cca_graph_rrr: Graph-regularized Reduced-Rank Regression for Canonical...

In ccar3: Canonical Correlation Analysis via Reduced Rank Regression

Graph-regularized Reduced-Rank Regression for Canonical Correlation Analysis

Description

Solves a sparse canonical correlation problem using a graph-constrained reduced-rank regression formulation. The problem is solved via an ADMM approach.

Usage

cca_graph_rrr(
  X,
  Y,
  Gamma,
  Sx = NULL,
  Sy = NULL,
  Sxy = NULL,
  lambda = 0,
  r,
  standardize = FALSE,
  LW_Sy = TRUE,
  rho = 10,
  niter = 10000,
  thresh = 1e-04,
  thresh_0 = 1e-06,
  verbose = FALSE,
  Gamma_dagger = NULL
)

Arguments

X	Matrix of predictors (n x p)
Y	Matrix of responses (n x q)
Gamma	Graph constraint matrix (g x p)
Sx	Optional covariance matrix for X. If NULL, computed as t(X) %*% X / n
Sy	Optional covariance matrix for Y. If NULL, computed similarly; optionally shrunk via Ledoit-Wolf
Sxy	Optional cross-covariance matrix (not currently used)
lambda	Regularization parameter for sparsity
r	Target rank
standardize	Whether to center and scale X and Y (default FALSE = center only)
LW_Sy	Whether to apply Ledoit-Wolf shrinkage to Sy
rho	ADMM penalty parameter
niter	Maximum number of ADMM iterations
thresh	Convergence threshold for ADMM
thresh_0	Threshold for small values in the coefficient matrix (default 1e-6)
verbose	Whether to print diagnostic output
Gamma_dagger	Optional pseudoinverse of Gamma (computed if NULL)

Value

A list with elements:

U

Canonical direction matrix for X (p x r)

V

Canonical direction matrix for Y (q x r)

cor

Canonical covariances

loss

The prediction error 1/n * \| XU - YV\|^2

ccar3 documentation built on Sept. 16, 2025, 9:11 a.m.