Non-negative Matrix Factorization using posrank-based approximation decompositions

Authors

Abstract

The present work addresses a particular issue related to the nonnegative factorisation of a matrix (NMF). When NMF is formulated as a nonlinear programming optimisation problem some algebraic properties concerning the dimensionality of the factorisation arise as especially important for the numerical resolution. Its importance comes in the form of a guarantee to obtain good quality approximations to the solutions of signal processing image problems. The focus of this work lies in the importance of the rank of the factor matrices, especially in the so-called posrank of the factorisation. We report computational tests that favor the conclusion that the value of the posrank has an important impact on the quality of the images recovered from the decomposition.

Keywords

image restoration, non negative matrix decomposition, non linear programming, feature extraction

Subject

Non negative Matrix Factorization, Feature extraction, Non linear programmimg, Optimisation

Conference

EUROCON 2015 - International Conference on Computer as a Tool (EUROCON), IEEE, September 2015

DOI