PearsonsCorrelation.java

  1. /*
  2.  * Licensed to the Apache Software Foundation (ASF) 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 ASF licenses this file to You under the Apache License, Version 2.0
  6.  * (the "License"); you may not use this file except in compliance with
  7.  * 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.  */

  18. /*
  19.  * This is not the original file distributed by the Apache Software Foundation
  20.  * It has been modified by the Hipparchus project
  21.  */
  22. package org.hipparchus.stat.correlation;

  24. import org.hipparchus.distribution.continuous.TDistribution;
  25. import org.hipparchus.exception.LocalizedCoreFormats;
  26. import org.hipparchus.exception.MathIllegalArgumentException;
  27. import org.hipparchus.linear.BlockRealMatrix;
  28. import org.hipparchus.linear.RealMatrix;
  29. import org.hipparchus.stat.LocalizedStatFormats;
  30. import org.hipparchus.stat.regression.SimpleRegression;
  31. import org.hipparchus.util.FastMath;
  32. import org.hipparchus.util.MathArrays;
  33. import org.hipparchus.util.MathUtils;

  35. /**
  36.  * Computes Pearson's product-moment correlation coefficients for pairs of arrays
  37.  * or columns of a matrix.
  38.  * <p>
  39.  * The constructors that take <code>RealMatrix</code> or
  40.  * <code>double[][]</code> arguments generate correlation matrices.  The
  41.  * columns of the input matrices are assumed to represent variable values.
  42.  * Correlations are given by the formula:
  43.  * <p>
  44.  * <code>cor(X, Y) = &Sigma;[(x<sub>i</sub> - E(X))(y<sub>i</sub> - E(Y))] / [(n - 1)s(X)s(Y)]</code>
  45.  * <p>
  46.  * where <code>E(X)</code> is the mean of <code>X</code>, <code>E(Y)</code>
  47.  * is the mean of the <code>Y</code> values and s(X), s(Y) are standard deviations.
  48.  * <p>
  49.  * To compute the correlation coefficient for a single pair of arrays, use {@link #PearsonsCorrelation()}
  50.  * to construct an instance with no data and then {@link #correlation(double[], double[])}.
  51.  * Correlation matrices can also be computed directly from an instance with no data using
  52.  * {@link #computeCorrelationMatrix(double[][])}. In order to use {@link #getCorrelationMatrix()},
  53.  * {@link #getCorrelationPValues()},  or {@link #getCorrelationStandardErrors()}; however, one of the
  54.  * constructors supplying data or a covariance matrix must be used to create the instance.
  55.  */
  56. public class PearsonsCorrelation {

  58.     /** correlation matrix */
  59.     private final RealMatrix correlationMatrix;

  61.     /** number of observations */
  62.     private final int nObs;

  64.     /**
  65.      * Create a PearsonsCorrelation instance without data.
  66.      */
  67.     public PearsonsCorrelation() {
  68.         super();
  69.         correlationMatrix = null;
  70.         nObs = 0;
  71.     }

  73.     /**
  74.      * Create a PearsonsCorrelation from a rectangular array
  75.      * whose columns represent values of variables to be correlated.
  76.      *
  77.      * Throws MathIllegalArgumentException if the input array does not have at least
  78.      * two columns and two rows.  Pairwise correlations are set to NaN if one
  79.      * of the correlates has zero variance.
  80.      *
  81.      * @param data rectangular array with columns representing variables
  82.      * @throws MathIllegalArgumentException if the input data array is not
  83.      * rectangular with at least two rows and two columns.
  84.      * @see #correlation(double[], double[])
  85.      */
  86.     public PearsonsCorrelation(double[][] data) {
  87.         this(new BlockRealMatrix(data));
  88.     }

  90.     /**
  91.      * Create a PearsonsCorrelation from a RealMatrix whose columns
  92.      * represent variables to be correlated.
  93.      *
  94.      * Throws MathIllegalArgumentException if the matrix does not have at least
  95.      * two columns and two rows.  Pairwise correlations are set to NaN if one
  96.      * of the correlates has zero variance.
  97.      *
  98.      * @param matrix matrix with columns representing variables to correlate
  99.      * @throws MathIllegalArgumentException if the matrix does not contain sufficient data
  100.      * @see #correlation(double[], double[])
  101.      */
  102.     public PearsonsCorrelation(RealMatrix matrix) {
  103.         nObs = matrix.getRowDimension();
  104.         correlationMatrix = computeCorrelationMatrix(matrix);
  105.     }

  107.     /**
  108.      * Create a PearsonsCorrelation from a {@link Covariance}.  The correlation
  109.      * matrix is computed by scaling the Covariance's covariance matrix.
  110.      * The Covariance instance must have been created from a data matrix with
  111.      * columns representing variable values.
  112.      *
  113.      * @param covariance Covariance instance
  114.      */
  115.     public PearsonsCorrelation(Covariance covariance) {
  116.         RealMatrix covarianceMatrix = covariance.getCovarianceMatrix();
  117.         MathUtils.checkNotNull(covarianceMatrix, LocalizedStatFormats.COVARIANCE_MATRIX);
  118.         nObs = covariance.getN();
  119.         correlationMatrix = covarianceToCorrelation(covarianceMatrix);
  120.     }

