| mahalanobis {stats} | R Documentation |
Returns the Mahalanobis distance of all rows in x and the
vector μ=center with respect to
Σ=cov.
This is (for vector x) defined as
D^2 = (x - μ)' Σ^{-1} (x - μ)
mahalanobis(x, center, cov, inverted=FALSE, tol.inv = 1e-7)
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. |
tol.inv |
tolerance to be used for computing the inverse (if
inverted is false), see solve. |
Friedrich Leisch
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 Euclidean distances
Sx <- cov(x)
D2 <- mahalanobis(x, rowMeans(x), 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')