Split gradient method for nonnegative matrix factorization

Author

Lanieri, Henri ; Theys, Celine ; Richard, Cedric ; Fevotte, Cedric

Author_Institution

Lab. Fizeau, Univ. de Nice Sophia-Antipolis, Nice, France

fYear

2010

fDate

23-27 Aug. 2010

Firstpage

1199

Lastpage

1203

Abstract

This article deals with an extension of the split gradient method (SGM) applied to the optimization of any divergence between two data fields, under positivity and flux conservation constraints. SGM is guaranteed to converge for convex cost functions. A SGM-based algorithm is also derived to solve the nonnegative matrix factorization (NMF) problem. It is shown that the multiplicative algorithms that are usually used for NMF, under positivity constraints, are particular cases of SGM. Finally, to validate the algorithm, we propose an example of application to hyperspectral data unmixing.

Keywords

gradient methods; hyperspectral imaging; image processing; matrix decomposition; optimisation; NMF problem; convex cost functions; data fields; flux conservation constraints; hyperspectral data unmixing; multiplicative algorithms; nonnegative matrix factorization; positivity conservation constraints; positivity constraints; split gradient method; Convergence; Gradient methods; Hyperspectral imaging; Image reconstruction; Maximum likelihood detection; Minimization; Signal processing algorithms;

fLanguage

English

Publisher

ieee

Conference_Titel

Signal Processing Conference, 2010 18th European

Conference_Location

Aalborg

ISSN

2219-5491

Type

conf

Filename

7096669