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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) 2014
+ 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 java.util.List;
+
+import de.lmu.ifi.dbs.elki.utilities.datastructures.arraylike.NumberArrayAdapter;
+import de.lmu.ifi.dbs.elki.utilities.documentation.Reference;
+import de.lmu.ifi.dbs.elki.utilities.optionhandling.AbstractParameterizer;
+
+/**
+ * Distance correlation.
+ *
+ * The value returned is the square root of the dCor² value. This matches the R
+ * implementation by the original authors.
+ *
+ * Reference:
+ * <p>
+ * Székely, G. J., Rizzo, M. L., & Bakirov, N. K.<br />
+ * Measuring and testing dependence by correlation of distances<br />
+ * The Annals of Statistics, 35(6), 2769-2794
+ * </p>
+ *
+ * Implementation notice: we exploit symmetry, and thus use diagonal matrixes.
+ * While initially the diagonal is zero, after double-centering the matrix these
+ * values can become non-zero!
+ *
+ * @author Marie Kiermeier
+ * @author Erich Schubert
+ */
+@Reference(authors = "Székely, G. J., Rizzo, M. L., & Bakirov, N. K.", //
+title = "Measuring and testing dependence by correlation of distances", //
+booktitle = "The Annals of Statistics, 35(6), 2769-2794", //
+url = "http://dx.doi.org/10.1214/009053607000000505")
+public class DistanceCorrelationDependenceMeasure extends AbstractDependenceMeasure {
+ /**
+ * Static instance.
+ */
+ public static final DistanceCorrelationDependenceMeasure STATIC = new DistanceCorrelationDependenceMeasure();
+
+ /**
+ * Constructor - use {@link #STATIC} instance instead!
+ */
+ protected DistanceCorrelationDependenceMeasure() {
+ super();
+ }
+
+ @Override
+ public <A, B> double dependence(NumberArrayAdapter<?, A> adapter1, A data1, NumberArrayAdapter<?, B> adapter2, B data2) {
+ final int len = size(adapter1, data1, adapter2, data2);
+ double[] dMatrixA = computeDistances(adapter1, data1);
+ double[] dMatrixB = computeDistances(adapter2, data2);
+
+ // distance variance
+ double dVarA = computeDCovar(dMatrixA, dMatrixA, len);
+ if(!(dVarA > 0.)) {
+ return 0.;
+ }
+ double dVarB = computeDCovar(dMatrixB, dMatrixB, len);
+ if(!(dVarB > 0.)) {
+ return 0.;
+ }
+ double dCovar = computeDCovar(dMatrixA, dMatrixB, len);
+ // distance correlation
+ return Math.sqrt(dCovar / Math.sqrt(dVarA * dVarB));
+ }
+
+ @Override
+ public <A> double[] dependence(NumberArrayAdapter<?, A> adapter, List<? extends A> data) {
+ final int dims = data.size();
+ final int len = size(adapter, data);
+ double[][] dMatrix = new double[dims][];
+ for(int i = 0; i < dims; i++) {
+ dMatrix[i] = computeDistances(adapter, data.get(i));
+ }
+ double[] dVar = new double[dims];
+ for(int i = 0; i < dims; i++) {
+ dVar[i] = computeDCovar(dMatrix[i], dMatrix[i], len);
+ }
+ double[] dCor = new double[(dims * (dims - 1)) >> 1];
+ for(int y = 1, c = 0; y < dims; y++) {
+ for(int x = 0; x < y; x++) {
+ if(!(dVar[x] * dVar[y] > 0.)) {
+ dCor[c++] = 0.;
+ continue;
+ }
+ double dCovar = computeDCovar(dMatrix[x], dMatrix[y], len);
+ dCor[c++] = Math.sqrt(dCovar / Math.sqrt(dVar[x] * dVar[y]));
+ }
+ }
+ return dCor;
+ }
+
+ /**
+ * Compute the double-centered delta matrix.
+ *
+ * @param adapter Data adapter
+ * @param data Input data
+ * @return Double-centered delta matrix.
+ */
+ protected static <A> double[] computeDistances(NumberArrayAdapter<?, A> adapter, A data) {
+ final int size = adapter.size(data);
+ double[] dMatrix = new double[(size * (size + 1)) >> 1];
+ for(int i = 0, c = 0; i < size; i++) {
+ for(int j = 0; j < i; j++) {
+ double dx = adapter.getDouble(data, i) - adapter.getDouble(data, j);
+ dMatrix[c++] = (dx < 0) ? -dx : dx; // Absolute difference.
+ }
+ c++; // Diagonal entry: zero
+ }
+ doubleCenterMatrix(dMatrix, size);
+ return dMatrix;
+ }
+
+ /**
+ * Computes the distance variance matrix of one axis.
+ *
+ * @param dMatrix distance matrix of the axis
+ * @param size Dimensionality
+ */
+ public static void doubleCenterMatrix(double[] dMatrix, int size) {
+ double[] rowMean = new double[size];
+ // row sum
+ for(int i = 0, c = 0; i < size; i++) {
+ for(int j = 0; j < i; j++) {
+ double v = dMatrix[c++];
+ rowMean[i] += v;
+ rowMean[j] += v;
+ }
+ assert (dMatrix[c] == 0.);
+ c++; // Diagonal entry. Must be zero!
+ }
+ // Normalize averages:
+ double matrixMean = 0.;
+ for(int i = 0; i < size; i++) {
+ matrixMean += rowMean[i];
+ rowMean[i] /= size;
+ }
+ matrixMean /= size * size;
+
+ for(int o = 0, c = 0; o < size; o++) {
+ // Including row mean!
+ for(int p = 0; p <= o; p++) {
+ dMatrix[c++] -= rowMean[o] + rowMean[p] - matrixMean;
+ }
+ }
+ }
+
+ /**
+ * Computes the distance covariance for two axis. Can also be used to compute
+ * the distance variance of one axis (dVarMatrixA = dVarMatrixB).
+ *
+ * @param dVarMatrixA distance variance matrix of the first axis
+ * @param dVarMatrixB distance variance matrix of the second axis
+ * @param n number of points
+ * @return distance covariance
+ */
+ protected double computeDCovar(double[] dVarMatrixA, double[] dVarMatrixB, int n) {
+ double result = 0.;
+ for(int i = 0, c = 0; i < n; i++) {
+ for(int j = 0; j < i; j++) {
+ result += 2. * dVarMatrixA[c] * dVarMatrixB[c];
+ c++;
+ }
+ // Diagonal entry.
+ result += dVarMatrixA[c] * dVarMatrixB[c];
+ c++;
+ }
+ return result / (n * n);
+ }
+
+ /**
+ * Parameterization class
+ *
+ * @author Marie Kiermeier
+ *
+ * @apiviz.exclude
+ */
+ public static class Parameterizer extends AbstractParameterizer {
+ @Override
+ protected DistanceCorrelationDependenceMeasure makeInstance() {
+ return STATIC;
+ }
+ }
+}