An uniqueness condition for the 4-way CANDECOMP/PARAFAC model with collinear loadings in three modes

David Brie (1) , Sebastian Miron (1) , Fabrice Caland (1, 2) , Christian Mustin (2)

1 CRAN - Centre de Recherche en Automatique de Nancy
2 LIMOS - Laboratoire des Interactions Microorganismes-Minéraux-Matière Organique dans les sols

In this paper we investigate the uniqueness of the 4-way CANDECOMP/PARAFAC (CP) model in the case where the only possible linear dependencies between the columns of the loading matrices take the form of collinear loadings. For this special configuration we state a necessary and sufficient condition for having full column rank of the Khatri-Rao product of two loading matrices. This allows to derive a sufficient condition for uniqueness of the 4-way CP model with collinear loadings in at most three modes. The result is illustrated by analyzing 4-way fluorescence data.

Mots clés: Multilinear algebra; CANDECOMP/PARAFAC; 4-way array; uniqueness; collinear loadings

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

David Brie, Sebastian Miron, Fabrice Caland, Christian Mustin. An uniqueness condition for the 4-way CANDECOMP/PARAFAC model with collinear loadings in three modes. 36th International Conference on Acoustics, Speech and Signal Processing, ICASSP 2011, May 2011, Prague, Czech Republic. pp.CDROM. ⟨hal-00558507⟩