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Posted to commits@commons.apache.org by tn...@apache.org on 2013/10/31 22:16:08 UTC
svn commit: r1537660 - in /commons/proper/math/trunk: pom.xml
src/changes/changes.xml
src/main/java/org/apache/commons/math3/stat/correlation/KendallsCorrelation.java
src/test/java/org/apache/commons/math3/stat/correlation/KendallsCorrelationTest.java
Author: tn
Date: Thu Oct 31 21:16:08 2013
New Revision: 1537660
URL: http://svn.apache.org/r1537660
Log:
[MATH-814] Added Kendalls tau correlation, Thanks to Matt Adereth.
Added:
commons/proper/math/trunk/src/main/java/org/apache/commons/math3/stat/correlation/KendallsCorrelation.java (with props)
commons/proper/math/trunk/src/test/java/org/apache/commons/math3/stat/correlation/KendallsCorrelationTest.java (with props)
Modified:
commons/proper/math/trunk/pom.xml
commons/proper/math/trunk/src/changes/changes.xml
Modified: commons/proper/math/trunk/pom.xml
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/pom.xml?rev=1537660&r1=1537659&r2=1537660&view=diff
==============================================================================
--- commons/proper/math/trunk/pom.xml (original)
+++ commons/proper/math/trunk/pom.xml Thu Oct 31 21:16:08 2013
@@ -148,6 +148,9 @@
<name>Rémi Arntzen</name>
</contributor>
<contributor>
+ <name>Matt Adereth</name>
+ </contributor>
+ <contributor>
<name>Jared Becksfort</name>
</contributor>
<contributor>
Modified: commons/proper/math/trunk/src/changes/changes.xml
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/changes/changes.xml?rev=1537660&r1=1537659&r2=1537660&view=diff
==============================================================================
--- commons/proper/math/trunk/src/changes/changes.xml (original)
+++ commons/proper/math/trunk/src/changes/changes.xml Thu Oct 31 21:16:08 2013
@@ -51,6 +51,9 @@ If the output is not quite correct, chec
</properties>
<body>
<release version="x.y" date="TBD" description="TBD">
+ <action dev="tn" type="add" issue="MATH-1051" due-to="Matt Adereth,devl">
+ Added Kendall's tau correlation (KendallsCorrelation).
+ </action>
<action dev="tn" type="fix" issue="MATH-1051">
"EigenDecomposition" may have failed to compute the decomposition for certain
non-symmetric matrices. Port of the respective bugfix in Jama-1.0.3.
Added: commons/proper/math/trunk/src/main/java/org/apache/commons/math3/stat/correlation/KendallsCorrelation.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math3/stat/correlation/KendallsCorrelation.java?rev=1537660&view=auto
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math3/stat/correlation/KendallsCorrelation.java (added)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math3/stat/correlation/KendallsCorrelation.java Thu Oct 31 21:16:08 2013
@@ -0,0 +1,261 @@
+/*
+ * 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.math3.stat.correlation;
+
+import org.apache.commons.math3.exception.DimensionMismatchException;
+import org.apache.commons.math3.linear.BlockRealMatrix;
+import org.apache.commons.math3.linear.MatrixUtils;
+import org.apache.commons.math3.linear.RealMatrix;
+import org.apache.commons.math3.util.FastMath;
+import org.apache.commons.math3.util.Pair;
+
+import java.util.Arrays;
+import java.util.Comparator;
+
+/**
+ * Implementation of Kendall's Tau-b rank correlation</a>.
+ * <p>
+ * A pair of observations (x<sub>1</sub>, y<sub>1</sub>) and
+ * (x<sub>2</sub>, y<sub>2</sub>) are considered <i>concordant</i> if
+ * x<sub>1</sub> < x<sub>2</sub> and y<sub>1</sub> < y<sub>2</sub>
+ * or x<sub>2</sub> < x<sub>1</sub> and y<sub>2</sub> < y<sub>1</sub>.
