bwproj: Bures-Wasserstein Projection
In maotai: Tools for Matrix Algebra, Optimization and Inference

bwproj

R Documentation

Bures-Wasserstein Projection

Description

Projects a set of high-dimensional Gaussian distributions specified by their means and covariance matrices onto a lower-dimensional subspace using the distance-preserving projection method.

Usage

bwproj(means, covs, target_dim = 2, max_iter = 100, verbose = TRUE)

Arguments

`means`	an `(n,p)` matrix of Gaussian means, where `n` is the number of Gaussians and `p` is the original dimension.
`covs`	a `(p,p,n)` array of Gaussian covariance matrices.
`target_dim`	an integer specifying the target lower dimension `d` (default is 2).
`max_iter`	an integer specifying the maximum number of iterations for the optimization (default is 100).
`verbose`	a logical flag indicating whether to print progress messages (default is TRUE).

Value

a named list containing

U: the (p,d) projection matrix mapping original space to the lower-dimensional space.
proj_means: the (n,d) matrix of projected Gaussian means.
proj_covs: the (d,d,n) array of projected Gaussian covariance matrices.
iter_obj: a vector of objective function values at each iteration.
iter_gnorm: a vector of gradient norms at each iteration.