Nonnegative Tensor Factorization using a proximal algorithm, application to 3D fluorescence spectroscopy

This is a Joint work with Xuan Vu, Nadège Thirion-Moreau and Sylvain Maire (LSIS, Toulon). We address the problem of third order nonnegative tensor factorization with penalization. More precisely, the Canonical Polyadic Decomposition (CPD) is considered. It constitutes a compact and informative model consisting of decomposing a tensor into a minimal sum of rank-one terms. This multi-linear decomposition has been widely studied in the litterature. Coupled with 3D fluorescence spectroscopy analysis, it has found numerous interesting applications in chemistry, chemometrics, data analysis for the environment, monitoring and so on. The resulting inverse problem at hand is often hard to solve especially when the tensor rank is unknown and when data corrupted by noise and large dimensions are considered. We adopted a variational approach and the factorization problem is thus formulated under a penalized minimization problem. Indeed, a new penalized nonnegative third order CPD algorithm has been derived based on a block coordinate variable metric forward-backward method. The proposed iterative algorithm have been successfully applied not only to synthetic data (showing its efficiency, robustness and flexibility) but also on real 3D fluorescence spectroscopy data.