R: Mahalanobis Distance

mahalanobis {base}

R Documentation

Mahalanobis Distance

Description

Returns the Mahalanobis distance of all rows in x and the vector \mu=center with respect to \Sigma=cov. This is (for vector x) defined as

D^2 = (x - \mu)' \Sigma^{-1} (x - \mu)

Usage

mahalanobis(x, center, cov, inverted=FALSE)

Arguments

x

vector or matrix of data with, say, p columns.

center

mean vector of the distribution or second data vector of length p.

cov

covariance matrix (p \times p) of the distribution.

inverted

logical. If TRUE, cov is supposed to contain the inverse of the covariance matrix.

Author(s)

Friedrich Leisch

Examples

ma <- cbind(1:6, 1:3)
(S <-  var(ma))
mahalanobis(c(0,0), 1:2, S)

x <- matrix(rnorm(100*3), ncol=3)
all(mahalanobis(x, 0, diag(ncol(x)))
    == apply(x*x, 1,sum)) ##- Here, D^2 = usual Euclidean distances
Sx <- cov(x)
D2 <- mahalanobis(x, apply(x,2,mean), Sx)
plot(density(D2, bw=.5), main="Mahalanobis distances, n=100, p=3"); rug(D2)
qqplot(qchisq(ppoints(100), df=3), D2,
	main = expression("Q-Q plot of Mahalanobis" * ~D^2 *
			" vs. quantiles of" * ~ chi[3]^2))
abline(0,1,col='gray')