mahalanobis(x, center, cov, inverted=FALSE)
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 x p) of the distribution. |
inverted
|
logical. If TRUE, cov is supposed to
contain the inverse of the covariance matrix.
|
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)
cov, var
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')