Partial Inverse Projection of a Subset of the Loading Matrix in cross_projector

This function obtains the "inverse" mapping for a columnwise subset of the loading matrix in the specified domain. In practice, if v_mat is not orthonormal or not square, we use a pseudoinverse approach (via MASS::ginv).

Usage

# S3 method for class 'cross_projector'
partial_inverse_projection(x, colind, domain = c("X", "Y"), ...)

Arguments

x

A cross_projector object.

colind

A numeric vector specifying the columns (indices) of the latent factors or loadings to invert. Typically these correspond to a subset of canonical components or principal components, etc.

domain

Either "X" or "Y", indicating which block's partial loadings we want to invert.

...

Additional arguments (unused by default, but may be used by subclasses).

Value

A matrix of shape (length(colind) x p_block) that, when multiplied by factor scores restricted to colind columns, yields an (n x p_block) reconstruction in the original domain block.

Details

By default, this is a minimal-norm solution for partial columns of v_mat. If you need a different approach (e.g., ridge, direct solve, etc.), you can override this method in your specific class or code.

Examples

# Suppose 'cp' is a cross_projector, and we want only columns 1:3 of
# the Y block factors. Then:
#   inv_mat_sub <- partial_inverse_projection(cp, colind=1:3, domain="Y")
# The shape will be (3 x pY), so factor_scores_sub (n x 3) %*% inv_mat_sub => (n x pY).