SPA: Successive projection algorithm for separable NMF

In swanjin/gillis.nmf: Nonnegetive Matrix Factorization

Description

At each step of the algorithm, the column of R maximizing ||.||_2 is extracted, and R is updated by projecting its columns onto the orthogonal complement of the extracted column. The residual R is initializd with X.

See N. Gillis and S.A. Vavasis, Fast and Robust Recursive Algorithms for Separable Nonnegative Matrix Factorization, IEEE Trans. on Pattern Analysis and Machine Intelligence 36 (4), pp. 698-714, 2014.

Usage

spa(X, r, options = list())

Arguments

X	an m-by-n matrix. Ideally admitting a near-separable factorization, that is, X = WH + N, where conv([W, 0]) has r vertices, H = [I,H']P where I is the identity matrix, H'>= 0 and its columns sum to at most one, P is a permutation matrix, and N is sufficiently small.
r	number of columns to be extracted.
options	list of string if options contain "normalize" := 1, will scale the columns of X so that they sum to one, hence matrix H will satisfy the assumption above for any nonnegative separable matrix X. "normalize" := 0, is the default value for which no scaling is performed. For example, in hyperspectral imaging, this assumption is already satisfied and normalization is not necessary. "precision" : stops the algorithm when max_k ||R(:,k)||_2 <= relerror * max_k ||X(:,k)||_2 where R is the residual, that is, R = X-X(:,K)H. default: 1e-6

Value

K index set of the extracted columns.

Examples

spa(matrix(1:16,4),2,c('normalize'))

swanjin/gillis.nmf documentation built on Dec. 23, 2021, 6:44 a.m.