+ * The pair is <i>discordant</i> if x<sub>1</sub> < x<sub>2</sub> and
+ * y<sub>2</sub> < y<sub>1</sub> or x<sub>2</sub> < x<sub>1</sub> and
+ * y<sub>1</sub> < y<sub>2</sub>. If either x<sub>1</sub> = x<sub>2</sub>
+ * or y<sub>1</sub> = y<sub>2</sub>, the pair is neither concordant nor
+ * discordant.
+ * <p>
+ * Kendall's Tau-b is defined as:
+ * <pre>
+ * tau<sub>b</sub> = (n<sub>c</sub> - n<sub>d</sub>) / sqrt((n<sub>0</sub> - n<sub>1</sub>) * (n<sub>0</sub> - n<sub>2</sub>))
+ * </pre>
+ * <p>
+ * where:
+ * <ul>
+ * <li>n<sub>0</sub> = n * (n - 1) / 2</li>
+ * <li>n<sub>c</sub> = Number of concordant pairs</li>
+ * <li>n<sub>d</sub> = Number of discordant pairs</li>
+ * <li>n<sub>1</sub> = sum of t<sub>i</sub> * (t<sub>i</sub> - 1) / 2 for all i</li>
+ * <li>n<sub>2</sub> = sum of u<sub>j</sub> * (u<sub>j</sub> - 1) / 2 for all j</li>
+ * <li>t<sub>i</sub> = Number of tied values in the i<sup>th</sup> group of ties in x</li>
+ * <li>u<sub>j</sub> = Number of tied values in the j<sup>th</sup> group of ties in y</li>
+ * </ul>
+ * <p>
+ * This implementation uses the O(n log n) algorithm described in
+ * William R. Knight's 1966 paper "A Computer Method for Calculating
+ * Kendall's Tau with Ungrouped Data" in the Journal of the American
+ * Statistical Association.
+ *
+ * @see <a href="http://en.wikipedia.org/wiki/Kendall_tau_rank_correlation_coefficient">
+ * Kendall tau rank correlation coefficient (Wikipedia)</a>
+ * @see <a href="http://www.jstor.org/stable/2282833">A Computer
+ * Method for Calculating Kendall's Tau with Ungrouped Data</a>
+ *
+ * @version $Id$
+ * @since 3.3
+ */
+public class KendallsCorrelation {
+
+ /** correlation matrix */
+ private final RealMatrix correlationMatrix;
+
+ /**
+ * Create a KendallsCorrelation instance without data.
+ */
+ public KendallsCorrelation() {
+ correlationMatrix = null;
+ }
+
+ /**
+ * Create a KendallsCorrelation from a rectangular array
+ * whose columns represent values of variables to be correlated.
+ *
+ * @param data rectangular array with columns representing variables
+ * @throws IllegalArgumentException if the input data array is not
+ * rectangular with at least two rows and two columns.
+ */
+ public KendallsCorrelation(double[][] data) {
+ this(MatrixUtils.createRealMatrix(data));
+ }
+
+ /**
+ * Create a KendallsCorrelation from a RealMatrix whose columns
+ * represent variables to be correlated.
+ *
+ * @param matrix matrix with columns representing variables to correlate
+ */
+ public KendallsCorrelation(RealMatrix matrix) {
+ correlationMatrix = computeCorrelationMatrix(matrix);
+ }
+
+ /**
+ * Returns the correlation matrix.
+ *
+ * @return correlation matrix
+ */
+ public RealMatrix getCorrelationMatrix() {
+ return correlationMatrix;
+ }
+
+ /**
+ * Computes the Kendall's Tau rank correlation matrix for the columns of
+ * the input matrix.
