Study of different strategies for the Canonical Polyadic decomposition of nonnegative third order tensors with application to the separation of spectra in 3D fluorescence spectroscopy

Abstract

In this communication, the problem of blind source separation in chemical analysis and more precisely in the fluorescence spectroscopy framework is addressed. Classically multi-linear Canonical Polyadic (CP or Candecomp/Parafac) decomposition algorithms are used to perform that task. Yet, as the constituent vectors of the loading matrices should be nonnegative since they stand for nonnegative quantities (spectra and concentrations), we focus on NonNegative CP decomposition algorithms (NNCP). In the unconstrained case, two types of trilinear (or triadic) decomposition model have been studied. Here, our aim is to investigate different strategies concerning the choice of models and optimization schemes in the case of a nonnegativity constraint. Computer simulations are performed on synthetic data to illustrate the robustness of the proposed approaches versus overfactoring problems but also the critical importance of the use of regularization terms.