nmfkc.rff.positive.gram: Block-wise Gram accumulation of positive random features for...

In nmfkc: Non-Negative Matrix Factorization with Kernel Covariates

Block-wise Gram accumulation of positive random features for large N

Description

The nmfkc.rff.positive counterpart of nmfkc.signed.rff.gram: walks the columns of U in blocks, generates the non-negative feature block \Phi_b with the same random map, accumulates S = \Phi\Phi^\top (D \times D) and G_0 = Y\Phi^\top (P \times D), and discards the block, so the D \times N feature matrix never exists in memory. Because the features are non-negative, the returned "nmfkc.gram" object is accepted by nmfkc (as well as by nmfkc.signed), and the NMF-LAB membership interpretation of B = \Theta\Phi is retained.

Usage

nmfkc.rff.positive.gram(
  Y,
  U,
  beta = NULL,
  D = NULL,
  seed = NULL,
  block.size = NULL,
  ...
)

Arguments

Y	Non-negative P \times N response matrix (e.g. one-hot labels). NA is not allowed.
U	A p \times N numeric matrix of inputs; columns are samples.
beta	Positive scalar. Gaussian kernel bandwidth. Ignored when pars is supplied.
D	Integer. Number of random features. Required (no N/2 default here). Ignored when pars is supplied.
seed	Optional integer seed for \omega; the caller's stream is restored. Ignored when pars is supplied.
block.size	Integer. Columns of U per block. Default: about 256 MB of features per block (2^25 / D columns), capped at N.
...	Hidden options pars (reuse a random map from nmfkc.rff.positive or a previous call) and hyperbolic (see nmfkc.rff.positive).

Value

An object of class "nmfkc.gram" with S, G0, N, D, type = "prf", signed = FALSE, pars, beta, block.size, n.blocks, A.block (block generator) and rownames = NULL. Features for new data: nmfkc.rff.positive(U.new, pars = g$pars)$Z.

Lifecycle

This function is experimental. The interface may change in future versions.

References

Choromanski, K. et al. (2021). Rethinking attention with Performers. ICLR. arXiv:2009.14794.

See Also

nmfkc.rff.positive, nmfkc, nmfkc.kernel.gram (Nystr\"om), nmfkc.signed.rff.gram

Examples

data(iris)
set.seed(1)
idx <- sample(nrow(iris), 100)
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))
U.test  <- t(scale(iris[-idx, 1:4], center = mn, scale = sc))
levs    <- levels(iris$Species)
Y.train <- sapply(iris$Species[idx], function(s) as.integer(levs == s))
rownames(Y.train) <- levs
beta <- nmfkc.kernel.beta.nearest.med(U.train)$beta

g <- nmfkc.rff.positive.gram(Y.train, U.train, beta = beta, D = 200,
                             seed = 1, block.size = 25)
g
res <- nmfkc(Y.train, A = g, rank = 3, verbose = FALSE)   # standard NMF-LAB
Z.test <- nmfkc.rff.positive(U.test, pars = g$pars)$Z
pred   <- predict(res, newA = Z.test, type = "class")
mean(pred == as.character(iris$Species[-idx]))

nmfkc documentation built on Oct. 30, 2026, 9:06 a.m.