+ *
+ * @param matrix matrix with columns representing variables to correlate
+ * @return correlation matrix
+ */
+ public RealMatrix computeCorrelationMatrix(final RealMatrix matrix) {
+ int nVars = matrix.getColumnDimension();
+ RealMatrix outMatrix = new BlockRealMatrix(nVars, nVars);
+ for (int i = 0; i < nVars; i++) {
+ for (int j = 0; j < i; j++) {
+ double corr = correlation(matrix.getColumn(i), matrix.getColumn(j));
+ outMatrix.setEntry(i, j, corr);
+ outMatrix.setEntry(j, i, corr);
+ }
+ outMatrix.setEntry(i, i, 1d);
+ }
+ return outMatrix;
+ }
+
+ /**
+ * Computes the Kendall's Tau rank correlation matrix for the columns of
+ * the input rectangular array. The columns of the array represent values
+ * of variables to be correlated.
+ *
+ * @param matrix matrix with columns representing variables to correlate
+ * @return correlation matrix
+ */
+ public RealMatrix computeCorrelationMatrix(final double[][] matrix) {
+ return computeCorrelationMatrix(new BlockRealMatrix(matrix));
+ }
+
+ /**
+ * Computes the Kendall's Tau rank correlation coefficient between the two arrays.
+ *
+ * @param xArray first data array
+ * @param yArray second data array
+ * @return Returns Kendall's Tau rank correlation coefficient for the two arrays
+ * @throws DimensionMismatchException if the arrays lengths do not match
+ */
+ public double correlation(final double[] xArray, final double[] yArray)
+ throws DimensionMismatchException {
+
+ if (xArray.length != yArray.length) {
+ throw new DimensionMismatchException(xArray.length, yArray.length);
+ }
+
+ final int n = xArray.length;
+ final int numPairs = n * (n - 1) / 2;
+
+ @SuppressWarnings("unchecked")
+ Pair<Double, Double>[] pairs = new Pair[n];
+ for (int i = 0; i < n; i++) {
+ pairs[i] = new Pair<Double, Double>(xArray[i], yArray[i]);
+ }
+
+ Arrays.sort(pairs, new Comparator<Pair<Double, Double>>() {
+ @Override
+ public int compare(Pair<Double, Double> pair1, Pair<Double, Double> pair2) {
+ int compareFirst = pair1.getFirst().compareTo(pair2.getFirst());
+ return compareFirst != 0 ? compareFirst : pair1.getSecond().compareTo(pair2.getSecond());
+ }
+ });
+
+ int tiedXPairs = 0;
+ int tiedXYPairs = 0;
+ int consecutiveXTies = 1;
+ int consecutiveXYTies = 1;
+ Pair<Double, Double> prev = pairs[0];
+ for (int i = 1; i < n; i++) {
+ final Pair<Double, Double> curr = pairs[i];
+ if (curr.getFirst().equals(prev.getFirst())) {
+ consecutiveXTies++;
+ if (curr.getSecond().equals(prev.getSecond())) {
+ consecutiveXYTies++;
+ } else {
+ tiedXYPairs += consecutiveXYTies * (consecutiveXYTies - 1) / 2;
+ consecutiveXYTies = 1;
+ }
+ } else {
+ tiedXPairs += consecutiveXTies * (consecutiveXTies - 1) / 2;
+ consecutiveXTies = 1;
+ tiedXYPairs += consecutiveXYTies * (consecutiveXYTies - 1) / 2;
+ consecutiveXYTies = 1;
+ }
+ prev = curr;
+ }
+ tiedXPairs += consecutiveXTies * (consecutiveXTies - 1) / 2;
+ tiedXYPairs += consecutiveXYTies * (consecutiveXYTies - 1) / 2;
+
+ int swaps = 0;
+ @SuppressWarnings("unchecked")
+ Pair<Double, Double>[] pairsDestination = new Pair[n];
+ for (int segmentSize = 1; segmentSize < n; segmentSize <<= 1) {
+ for (int offset = 0; offset < n; offset += 2 * segmentSize) {
+ int i = offset;
+ final int iEnd = FastMath.min(i + segmentSize, n);
+ int j = iEnd;
+ final int jEnd = FastMath.min(j + segmentSize, n);
+
+ int copyLocation = offset;
+ while (i < iEnd || j < jEnd) {
+ if (i < iEnd) {
+ if (j < jEnd) {
+ if (pairs[i].getSecond().compareTo(pairs[j].getSecond()) <= 0) {
