Some issues in computing the CP decomposition of NonNegative Tensors

Mohamad Jouni (1) , Mauro Dalla Mura (1) , Pierre Comon (2)

1 GIPSA-SIGMAPHY - GIPSA - Signal Images Physique
2 GIPSA-CICS - GIPSA - Communication Information and Complex Systems

Tensor decompositions are still in the process of study and development. In this paper, we point out a problem existing in nonnega-tive tensor decompositions, stemming from the representation of decom-posable tensors by outer products of vectors, and propose approaches to solve it. In fact, a scaling indeterminacy appears whereas it is not inherent in the decomposition, and the choice of scaling factors has an impact during the execution of iterative algorithms and should not be overlooked. Computer experiments support the interest in the greedy algorithm proposed, in the case of the CP decomposition.

Domaines: Traitement du signal et de l'image [eess.SP]; Apprentissage [cs.LG]

Mohamad Jouni, Mauro Dalla Mura, Pierre Comon. Some issues in computing the CP decomposition of NonNegative Tensors. LVA/ICA 2018 - 14th International Conference on Latent Variable Analysis and Signal Separation, Jul 2018, Guildford, United Kingdom. pp.57-66, ⟨10.1007/978-3-319-93764-9_6⟩. ⟨hal-01784370v2⟩