Decorrelation projection — decorrelate • decorrelate

Efficient decorrelation projection using eclairs decomposition

Usage

decorrelate(X, ecl, lambda, transpose = FALSE, alpha = -1/2)

Arguments

X: matrix to be transformed so *columns* are independent
ecl: estimate of covariance/correlation matrix from eclairs storing \(U\), \(d_1^2\), \(\lambda\) and \(\nu\)
lambda: specify lambda and override value from ecl
transpose: logical, (default FALSE) indicating if X should be transposed first
alpha: default = -1/2. Exponent of eigen-values

Value

a matrix following the decorrelation transformation

Details

Apply a decorrelation transform using the implicit covariance approach to avoid directly evaluating the covariance matrix

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)

# whitened Y
Y.transform <- decorrelate(Y, ecl)
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