Existence of the best low-rank tensor approximate - CICS Accéder directement au contenu
Communication Dans Un Congrès Année : 2013

Existence of the best low-rank tensor approximate

Résumé

The so-called Canonical Polyadic (CP) tensor decomposition, sometimes referred to as Parafac, is now widely utilized in Chemometrics, and in particular in the analysis of Fluorescence Emission Excitation Matrices (FEEM), if a set of several such matrices is available. Four messages are put forward: (i) the parameterization is important, and should fix the scaling indeterminacy; (ii) Kruskal's lemma guarantees uniqueness of a rank-R decomposition, but is not adequate for nonnegative tensors, nor for low-rank approximations; (iii) the best low-rank approximate does not always exist, but it does if the nonnegativity constraint is imposed; (iv) hence it is mandatory to use numerical algorithms imposing the nonnegativity constraint, otherwise spurious components may appear.
Fichier non déposé

Dates et versions

hal-00985656 , version 1 (30-04-2014)

Identifiants

  • HAL Id : hal-00985656 , version 1

Citer

Pierre Comon. Existence of the best low-rank tensor approximate. WOMS 2013 - International Workshop on Organic Matter Spectroscopy (WOMS'2013), Jul 2013, Toulon, France. ⟨hal-00985656⟩
152 Consultations
0 Téléchargements

Partager

Gmail Facebook X LinkedIn More