  122.     /**
  123.      * Create a PearsonsCorrelation from a covariance matrix. The correlation
  124.      * matrix is computed by scaling the covariance matrix.
  125.      *
  126.      * @param covarianceMatrix covariance matrix
  127.      * @param numberOfObservations the number of observations in the dataset used to compute
  128.      * the covariance matrix
  129.      */
  130.     public PearsonsCorrelation(RealMatrix covarianceMatrix, int numberOfObservations) {
  131.         nObs = numberOfObservations;
  132.         correlationMatrix = covarianceToCorrelation(covarianceMatrix);
  133.     }

  135.     /**
  136.      * Returns the correlation matrix.
  137.      *
  138.      * <p>This method will return null if the argumentless constructor was used
  139.      * to create this instance, even if {@link #computeCorrelationMatrix(double[][])}
  140.      * has been called before it is activated.</p>
  141.      *
  142.      * @return correlation matrix
  143.      */
  144.     public RealMatrix getCorrelationMatrix() {
  145.         return correlationMatrix;
  146.     }

  148.     /**
  149.      * Returns a matrix of standard errors associated with the estimates
  150.      * in the correlation matrix.<br>
  151.      * <code>getCorrelationStandardErrors().getEntry(i,j)</code> is the standard
  152.      * error associated with <code>getCorrelationMatrix.getEntry(i,j)</code>
  153.      *
  154.      * <p>The formula used to compute the standard error is <br>
  155.      * <code>SE<sub>r</sub> = ((1 - r<sup>2</sup>) / (n - 2))<sup>1/2</sup></code>
  156.      * where <code>r</code> is the estimated correlation coefficient and
  157.      * <code>n</code> is the number of observations in the source dataset.</p>
  158.      *
  159.      * <p>To use this method, one of the constructors that supply an input
  160.      * matrix must have been used to create this instance.</p>
  161.      *
  162.      * @return matrix of correlation standard errors
  163.      * @throws NullPointerException if this instance was created with no data
  164.      */
  165.     public RealMatrix getCorrelationStandardErrors() {
  166.         int nVars = correlationMatrix.getColumnDimension();
  167.         double[][] out = new double[nVars][nVars];
  168.         for (int i = 0; i < nVars; i++) {
  169.             for (int j = 0; j < nVars; j++) {
  170.                 double r = correlationMatrix.getEntry(i, j);
  171.                 out[i][j] = FastMath.sqrt((1 - r * r) /(nObs - 2));
  172.             }
  173.         }
  174.         return new BlockRealMatrix(out);
  175.     }

  177.     /**
  178.      * Returns a matrix of p-values associated with the (two-sided) null
  179.      * hypothesis that the corresponding correlation coefficient is zero.
  180.      *
  181.      * <p><code>getCorrelationPValues().getEntry(i,j)</code> is the probability
  182.      * that a random variable distributed as <code>t<sub>n-2</sub></code> takes
  183.      * a value with absolute value greater than or equal to <br>
  184.      * <code>|r|((n - 2) / (1 - r<sup>2</sup>))<sup>1/2</sup></code></p>
  185.      *
  186.      * <p>The values in the matrix are sometimes referred to as the
  187.      * <i>significance</i> of the corresponding correlation coefficients.</p>
  188.      *
  189.      * <p>To use this method, one of the constructors that supply an input
  190.      * matrix must have been used to create this instance.</p>
  191.      *
  192.      * @return matrix of p-values
  193.      * @throws org.hipparchus.exception.MathIllegalStateException
  194.      * if an error occurs estimating probabilities
  195.      * @throws NullPointerException if this instance was created with no data
  196.      */
  197.     public RealMatrix getCorrelationPValues() {
  198.         TDistribution tDistribution = new TDistribution(nObs - 2);
  199.         int nVars = correlationMatrix.getColumnDimension();
  200.         double[][] out = new double[nVars][nVars];
  201.         for (int i = 0; i < nVars; i++) {
  202.             for (int j = 0; j < nVars; j++) {
  203.                 if (i == j) {
  204.                     out[i][j] = 0d;
  205.                 } else {
  206.                     double r = correlationMatrix.getEntry(i, j);
  207.                     double t = FastMath.abs(r * FastMath.sqrt((nObs - 2)/(1 - r * r)));
  208.                     out[i][j] = 2 * tDistribution.cumulativeProbability(-t);
  209.                 }
  210.             }
  211.         }
  212.         return new BlockRealMatrix(out);
  213.     }


