Performance Index for Tensor Polyadic Decompositions

Pierre Comon (1) , Khalid Minaoui (2) , Awatif Rouijel (2) , Driss Aboutajdine (3)

1 GIPSA-CICS - GIPSA - Communication Information and Complex Systems
2 LRIT - Laboratoire de Recherche Informatique et Télécommunications
3 GSCM-LRIT - Laboratoire de Recherche en Informatique et Télécommunications [Rabat]

It is proposed to isolate the computation of the scaling matrix in CP tensor decompositions. This has two implications. First, the conditioning of the problem shows up explicitly, and could be controlled via a constraint on the so-called coherences. Second, a performance measure concerning only the factor matrices can be exactly calculated, and does not present the optimistic bias of the minimal error generally utilized in the literature. In fact, for tensors of order $d$, it suffices to solve a degree-2 polynomial system in $d$ variables. We subsequently give an explicit solution when d=3.

Mots clés: Blind; Source separation; Data mining; Identification; Array; Tensor; CP; Canonical polyadic; Candecomp; Parafac; Performance; Coherence

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

Pierre Comon, Khalid Minaoui, Awatif Rouijel, Driss Aboutajdine. Performance Index for Tensor Polyadic Decompositions. EUSIPCO 2013 - 21th European Signal Processing Conference, Sep 2013, Marrakech, Morocco. 5 p. ⟨hal-00842864⟩