mahalanobisDistance: Mahalanobis Distance

In decorrelate: Decorrelation Projection Scalable to High Dimensional Data

Mahalanobis Distance

Description

Mahalanobis Distance using eclairs() decomposition

Usage

mahalanobisDistance(ecl, X, lambda, center = FALSE)

Arguments

ecl	estimate of covariance/correlation matrix from eclairs storing U, d_1^2, \lambda and \nu
X	data matrix
lambda	specify lambda and override value from ‘ecl’
center	logical: should columns be centered internally

Details

Evaluate quadratic form (X-\mu)^T \Sigma^{-1} (X-\mu) where covariance is estimated from finite sample

Value

array of distances

Examples

library(Rfast)

n <- 800 # number of samples
p <- 200 # number of features

# create correlation matrix
Sigma <- autocorr.mat(p, .9)

# draw data from correlation matrix Sigma
Y <- rmvnorm(n, rep(0, p), sigma = Sigma * 5.1, seed = 1)

# eclairs decomposition
ecl <- eclairs(Y)

# Mahalanobis distance after mean centering
Y_center <- scale(Y, scale = FALSE)
mu <- colMeans(Y)

# Standard R method
a <- mahalanobis(Y, mu, cov = cov(Y))

# distance using eclairs decomposition, no shrinage
b <- mahalanobisDistance(ecl, Y_center, lambda = 0)
range(a - b)

# with shrinkage
d <- mahalanobisDistance(ecl, Y_center)

# centering internally
e <- mahalanobisDistance(ecl, Y, center = TRUE)
range(d - e)
#

decorrelate documentation built on Aug. 8, 2025, 7:55 p.m.