mahalanobis {stats} | R Documentation |
Returns the squared 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)
mahalanobis(x, center, cov, inverted = FALSE, ...)
x |
vector or matrix of data with, say, |
center |
mean vector of the distribution or second data vector of
length |
cov |
covariance matrix ( |
inverted |
logical. If |
... |
passed to |
require(graphics)
ma <- cbind(1:6, 1:3)
(S <- var(ma))
mahalanobis(c(0, 0), 1:2, S)
x <- matrix(rnorm(100*3), ncol = 3)
stopifnot(mahalanobis(x, 0, diag(ncol(x))) == rowSums(x*x))
##- Here, D^2 = usual squared Euclidean distances
Sx <- cov(x)
D2 <- mahalanobis(x, colMeans(x), Sx)
plot(density(D2, bw = 0.5),
main="Squared 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')