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package de.lmu.ifi.dbs.elki.math;
/*
This file is part of ELKI:
Environment for Developing KDD-Applications Supported by Index-Structures
Copyright (C) 2015
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/>.
*/
/**
* Class to incrementally compute pearson correlation.
*
* In fact, this actually computes Var(X), Var(Y) and Cov(X, Y), all of which
* can be obtained from this class. If you need more than two variables, use
* {@link de.lmu.ifi.dbs.elki.math.linearalgebra.CovarianceMatrix} which uses
* slightly more memory (by using arrays) but essentially does the same.
*
* @author Erich Schubert
*/
public class PearsonCorrelation {
/**
* Aggregation for squared residuals - we are not using sum-of-squares!
*/
private double sumXX = 0., sumYY = 0., sumXY = 0.;
/**
* Current mean for X and Y.
*/
private double meanX = 0., meanY = 0.;
/**
* Weight sum.
*/
private double sumWe = 0.;
/**
* Constructor.
*/
public PearsonCorrelation() {
super();
}
/**
* Put a single value into the correlation statistic.
*
* @param x Value in X
* @param y Value in Y
* @param w Weight
*/
public void put(double x, double y, double w) {
if(sumWe <= 0.) {
meanX = x;
meanY = y;
sumWe = w;
return;
}
// Incremental update
sumWe += w;
// Delta to previous mean
final double deltaX = x - meanX;
final double deltaY = y - meanY;
// Update means
meanX += deltaX * w / sumWe;
meanY += deltaY * w / sumWe;
// Delta to new mean
final double neltaX = x - meanX;
final double neltaY = y - meanY;
// Update
sumXX += w * deltaX * neltaX;
sumYY += w * deltaY * neltaY;
// should equal weight * deltaY * neltaX!
sumXY += w * deltaX * neltaY;
}
/**
* Put a single value into the correlation statistic.
*
* @param x Value in X
* @param y Value in Y
*/
public void put(double x, double y) {
put(x, y, 1.);
}
/**
* Get the Pearson correlation value.
*
* @return Correlation value
*/
public double getCorrelation() {
if(!(sumXX > 0. && sumYY > 0.)) {
return (sumXX == sumYY) ? 1. : 0.;
}
return sumXY / Math.sqrt(sumXX * sumYY);
}
/**
* Get the number of points the average is based on.
*
* @return number of data points
*/
public double getCount() {
return sumWe;
}
/**
* Return mean of X
*
* @return mean
*/
public double getMeanX() {
return meanX;
}
/**
* Return mean of Y
*
* @return mean
*/
public double getMeanY() {
return meanY;
}
/**
* Get the covariance of X and Y (not taking sampling into account)
*
* @return Covariance
*/
public double getNaiveCovariance() {
return sumXY / sumWe;
}
/**
* Get the covariance of X and Y (with sampling correction)
*
* @return Covariance
*/
public double getSampleCovariance() {
assert (sumWe > 1.);
return sumXY / (sumWe - 1.);
}
/**
* Return the naive variance (not taking sampling into account)
*
* Note: usually, you should be using {@link #getSampleVarianceX} instead!
*
* @return variance
*/
public double getNaiveVarianceX() {
return sumXX / sumWe;
}
/**
* Return sample variance.
*
* @return sample variance
*/
public double getSampleVarianceX() {
assert (sumWe > 1.);
return sumXX / (sumWe - 1.);
}
/**
* Return standard deviation using the non-sample variance
*
* Note: usually, you should be using {@link #getSampleStddevX} instead!
*
* @return standard deviation
*/
public double getNaiveStddevX() {
return Math.sqrt(getNaiveVarianceX());
}
/**
* Return standard deviation
*
* @return standard deviation
*/
public double getSampleStddevX() {
return Math.sqrt(getSampleVarianceX());
}
/**
* Return the naive variance (not taking sampling into account)
*
* Note: usually, you should be using {@link #getSampleVarianceY} instead!
*
* @return variance
*/
public double getNaiveVarianceY() {
return sumYY / sumWe;
}
/**
* Return sample variance.
*
* @return sample variance
*/
public double getSampleVarianceY() {
assert (sumWe > 1.);
return sumYY / (sumWe - 1.);
}
/**
* Return standard deviation using the non-sample variance
*
* Note: usually, you should be using {@link #getSampleStddevY} instead!
*
* @return stddev
*/
public double getNaiveStddevY() {
return Math.sqrt(getNaiveVarianceY());
}
/**
* Return standard deviation
*
* @return stddev
*/
public double getSampleStddevY() {
return Math.sqrt(getSampleVarianceY());
}
/**
* Reset the value.
*/
public void reset() {
sumXX = 0.;
sumXY = 0.;
sumYY = 0.;
meanX = 0.;
meanY = 0.;
sumWe = 0.;
}
}
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