR_NO_BIAS = {
98 { 1.0194521, -1.0540926 },
99 { 1.5464984, 1.5811388 },
100 { -0.1889822, 0.0 },
101 { 0.0745409, -1.0540926 },
102 { -2.451509, 0.5270463 },
103 };
104 public static final double DELTA = 0.000001;
105
106 @Test
107 public void defaultSettings() {
108 PCA pca = new PCA(2);
109 Assert.assertEquals(2, pca.getNumComponents());
110 Assert.assertFalse(pca.isScale());
111 Assert.assertTrue(pca.isBiasCorrection());
112 }
113
114 @Test
115 public void covariance() {
116 PCA pca = new PCA(2);
117 double[][] actual = pca.fitAndTransform(SCORES);
118 Assert.assertArrayEquals(EXPECTED_MEAN, pca.getCenter(), DELTA);
119 Assert.assertArrayEquals(EXPECTED_VARIANCE, pca.getVariance(), DELTA);
120 assertExpected(EXPECTED_COMPONENTS, pca.getComponents());
121 assertExpected(EXPECTED_COV, actual);
122
123 // calling fit and transform individually should be the same as combo method
124 pca = new PCA(2);
125 actual = pca.fit(SCORES).transform(SCORES);
126 Assert.assertArrayEquals(EXPECTED_MEAN, pca.getCenter(), DELTA);
127 assertExpected(EXPECTED_COV, actual);
128 }
129
130 @Test
131 public void correlation() {
132 PCA pca = new PCA(2, true, true);
133 double[][] actual = pca.fitAndTransform(SCORES);
134 assertExpected(EXPECTED_COR, actual);
135 }
136
137 @Test
138 public void correlationNoBias() {
139 PCA pca = new PCA(2, true, false);
140 double[][] actual = pca.fitAndTransform(SCORES);
141 assertExpected(EXPECTED_COR_NO_BIAS, actual);
142 }
143
144 @Test
145 public void transformWithoutFit() {
146 PCA pca = new PCA(2);
147 try {
148 pca.transform(SCORES);
149 Assert.fail("an exception should have been thrown");
150 } catch (MathIllegalStateException mise) {
151 Assert.assertEquals(LocalizedStatFormats.ILLEGAL_STATE_PCA, mise.getSpecifier());
152 Assert.assertEquals("transform", mise.getParts()[0]);
153 }
154 }
155
156 private static void assertExpected(double[][] expected, double[][] actual) {
157 for (int i = 0; i < expected.length; i++) {
158 double[] e = expected[i];
159 double[] t = actual[i];
160 Assert.assertArrayEquals(e, t, DELTA);
161 }
162 }
163 }