/*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 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 General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
*/
/*
* MahalanobisEstimator.java
* Copyright (C) 1999 Len Trigg
*
*/
package weka.estimators;
import java.util.*;
import weka.core.*;
/**
* Simple probability estimator that places a single normal distribution
* over the observed values.
*
* @author Len Trigg (trigg@cs.waikato.ac.nz)
* @version $Revision: 1.1.1.1 $
*/
public class MahalanobisEstimator implements Estimator {
/** The inverse of the covariance matrix */
private Matrix m_CovarianceInverse;
/** The determinant of the covariance matrix */
private double m_Determinant;
/**
* The difference between the conditioning value and the conditioning mean
*/
private double m_ConstDelta;
/** The mean of the values */
private double m_ValueMean;
/** 2 * PI */
private static double TWO_PI = 2 * Math.PI;
/**
* Returns value for normal kernel
*
* @param x the argument to the kernel function
* @param variance the variance
* @return the value for a normal kernel
*/
private double normalKernel(double x) {
Matrix thisPoint = new Matrix(1, 2);
thisPoint.setElement(0, 0, x);
thisPoint.setElement(0, 1, m_ConstDelta);
return Math.exp(-thisPoint.multiply(m_CovarianceInverse).
multiply(thisPoint.transpose()).getElement(0, 0)
/ 2) / (Math.sqrt(TWO_PI) * m_Determinant);
}
/**
* Constructor
*
* @param the number of possible symbols
*/
public MahalanobisEstimator(Matrix covariance, double constDelta,
double valueMean) {
m_CovarianceInverse = null;
if ((covariance.numRows() == 2) && (covariance.numColumns() == 2)) {
double a = covariance.getElement(0, 0);
double b = covariance.getElement(0, 1);
double c = covariance.getElement(1, 0);
double d = covariance.getElement(1, 1);
if (a == 0) {
a = c; c = 0;
double temp = b;
b = d; d = temp;
}
if (a == 0) {
return;
}
double denom = d - c * b / a;
if (denom == 0) {
return;
}
m_Determinant = covariance.getElement(0, 0) * covariance.getElement(1, 1)
- covariance.getElement(1, 0) * covariance.getElement(0, 1);
m_CovarianceInverse = new Matrix(2, 2);
m_CovarianceInverse.setElement(0, 0, 1.0 / a + b * c / a / a / denom);
m_CovarianceInverse.setElement(0, 1, -b / a / denom);
m_CovarianceInverse.setElement(1, 0, -c / a / denom);
m_CovarianceInverse.setElement(1, 1, 1.0 / denom);
m_ConstDelta = constDelta;
m_ValueMean = valueMean;
}
}
/**
* Add a new data value to the current estimator. Does nothing because the
* data is provided in the constructor.
*
* @param data the new data value
* @param weight the weight assigned to the data value
*/
public void addValue(double data, double weight) {
}
/**
* Get a probability estimate for a value
*
* @param data the value to estimate the probability of
* @return the estimated probability of the supplied value
*/
public double getProbability(double data) {
double delta = data - m_ValueMean;
if (m_CovarianceInverse == null) {
return 0;
}
return normalKernel(delta);
}
/** Display a representation of this estimator */
public String toString() {
if (m_CovarianceInverse == null) {
return "No covariance inverse\n";
}
return "Mahalanovis Distribution. Mean = "
+ Utils.doubleToString(m_ValueMean, 4, 2)
+ " ConditionalOffset = "
+ Utils.doubleToString(m_ConstDelta, 4, 2) + "\n"
+ "Covariance Matrix: Determinant = " + m_Determinant
+ " Inverse:\n" + m_CovarianceInverse;
}
/**
* Main method for testing this class.
*
* @param argv should contain a sequence of numeric values
*/
public static void main(String [] argv) {
try {
double delta = 0.5;
double xmean = 0;
double lower = 0;
double upper = 10;
Matrix covariance = new Matrix(2, 2);
covariance.setElement(0, 0, 2);
covariance.setElement(0, 1, -3);
covariance.setElement(1, 0, -4);
covariance.setElement(1, 1, 5);
if (argv.length > 0) {
covariance.setElement(0, 0, Double.valueOf(argv[0]).doubleValue());
}
if (argv.length > 1) {
covariance.setElement(0, 1, Double.valueOf(argv[1]).doubleValue());
}
if (argv.length > 2) {
covariance.setElement(1, 0, Double.valueOf(argv[2]).doubleValue());
}
if (argv.length > 3) {
covariance.setElement(1, 1, Double.valueOf(argv[3]).doubleValue());
}
if (argv.length > 4) {
delta = Double.valueOf(argv[4]).doubleValue();
}
if (argv.length > 5) {
xmean = Double.valueOf(argv[5]).doubleValue();
}
MahalanobisEstimator newEst = new MahalanobisEstimator(covariance,
delta, xmean);
if (argv.length > 6) {
lower = Double.valueOf(argv[6]).doubleValue();
if (argv.length > 7) {
upper = Double.valueOf(argv[7]).doubleValue();
}
double increment = (upper - lower) / 50;
for(double current = lower; current <= upper; current+= increment)
System.out.println(current + " " + newEst.getProbability(current));
} else {
System.out.println("Covariance Matrix\n" + covariance);
System.out.println(newEst);
}
} catch (Exception e) {
System.out.println(e.getMessage());
}
}
}