normdiff {gaussDiff}

Difference measures for multivariate Gaussian pdfs

Description

Various difference measures for Gaussian pdfs are implemented: Euclidean distance of the means, Mahalanobis distance, Kullback-Leibler divergence, J-Coefficient, Minkowski L2-distance, Chi-square divergence and the Hellinger coefficient which is a similarity measure.

Usage

normdiff(mu1,sigma1=NULL,mu2,sigma2=sigma1,inv=FALSE,s=0.5,
method=c("Mahalanobis","KL","J","Chisq",
"Hellinger","L2","Euclidean"))

Arguments

mu1

mean value of pdf 1, a vector

sigma1

covariance matrix of pdf 1

mu2

mean value of pdf 2, a vector

sigma2

covariance matrix of pdf 2

method

difference measure to be used, see below

inv

if TRUE, 1-Hellinger is reported, default: inv=FALSE

s

exponent for Hellinger coefficient, default: s=0.5

Details

Equations can be found in H.-H. Bock, Analysis of Symbolic Data, Chapter Dissimilarity Measures for Probability Distributions

Value

A scalar object of class normdiff reporting the distance.

Author(s)

Henning Rust, [e-mail]

References

H.-H. Bock, Analysis of Symbolic Data, Chapter Dissimilarity measures for Probabilistic Distributions

Examples

library(gaussDiff)
mu1 <- c(0,0,0)
sig1 <- diag(c(1,1,1))
mu2 <- c(1,1,1)
sig2 <- diag(c(0.5,0.5,0.5))

## Euclidean distance
normdiff(mu1=mu1,mu2=mu2,method="Euclidean")

## Mahalanobis distance
normdiff(mu1=mu1,sigma1=sig1,mu2=mu2,method="Mahalanobis")

## Kullback-Leibler divergence
normdiff(mu1=mu1,sigma1=sig1,mu2=mu2,sigma2=sig2,method="KL")

## J-Coefficient
normdiff(mu1=mu1,sigma1=sig1,mu2=mu2,sigma2=sig2,method="J")

## Chi-sqr divergence
normdiff(mu1=mu1,sigma1=sig1,mu2=mu2,sigma2=sig2,method="Chisq")

## Minkowsi L2 distance
normdiff(mu1=mu1,sigma1=sig1,mu2=mu2,sigma2=sig2,method="L2")

## Hellinger coefficient
normdiff(mu1=mu1,sigma1=sig1,mu2=mu2,sigma2=sig2,method="Hellinger")