mmd {robustmatrix}

Matrix Mahalanobis distance

Description

Matrix Mahalanobis distance

Usage

mmd(X, mu, cov_row, cov_col, inverted = FALSE)

Arguments

X

a 3d array of dimension (p,q,n), containing n matrix-variate samples of p rows and q columns in each slice.

mu

a p \times q matrix containing the means.

cov_row

a p \times p positive-definite symmetric matrix specifying the rowwise covariance matrix

cov_col

a q \times q positive-definite symmetric matrix specifying the columnwise covariance matrix

inverted

Logical. FALSE by default. If TRUE cov_row and cov_col are supposed to contain the inverted rowwise and columnwise covariance matrices, respectively.

Value

Squared Mahalanobis distance(s) of observation(s) in X.

Examples

n = 1000; p = 2; q = 3
mu = matrix(rep(0, p*q), nrow = p, ncol = q)
cov_row = matrix(c(1,0.5,0.5,1), nrow = p, ncol = p)
cov_col = matrix(c(3,2,1,2,3,2,1,2,3), nrow = q, ncol = q)
X <- rmatnorm(n = 1000, mu, cov_row, cov_col)
ind <- sample(1:n, 0.3*n)
X[,,ind] <- rmatnorm(n = length(ind), matrix(rep(10, p*q), nrow = p, ncol = q), cov_row, cov_col)
distances <- mmd(X, mu, cov_row, cov_col)
plot(distances)
abline(h = qchisq(0.99, p*q), lty = 2, col = "red")