mult_eclairs: Multiply by eclairs matrix

In decorrelate: Decorrelation Projection Scalable to High Dimensional Data

Multiply by eclairs matrix

Description

Multiply by eclairs matrix using special structure to achieve linear instead of cubic time complexity.

Usage

mult_eclairs(X, U1, dSq1, lambda, nu, alpha, sigma, transpose = FALSE)

Arguments

X	matrix to be transformed so *columns* are independent
U1	orthonormal matrix with k columns representing the low rank component
dSq1	eigen values so that U_1 diag(d_1^2) U_1^T is the low rank component
lambda	shrinkage parameter for the convex combination.
nu	diagonal value of target matrix in shrinkage
alpha	exponent to be evaluated
sigma	standard deviation of each feature
transpose	logical, (default FALSE) indicating if X should be transposed first

Details

Let \Sigma = U_1 diag(d_1^2) U_1^T * (1-\lambda) + diag(\nu\lambda, p), where \lambda shrinkage parameter for the convex combination between a low rank matrix and the diagonal matrix with values \nu.

Evaluate X \Sigma^\alpha using special structure of the eclairs decomposition in O(k^2p) when there are k components in the decomposition.

Value

a matrix product

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