An uniqueness condition for the 4-way CANDECOMP/PARAFAC model with collinear loadings in three modes
(Citations: 1)
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�Ä uorescence data.