+ pairsDestination[copyLocation] = pairs[i];
+ i++;
+ } else {
+ pairsDestination[copyLocation] = pairs[j];
+ j++;
+ swaps += iEnd - i;
+ }
+ } else {
+ pairsDestination[copyLocation] = pairs[i];
+ i++;
+ }
+ } else {
+ pairsDestination[copyLocation] = pairs[j];
+ j++;
+ }
+ copyLocation++;
+ }
+ }
+ final Pair<Double, Double>[] pairsTemp = pairs;
+ pairs = pairsDestination;
+ pairsDestination = pairsTemp;
+ }
+
+ int tiedYPairs = 0;
+ int consecutiveYTies = 1;
+ prev = pairs[0];
+ for (int i = 1; i < n; i++) {
+ final Pair<Double, Double> curr = pairs[i];
+ if (curr.getSecond().equals(prev.getSecond())) {
+ consecutiveYTies++;
+ } else {
+ tiedYPairs += consecutiveYTies * (consecutiveYTies - 1) / 2;
+ consecutiveYTies = 1;
+ }
+ prev = curr;
+ }
+ tiedYPairs += consecutiveYTies * (consecutiveYTies - 1) / 2;
+
+ int concordantMinusDiscordant = numPairs - tiedXPairs - tiedYPairs + tiedXYPairs - 2 * swaps;
+ return concordantMinusDiscordant / FastMath.sqrt((numPairs - tiedXPairs) * (numPairs - tiedYPairs));
+ }
+}
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Added: commons/proper/math/trunk/src/test/java/org/apache/commons/math3/stat/correlation/KendallsCorrelationTest.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/test/java/org/apache/commons/math3/stat/correlation/KendallsCorrelationTest.java?rev=1537660&view=auto
==============================================================================
--- commons/proper/math/trunk/src/test/java/org/apache/commons/math3/stat/correlation/KendallsCorrelationTest.java (added)
+++ commons/proper/math/trunk/src/test/java/org/apache/commons/math3/stat/correlation/KendallsCorrelationTest.java Thu Oct 31 21:16:08 2013
@@ -0,0 +1,235 @@
+package org.apache.commons.math3.stat.correlation;
+
+import org.apache.commons.math3.TestUtils;
+import org.apache.commons.math3.linear.BlockRealMatrix;
+import org.apache.commons.math3.linear.RealMatrix;
+import org.junit.Assert;
+import org.junit.Before;
+import org.junit.Test;
+
+/**
+ * Test cases for Kendall's Tau rank correlation.
+ */
+public class KendallsCorrelationTest extends PearsonsCorrelationTest {
+
+ private KendallsCorrelation correlation;
+
+ @Before
+ public void setUp() {
+ correlation = new KendallsCorrelation();
+ }
+
+ /**
+ * Test Longley dataset against R.
+ */
+ @Override
+ @Test
+ public void testLongly() {
+ RealMatrix matrix = createRealMatrix(longleyData, 16, 7);
+ KendallsCorrelation corrInstance = new KendallsCorrelation(matrix);
+ RealMatrix correlationMatrix = corrInstance.getCorrelationMatrix();
+ double[] rData = new double[] {
+ 1, 0.9166666666666666, 0.9333333333333332, 0.3666666666666666, 0.05, 0.8999999999999999,
+ 0.8999999999999999, 0.9166666666666666, 1, 0.9833333333333333, 0.45, 0.03333333333333333,
+ 0.9833333333333333, 0.9833333333333333, 0.9333333333333332, 0.9833333333333333, 1,
+ 0.4333333333333333, 0.05, 0.9666666666666666, 0.9666666666666666, 0.3666666666666666,
+ 0.45, 0.4333333333333333, 1, -0.2166666666666666, 0.4666666666666666, 0.4666666666666666, 0.05,
+ 0.03333333333333333, 0.05, -0.2166666666666666, 1, 0.05, 0.05, 0.8999999999999999, 0.9833333333333333,
+ 0.9666666666666666, 0.4666666666666666, 0.05, 1, 0.9999999999999999, 0.8999999999999999,
+ 0.9833333333333333, 0.9666666666666666, 0.4666666666666666, 0.05, 0.9999999999999999, 1
+ };
+ TestUtils.assertEquals("Kendall's correlation matrix", createRealMatrix(rData, 7, 7), correlationMatrix, 10E-15);
+ }
+
+ /**
+ * Test R swiss fertility dataset.
