Non-negative Tensor Approximations

Yang Qi (1) , Pierre Comon (1)

1 GIPSA-lab - Grenoble Images Parole Signal Automatique

Necessary conditions are derived for a rank-r tensor to be a best rank-r approximation of a given tensor. It is shown that a positive tensor with rank > 1 has a unique rank one approximation, and that a non negative tensor generally has a unique low-rank nonnegative approximate. We discuss the notion of r-singular values and their corresponding r-singular vector tuples, which is closely related to best rank-r approximations. We then show that a generic tensor has a finite number of r-singular vector tuples for some r.

Mots clés: tensor; approximation; nonnegative; singular vector

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

Yang Qi, Pierre Comon. Non-negative Tensor Approximations. 2014. ⟨hal-01015519v2⟩