Element-wise Cross-Validation for nmfae (Wold's CV)

nmfae.ecv performs k-fold element-wise cross-validation by randomly holding out individual elements of \(Y_1\), assigning them a weight of 0 via Y1.weights, and evaluating the reconstruction error on those held-out elements.

This method (also known as Wold's CV) is suitable for determining the optimal rank pair \((Q, R)\) in three-layer NMF. Both rank1 and rank2 accept vector inputs. When rank2 = NULL (default), rank2 is set equal to rank1 and pairs are evaluated element-wise (i.e., \((Q_1, R_1), (Q_2, R_2), \dots\)). When rank.encoder is explicitly specified, all combinations of rank and rank.encoder are evaluated via expand.grid.

Usage

nmf.rrr.ecv(Y1, Y2 = Y1, rank1 = 1:2, rank2 = NULL, ...)

Arguments

Y1

Output matrix \(Y_1\) (P1 x N).

Y2

Input matrix \(Y_2\) (P2 x N). Default is Y1.

rank1

Integer vector of response-basis ranks to evaluate. Default is 1:2.

rank2

Integer vector of covariate-basis ranks to evaluate. Default is NULL, which sets rank2 = rank1 and evaluates element-wise pairs.

...

Additional arguments passed to nmf.rrr (e.g., epsilon, maxit). Also accepts: nfolds (number of folds, default 5; div also accepted), seed (integer seed, default 123), and cores (evaluate the \((Q,R)\)-pair \(\times\) fold grid in parallel; default getOption("mc.cores", 1L), PSOCK on Windows / forking elsewhere). Each task is an independent self-seeded fit and results are aggregated in order, so the returned object is identical for any cores. For backward compatibility, Q and R are accepted as aliases for rank and rank.encoder.

Rank aliases accepted here for backward compatibility: Q for rank1, R for rank2.

Value

A list with components:

objfunc: Named numeric vector of mean MSE for each (Q, R) pair.
sigma: Named numeric vector of RMSE (square root of MSE) for each pair.
objfunc.fold: Named list of per-fold MSE vectors for each pair.
folds: List of length div containing the held-out element indices for each fold.
QR: Data frame with columns Q and R listing the evaluated pairs.

Lifecycle

This function is experimental. The interface may change in future versions; details are to be described in an upcoming paper.

Examples

Y <- t(iris[1:30, 1:4])
# Default: rank2=NULL -> paired rank1=rank2
res <- nmf.rrr.ecv(Y, rank1 = 1:2, nfolds = 3, maxit = 200)
#> Element-wise CV: 2 (Q,R) pairs, 3-fold, 6 tasks...
#>   Q=1, R=1: MSE=0.021319, sigma=0.1460
#>   Q=2, R=2: MSE=0.021287, sigma=0.1459
res$sigma
#>   Q=1,R=1   Q=2,R=2 
#> 0.1460097 0.1459009 
# Explicit rank2: full grid (kept small so the example stays under CRAN's
# 10s budget -- a real sweep would use wider ranges and a larger maxit)
res2 <- nmf.rrr.ecv(Y, rank1 = 1:2, rank2 = 1:2, nfolds = 3, maxit = 200)
#> Element-wise CV: 4 (Q,R) pairs, 3-fold, 12 tasks...
#>   Q=1, R=1: MSE=0.021319, sigma=0.1460
#>   Q=2, R=1: MSE=0.021319, sigma=0.1460
#>   Q=1, R=2: MSE=0.021321, sigma=0.1460
#>   Q=2, R=2: MSE=0.021287, sigma=0.1459
res2$sigma
#>   Q=1,R=1   Q=2,R=1   Q=1,R=2   Q=2,R=2 
#> 0.1460097 0.1460097 0.1460179 0.1459009