+ */
+ @Test
+ public void testSwiss() {
+ RealMatrix matrix = createRealMatrix(swissData, 47, 5);
+ KendallsCorrelation corrInstance = new KendallsCorrelation(matrix);
+ RealMatrix correlationMatrix = corrInstance.getCorrelationMatrix();
+ double[] rData = new double[] {
+ 1, 0.1795465254708308, -0.4762437404200669, -0.3306111613580587, 0.2453703703703704,
+ 0.1795465254708308, 1, -0.4505221560842292, -0.4761645631778491, 0.2054604569820847,
+ -0.4762437404200669, -0.4505221560842292, 1, 0.528943683925829, -0.3212755391722673,
+ -0.3306111613580587, -0.4761645631778491, 0.528943683925829, 1, -0.08479652265379604,
+ 0.2453703703703704, 0.2054604569820847, -0.3212755391722673, -0.08479652265379604, 1
+ };
+ TestUtils.assertEquals("Kendall's correlation matrix", createRealMatrix(rData, 5, 5), correlationMatrix, 10E-15);
+ }
+
+ @Test
+ public void testSimpleOrdered() {
+ final int length = 10;
+ final double[] xArray = new double[length];
+ final double[] yArray = new double[length];
+ for (int i = 0; i < length; i++) {
+ xArray[i] = i;
+ yArray[i] = i;
+ }
+ Assert.assertEquals(1.0, correlation.correlation(xArray, yArray), Double.MIN_VALUE);
+ }
+
+ @Test
+ public void testSimpleReversed() {
+ final int length = 10;
+ final double[] xArray = new double[length];
+ final double[] yArray = new double[length];
+ for (int i = 0; i < length; i++) {
+ xArray[length - i - 1] = i;
+ yArray[i] = i;
+ }
+ Assert.assertEquals(-1.0, correlation.correlation(xArray, yArray), Double.MIN_VALUE);
+ }
+
+ @Test
+ public void testSimpleOrderedPowerOf2() {
+ final int length = 16;
+ final double[] xArray = new double[length];
+ final double[] yArray = new double[length];
+ for (int i = 0; i < length; i++) {
+ xArray[i] = i;
+ yArray[i] = i;
+ }
+ Assert.assertEquals(1.0, correlation.correlation(xArray, yArray), Double.MIN_VALUE);
+ }
+
+ @Test
+ public void testSimpleReversedPowerOf2() {
+ final int length = 16;
+ final double[] xArray = new double[length];
+ final double[] yArray = new double[length];
+ for (int i = 0; i < length; i++) {
+ xArray[length - i - 1] = i;
+ yArray[i] = i;
+ }
+ Assert.assertEquals(-1.0, correlation.correlation(xArray, yArray), Double.MIN_VALUE);
+ }
+
+ @Test
+ public void testSimpleJumble() {
+ // A B C D
+ final double[] xArray = new double[] {1.0, 2.0, 3.0, 4.0};
+ final double[] yArray = new double[] {1.0, 3.0, 2.0, 4.0};
+
+ // 6 pairs: (A,B) (A,C) (A,D) (B,C) (B,D) (C,D)
+ // (B,C) is discordant, the other 5 are concordant
+
+ Assert.assertEquals((5 - 1) / (double) 6,
+ correlation.correlation(xArray, yArray),
+ Double.MIN_VALUE);
+ }
+
+ @Test
+ public void testBalancedJumble() {
+ // A B C D
+ final double[] xArray = new double[] {1.0, 2.0, 3.0, 4.0};
+ final double[] yArray = new double[] {1.0, 4.0, 3.0, 2.0};
+
+ // 6 pairs: (A,B) (A,C) (A,D) (B,C) (B,D) (C,D)
+ // (A,B) (A,C), (A,D) are concordant, the other 3 are discordant
+
+ Assert.assertEquals(0.0,
+ correlation.correlation(xArray, yArray),
+ Double.MIN_VALUE);
+ }
+
+ @Test
+ public void testOrderedTies() {
+ final int length = 10;
+ final double[] xArray = new double[length];
+ final double[] yArray = new double[length];
+ for (int i = 0; i < length; i++) {
+ xArray[i] = i / 2;
+ yArray[i] = i / 2;
+ }
+ // 5 pairs of points that are tied in both values.
