rpls: Regularised / Generalised Partial Least Squares (RPLS / GPLS)

In genpca: Generalized Principal Component Analysis

Regularised / Generalised Partial Least Squares (RPLS / GPLS)

Description

Implements the algorithm of Allen et al. (2013) for supervised dimension-reduction with optional sparsity (\ell_1) or ridge (\ell_2) penalties and the generalised extension that operates in a user-supplied quadratic form Q.

Usage

rpls(
  X,
  Y,
  K = 2,
  lambda = 0.1,
  penalty = c("l1", "ridge"),
  Q = NULL,
  nonneg = FALSE,
  preproc_x = multivarious::pass(),
  preproc_y = multivarious::pass(),
  tol = 1e-06,
  maxiter = 200,
  verbose = FALSE,
  ...
)

Arguments

X	Numeric matrix (n \times p) — predictors.
Y	Numeric matrix (n \times q) — responses.
K	Integer, number of latent factors to extract. Default 2.
lambda	Scalar or length-K numeric vector of penalties.
penalty	Either "l1" (lasso) or "ridge".
Q	Optional positive-(semi)definite p \times p matrix inducing generalised PLS. NULL means identity.
nonneg	Logical, force non-negative loadings when penalty = "l1". Note: This option is currently ignored when penalty = "ridge".
preproc_x, preproc_y	Optional multivarious preprocessing objects (see fit_transform). By default they pass the data through unchanged using pass().
tol	Relative tolerance for the inner iterations convergence check. Default 1e-6.
maxiter	Maximum number of inner iterations per component. Default 200.
verbose	Logical; print progress messages during component extraction. Default FALSE.
...	Further arguments (e.g., custom stopping criteria if implemented) are stored in the returned object (they are not used by fit_rpls).

Details

Unlike genpls(), which handles separate row and column metrics (Mx, Ax, My, Ay) with a Gram–Schmidt orthogonalisation step, rpls() uses a single metric Q and the simpler penalised updates of Allen et al.

Value

An object of class c("rpls","cross_projector","projector") with at least the elements

vx

p \times K matrix of X-loadings.

vy

q \times K matrix of Y-loadings.

ncomp

Number of components actually extracted (may be < K).

penalty

Penalty type used ("l1" or "ridge").

lambda

The lambda value(s) used.

tol

The convergence tolerance used.

maxiter

The maximum number of inner iterations used per component.

nonneg

Logical flag for the non-negativity constraint on l1.

Q_used

Logical; TRUE if a custom Q metric was supplied to induce generalised RPLS, FALSE for standard (identity-metric) RPLS. Note the field is named Q_used, not Q: the metric matrix itself is not retained on the returned object.

verbose

The verbose flag used.

preproc_x, preproc_y

Pre-processing transforms used.

rpls objects store no row (X-)scores: the factors z_k are computed internally during fitting to drive deflation and are then discarded, so use multivarious::project() on X to obtain scores for any rows of interest.

The object supports predict(), project(), transfer(), coef() and other multivarious generics.

Method

The routine follows Algorithm 1 of Allen et al. (2013, Stat. Anal. Data Min., 6 : 302–314) — see the paper for details. Briefly, with C = X^\top Y the cross-product of the (preprocessed) blocks, each component maximises

\max_{u,v}\; v^\top Q C u - \lambda \, P(v)

with Q = I_p for standard RPLS. The alternating updates are: u \leftarrow C^\top Q v / \|C^\top Q v\|_2, then a penalised (possibly non-negative) regression for v, normalised in the Q-norm.

References

Allen, G. I., Peterson, C., Vannucci, M., & Maletić-Savatić, M. (2013). Regularized Partial Least Squares with an Application to NMR Spectroscopy. Statistical Analysis and Data Mining, 6(4), 302-314. DOI:10.1002/sam.11169.

Examples

# Generate sample data
set.seed(123)
n <- 50
p <- 20
q <- 10
X <- matrix(rnorm(n * p), n, p)
Y <- X[, 1:5] %*% matrix(rnorm(5 * q), 5, q) + matrix(rnorm(n * q), n, q)

# Fit regularized PLS with L1 penalty
fit_l1 <- rpls(X, Y, K = 3, lambda = 0.1, penalty = "l1")
print(fit_l1)

# Fit regularized PLS with ridge penalty
fit_ridge <- rpls(X, Y, K = 3, lambda = 0.1, penalty = "ridge")
print(fit_ridge)

genpca documentation built on Sept. 17, 2026, 1:09 a.m.