Fits principal components with sparse loading vectors for
interpretable dimension reduction. Variable projection combines an
orthogonal reconstruction factor with elastic net or cardinality
regularization of the loadings. Deterministic, randomized, and robust
algorithms support exploratory analysis of high-dimensional data;
the randomized algorithm also supports sparse input matrices through
implicit centering and scaling. A robust formulation separates
entrywise outliers from the low-rank reconstruction. Regularization
paths and approximate feature-count searches reuse matrix factorizations,
and prediction applies the fitted transformation to new observations.
The methods are described in
Erichson et al. (2020)