+ // 16 + 12 + 8 + 4 = 40 concordant
+ // (40 - 0) / Math.sqrt((45 - 5) * (45 - 5)) = 1
+ Assert.assertEquals(1.0, correlation.correlation(xArray, yArray), Double.MIN_VALUE);
+ }
+
+
+ @Test
+ public void testAllTiesInBoth() {
+ final int length = 10;
+ final double[] xArray = new double[length];
+ final double[] yArray = new double[length];
+ Assert.assertEquals(Double.NaN, correlation.correlation(xArray, yArray), 0);
+ }
+
+ @Test
+ public void testAllTiesInX() {
+ final int length = 10;
+ final double[] xArray = new double[length];
+ final double[] yArray = new double[length];
+ for (int i = 0; i < length; i++) {
+ xArray[i] = i;
+ }
+ Assert.assertEquals(Double.NaN, correlation.correlation(xArray, yArray), 0);
+ }
+
+ @Test
+ public void testAllTiesInY() {
+ final int length = 10;
+ final double[] xArray = new double[length];
+ final double[] yArray = new double[length];
+ for (int i = 0; i < length; i++) {
+ yArray[i] = i;
+ }
+ Assert.assertEquals(Double.NaN, correlation.correlation(xArray, yArray), 0);
+ }
+
+ @Test
+ public void testSingleElement() {
+ final int length = 1;
+ final double[] xArray = new double[length];
+ final double[] yArray = new double[length];
+ Assert.assertEquals(Double.NaN, correlation.correlation(xArray, yArray), 0);
+ }
+
+ @Test
+ public void testTwoElements() {
+ final double[] xArray = new double[] {2.0, 1.0};
+ final double[] yArray = new double[] {1.0, 2.0};
+ Assert.assertEquals(-1.0, correlation.correlation(xArray, yArray), Double.MIN_VALUE);
+ }
+
+ @Test
+ public void test2dDoubleArray() {
+ final double[][] input = new double[][] {
+ new double[] {2.0, 1.0, 2.0},
+ new double[] {1.0, 2.0, 1.0},
+ new double[] {0.0, 0.0, 0.0}
+ };
+
+ final double[][] expected = new double[][] {
+ new double[] {1.0, 1.0 / 3.0, 1.0},
+ new double[] {1.0 / 3.0, 1.0, 1.0 / 3.0},
+ new double[] {1.0, 1.0 / 3.0, 1.0}};
+
+ Assert.assertEquals(correlation.computeCorrelationMatrix(input),
+ new BlockRealMatrix(expected));
+
+ }
+
+ @Test
+ public void testBlockMatrix() {
+ final double[][] input = new double[][] {
+ new double[] {2.0, 1.0, 2.0},
+ new double[] {1.0, 2.0, 1.0},
+ new double[] {0.0, 0.0, 0.0}
+ };
+
+ final double[][] expected = new double[][] {
+ new double[] {1.0, 1.0 / 3.0, 1.0},
+ new double[] {1.0 / 3.0, 1.0, 1.0 / 3.0},
+ new double[] {1.0, 1.0 / 3.0, 1.0}};
+
+ Assert.assertEquals(
+ correlation.computeCorrelationMatrix(new BlockRealMatrix(input)),
+ new BlockRealMatrix(expected));
+ }
+
+}
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