  216.     /**
  217.      * Computes the correlation matrix for the columns of the
  218.      * input matrix, using {@link #correlation(double[], double[])}.
  219.      *
  220.      * Throws MathIllegalArgumentException if the matrix does not have at least
  221.      * two columns and two rows.  Pairwise correlations are set to NaN if one
  222.      * of the correlates has zero variance.
  223.      *
  224.      * @param matrix matrix with columns representing variables to correlate
  225.      * @return correlation matrix
  226.      * @throws MathIllegalArgumentException if the matrix does not contain sufficient data
  227.      * @see #correlation(double[], double[])
  228.      */
  229.     public RealMatrix computeCorrelationMatrix(RealMatrix matrix) {
  230.         checkSufficientData(matrix);
  231.         int nVars = matrix.getColumnDimension();
  232.         RealMatrix outMatrix = new BlockRealMatrix(nVars, nVars);
  233.         for (int i = 0; i < nVars; i++) {
  234.             for (int j = 0; j < i; j++) {
  235.               double corr = correlation(matrix.getColumn(i), matrix.getColumn(j));
  236.               outMatrix.setEntry(i, j, corr);
  237.               outMatrix.setEntry(j, i, corr);
  238.             }
  239.             outMatrix.setEntry(i, i, 1d);
  240.         }
  241.         return outMatrix;
  242.     }

  244.     /**
  245.      * Computes the correlation matrix for the columns of the
  246.      * input rectangular array.  The columns of the array represent values
  247.      * of variables to be correlated.
  248.      *
  249.      * Throws MathIllegalArgumentException if the matrix does not have at least
  250.      * two columns and two rows or if the array is not rectangular. Pairwise
  251.      * correlations are set to NaN if one of the correlates has zero variance.
  252.      *
  253.      * @param data matrix with columns representing variables to correlate
  254.      * @return correlation matrix
  255.      * @throws MathIllegalArgumentException if the array does not contain sufficient data
  256.      * @see #correlation(double[], double[])
  257.      */
  258.     public RealMatrix computeCorrelationMatrix(double[][] data) {
  259.        return computeCorrelationMatrix(new BlockRealMatrix(data));
  260.     }

  262.     /**
  263.      * Computes the Pearson's product-moment correlation coefficient between two arrays.
  264.      *
  265.      * <p>Throws MathIllegalArgumentException if the arrays do not have the same length
  266.      * or their common length is less than 2.  Returns {@code NaN} if either of the arrays
  267.      * has zero variance (i.e., if one of the arrays does not contain at least two distinct
  268.      * values).</p>
  269.      *
  270.      * @param xArray first data array
  271.      * @param yArray second data array
  272.      * @return Returns Pearson's correlation coefficient for the two arrays
  273.      * @throws MathIllegalArgumentException if the arrays lengths do not match
  274.      * @throws MathIllegalArgumentException if there is insufficient data
  275.      */
  276.     public double correlation(final double[] xArray, final double[] yArray) {
  277.         MathArrays.checkEqualLength(xArray, yArray);
  278.         if (xArray.length < 2) {
  279.             throw new MathIllegalArgumentException(LocalizedCoreFormats.INSUFFICIENT_DIMENSION,
  280.                                                    xArray.length, 2);
  281.         }

  283.         SimpleRegression regression = new SimpleRegression();
  284.         for(int i = 0; i < xArray.length; i++) {
  285.             regression.addData(xArray[i], yArray[i]);
  286.         }
  287.         return regression.getR();
  288.     }

  290.     /**
  291.      * Derives a correlation matrix from a covariance matrix.
  292.      *
  293.      * <p>Uses the formula <br>
  294.      * <code>r(X,Y) = cov(X,Y)/s(X)s(Y)</code> where
  295.      * <code>r(&middot;,&middot;)</code> is the correlation coefficient and
  296.      * <code>s(&middot;)</code> means standard deviation.</p>
  297.      *
  298.      * @param covarianceMatrix the covariance matrix
  299.      * @return correlation matrix
  300.      */
  301.     public RealMatrix covarianceToCorrelation(RealMatrix covarianceMatrix) {
  302.         int nVars = covarianceMatrix.getColumnDimension();
  303.         RealMatrix outMatrix = new BlockRealMatrix(nVars, nVars);
  304.         for (int i = 0; i < nVars; i++) {
  305.             double sigma = FastMath.sqrt(covarianceMatrix.getEntry(i, i));
  306.             outMatrix.setEntry(i, i, 1d);
  307.             for (int j = 0; j < i; j++) {
  308.                 double entry = covarianceMatrix.getEntry(i, j) /
  309.                        (sigma * FastMath.sqrt(covarianceMatrix.getEntry(j, j)));
  310.                 outMatrix.setEntry(i, j, entry);
  311.                 outMatrix.setEntry(j, i, entry);
  312.             }
  313.         }
  314.         return outMatrix;
  315.     }

  317.     /**
  318.      * Throws MathIllegalArgumentException if the matrix does not have at least
  319.      * two columns and two rows.
  320.      *
  321.      * @param matrix matrix to check for sufficiency
  322.      * @throws MathIllegalArgumentException if there is insufficient data
  323.      */
  324.     private void checkSufficientData(final RealMatrix matrix) {
  325.         int nRows = matrix.getRowDimension();
  326.         int nCols = matrix.getColumnDimension();
  327.         if (nRows < 2 || nCols < 2) {
  328.             throw new MathIllegalArgumentException(LocalizedCoreFormats.INSUFFICIENT_ROWS_AND_COLUMNS,
  329.                                                    nRows, nCols);
  330.         }
  331.     }
  332. }
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