mahalanobis {stats} | R Documentation |
Returns the squared 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, ...)
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. |
... |
passed to solve for computing the inverse of
the covariance matrix (if inverted is false). |
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=.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')