Multiplicative updates from Lee et al. (2001) for
standard Nonnegative Matrix Factorization models
\approx W H, where the distance between the target
matrix and its NMF estimate is measured by the --
euclidean -- Frobenius norm.
nmf_update.euclidean.h_R implement the same
updates in plain R.
nmf_update.euclidean.h(v, w, h, eps = 10^-9, nbterms = 0L, ncterms = 0L, copy = TRUE) nmf_update.euclidean.h_R(v, w, h, wh = NULL, eps = 10^-9) nmf_update.euclidean.w(v, w, h, eps = 10^-9, nbterms = 0L, ncterms = 0L, weight = NULL, copy = TRUE) nmf_update.euclidean.w_R(v, w, h, wh = NULL, eps = 10^-9)
FALSE) or on a copy (
TRUE- default). With
copy=FALSEthe memory footprint is very small, and some speed-up may be achieved in the case of big matrices. However, greater care should be taken due the side effect. We recommend that only experienced users use
a matrix of the same dimension as the input matrix to
the returned matrix uses the same memory as the input
nmf_update.euclidean.h compute the updated basis
and coefficient matrices respectively. They use a
C++ implementation which is optimised for speed
and memory usage.
The coefficient matrix (
H) is updated as follows:
H_kj <- max(H_kj (W^T V)_kj, eps) / ( (W^T W H)_kj + eps )
The basis matrix (
W) is updated as follows:W_ik <- max(W_ik (V H^T)_ik, eps) / ( (W H H^T)_ik + eps )
Lee DD and Seung H (2001). "Algorithms for non-negative
matrix factorization." _Advances in neural information