Computing the nonnegative 3-way tensor factorization using Tikhonov regularization

Jean-Philip Royer (1) , Pierre Comon (1) , Nadège Thirion-Moreau (2)

1 Laboratoire d'Informatique, Signaux, et Systèmes de Sophia-Antipolis (I3S) / Equipe SIGNAL
2 LSEET - Laboratoire de sondages électromagnétiques de l'environnement terrestre

This paper deals with the minimum polyadic decomposition of a nonnegative three-way array. The main advantage of the nonnegativity constraint is that the approximation problem becomes well posed. To tackle this problem, we suggest the use of a cost function including penalty terms built with matrix exponentials. Gradient components are then derived, allowing to efficiently implement the decomposition using classical optimization algorithms. In our case, Alternating Least Squares (ALS) and conjugate gradient algorithms are studied and compared with another existing algorithm, thanks to computer simulations performed in the context of data analysis.

Mots clés: Data analysis; data mining; non linear conjugate gradient; nonnegative 3-way array; Canonical Polyadic decomposition; Tikhonov regularization

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

Jean-Philip Royer, Pierre Comon, Nadège Thirion-Moreau. Computing the nonnegative 3-way tensor factorization using Tikhonov regularization. ICASSP, May 2011, Prague, Czech Republic. pp.2732-2735. ⟨hal-00641065⟩