nmfkc.signed.rff: Random Fourier Features for nmfkc.signed()

In nmfkc: Non-Negative Matrix Factorization with Kernel Covariates

Random Fourier Features for nmfkc.signed()

Description

Generates RFF random parameters \omega_d \sim \mathcal{N}(0, 2\beta I_p), b_d \sim \mathrm{Uniform}(0, 2\pi) (Rahimi & Recht, 2007) and applies the RFF transform

z_d(u) = \sqrt{2/D}\, \cos(\omega_d^\top u + b_d)

to each column of U, yielding a sign-unrestricted D \times N feature matrix Z such that Z^\top Z \approx K, the Gaussian kernel matrix with bandwidth beta.

The return value is a list with the feature matrix Z and the generating parameters pars = list(omega, b, D, beta) so that the same random map can be re-applied to new data (by passing pars back) and nmfkc.signed can record the parameters for downstream summary.

Usage

nmfkc.signed.rff(U, beta = NULL, D = ceiling(ncol(U)/2), seed = NULL, ...)

Arguments

U	A p \times N numeric matrix; columns are data points.
beta	Positive scalar. Gaussian kernel bandwidth parameter. Can be obtained via nmfkc.kernel.beta.nearest.med. May be NULL only when pars is supplied through ....
D	Integer. Number of random features. Defaults to ceiling(ncol(U) / 2). This default is intended for the training-time fresh generation only; for test data, always supply pars via ... to inherit the training D together with \omega, b. For very large N the default may be excessive (direct MU cost is O(QD^2)); choose a smaller D manually. For very small N, RFF is not recommended; use a full kernel matrix with nmfkc instead.
seed	Optional integer passed to set.seed() before generating \omega, b, for reproducibility. Ignored when pars is supplied.
...	Hidden option pars: a list list(omega, b, D, beta) obtained from a previous call (Ztrain$pars). When supplied, \omega, b are reused and the beta, D, seed arguments are ignored. Use this to apply the same random map to test data.

Value

A list with two elements:

Z

A D \times N sign-unrestricted numeric matrix. Pass this to nmfkc.signed as its A argument.

pars

A list list(omega, b, D, beta). Pass this to nmfkc.signed via its pars argument (for summary display) and to subsequent nmfkc.signed.rff() calls (to reuse the same random map on new data).

Lifecycle

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

See Also

nmfkc.signed, nmfkc.kernel.beta.nearest.med

Examples

## Iris 3-class classification with RFF + direct MU (Ding-Li-Jordan)
data(iris)
set.seed(1)
idx <- sample(nrow(iris), 100)    # 100 training, 50 test

## Scale features using TRAINING mean/sd; transpose to p x N layout
mn      <- colMeans(iris[idx, 1:4])
sc      <- apply(iris[idx, 1:4], 2, sd)
U.train <- t(scale(iris[idx,  1:4], center = mn, scale = sc))   # 4 x 100
U.test  <- t(scale(iris[-idx, 1:4], center = mn, scale = sc))   # 4 x  50

## One-hot encode training labels as a Q_obs x N target matrix
levs      <- levels(iris$Species)
Y.train   <- sapply(iris$Species[idx], function(s) as.integer(levs == s))
rownames(Y.train) <- levs                                       # 3 x 100
lab.train <- iris$Species[idx]
lab.test  <- iris$Species[-idx]

## Beta candidates from nearest-neighbour median heuristic
beta_info <- nmfkc.kernel.beta.nearest.med(U.train)
betas     <- beta_info$beta_candidates

## CV over beta candidates: for each beta, generate RFF, fit, and
## evaluate column-wise CV-MSE on training data
cv_mse <- numeric(length(betas))
for (i in seq_along(betas)) {
  rff_i   <- nmfkc.signed.rff(U.train, beta = betas[i], D = 50, seed = 1)
  cv_i    <- nmfkc.signed.cv(Y.train, A = rff_i$Z, rank = 3, seed = 123)
  cv_mse[i] <- cv_i$objfunc
}
beta_best <- betas[which.min(cv_mse)]

## Generate signed RFF features with the best beta
rff.train <- nmfkc.signed.rff(U.train, beta = beta_best, D = 50, seed = 1)
rff.test  <- nmfkc.signed.rff(U.test, pars = rff.train$pars)

## Fit on training data only
res <- nmfkc.signed(Y.train, A = rff.train$Z, rank = 3,
                    pars = rff.train$pars, verbose = FALSE)

## Predict on training and test separately
pred.train <- predict(res, newA = rff.train$Z, type = "class")
pred.test  <- predict(res, newA = rff.test$Z,  type = "class")
mean(pred.train == as.character(lab.train))
mean(pred.test  == as.character(lab.test))

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