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

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 con guration we state a necessary and suf cient condition for having full column rank of the Khatri-Rao product of two loading matrices. This allows to derive a suf cient 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 uorescence data.

• Type: Journal
• Year: 2011
• Where: ICASSP
• Authors: David Brie, Sebastian Miron, Fabrice Caland, Christian Mustin
• Keywords: Collinear Loadings, ICASSP 2011, Loading Matrices, Signal Processing, Suf Cient Condition