A new stochastic optimization algorithm to decompose large nonnegative tensors

Xuan Thanh Vu † (1, 2) , Sylvain Maire (3, 1) , Caroline Chaux (2) , Nadège Thirion-Moreau (4, 5, 6)

1 LSIS - Laboratoire des Sciences de l'Information et des Systèmes
2 I2M - Institut de Mathématiques de Marseille
3 TOSCA - TO Simulate and CAlibrate stochastic models
4 LIS - Laboratoire d'Informatique et des Systèmes (LIS) (Marseille, Toulon)
5 SIIM - Signal et Image
6 UTLN SeaTech - Université de Toulon - École d’ingénieurs SeaTech

In this letter, the problem of nonnegative tensor decompositions is addressed. Classically, this problem is carried out using iterative (either alternating or global) deterministic optimization algorithms. Here, a rather different stochastic approach is suggested. In addition, the ever-increasing volume of data requires the development of new and more efficient approaches to be able to process " Big data " tensors to extract relevant information. The stochastic algorithm outlined here comes within this framework. Both flexible and easy to implement, it is designed to solve the problem of the CP (Candecomp/Parafac) decomposition of huge nonnegative 3-way tensors while simultaneously enabling to handle possible missing data.

Mots clés: Candecomp/Parafac (CP) decomposi- tion; multi-linear algebra; Nonnegative Tensor Factorization (NTF); stochastic optimization; missing data; Big data/tensors

Domaines: Traitement du signal et de l'image [eess.SP]

Xuan Thanh Vu †, Sylvain Maire, Caroline Chaux, Nadège Thirion-Moreau. A new stochastic optimization algorithm to decompose large nonnegative tensors. IEEE Signal Processing Letters, 2015, 12 pp. ⟨hal-01146443⟩