nmfkc.cv: Perform k-fold cross-validation for NMF with kernel...

In nmfkc: Non-Negative Matrix Factorization with Kernel Covariates

Perform k-fold cross-validation for NMF with kernel covariates

Description

nmfkc.cv performs k-fold cross-validation for the tri-factorization model Y \approx X C A = X B, where

• Y(P,N) is the observation matrix,

• A(R,N) is the covariate (or kernel) matrix,

• X(P,Q) is the basis matrix,

• C(Q,R) is the parameter matrix, and

• B(Q,N) is the coefficient matrix (B = C A).

Given Y (and optionally A), X and C are fitted on each training split and predictive performance is evaluated on the held-out split.

Usage

nmfkc.cv(Y, A = NULL, rank = 2, data, ...)

Arguments

Y	Observation matrix, or a formula (see nmfkc for Formula Mode).
A	Covariate matrix. If NULL, the identity matrix is used. Ignored when Y is a formula.
rank	Rank of the basis matrix X. Default is 2.
data	A data frame (required when Y is a formula with column names).
...	Additional arguments controlling CV and the internal nmfkc call: Y.weights Non-negative weight matrix or vector (lm()-style: loss \sum W \, r^2). Binary {0,1} masks (TRUE / FALSE also accepted) are the typical ECV usage – 0/FALSE excludes an element. See nmfkc for full details. div Number of folds (k); default: 5. seed Integer seed for reproducible partitioning; default: 123. shuffle Logical. If TRUE (default), randomly shuffles samples (standard CV); if FALSE, splits sequentially (block CV; recommended for time series). Q (Deprecated) Alias for rank. Arguments passed to nmfkc e.g., C.L1, epsilon, maxit, method ("EU" or "KL"), X.restriction, X.init, etc.

Value

A list with components:

objfunc

Mean loss per valid entry over all folds (MSE for method="EU").

sigma

Residual standard error (RMSE). Available only if method="EU"; on the same scale as Y.

objfunc.block

Loss for each fold.

block

Vector of fold indices (1, …, div) assigned to each column of Y.

See Also

nmfkc, nmfkc.kernel.beta.cv, nmfkc.ar.degree.cv

Examples

# Example 1 (with explicit covariates):
Y <- matrix(cars$dist, nrow = 1)
A <- rbind(1, cars$speed)
res <- nmfkc.cv(Y, A, rank = 1)
res$objfunc

# Example 2 (kernel A and beta sweep):
Y <- matrix(cars$dist, nrow = 1)
U <- matrix(c(5, 10, 15, 20, 25), nrow = 1)
V <- matrix(cars$speed, nrow = 1)
betas <- 25:35/1000
obj <- numeric(length(betas))
for (i in seq_along(betas)) {
  A <- nmfkc.kernel(U, V, beta = betas[i])
  obj[i] <- nmfkc.cv(Y, A, rank = 1, nfolds = 10)$objfunc
}
betas[which.min(obj)]

nmfkc documentation built on July 14, 2026, 1:07 a.m.