MAHI 2013 workshop: Methodological Aspects of Hyperspectral Imaging

Abstract

Regularized Multiplicative Algorithms for Nonnegative Matrix Factorization
Christine De Mol, Université Libre de Bruxelles, (BE)

We consider iterative algorithms for nonnegative matrix factorizations which consist in alternating multiplicative update rules. In a variational framework, we use least-squares and Kullback-Leibler fidelity terms as well as different regularizing penalties. The algorithms are derived via the use of surrogate cost functions and of a majorization-minimization approach. This ensures a monotonic decrease of the cost function and allows us to prove convergence of the iterates to a stationary point. We also report results of some numerical simulations. This is joint work with Loic Lecharlier.