Uni-mode uniqueness conditions for CANDECOMP/PARAFAC decomposition of n-way arrays with linearly dependent loadings

Guo, Miron, Brie and Stegeman [X. Guo, S. Miron, D. Brie, A. Stegeman, Uni-mode and partial uniqueness conditions for CANDECOMP/PARAFAC of three-way arrays with linearly dependent loadings, SIAM J. Matrix Anal. Appl. 33 (2012) 111-129] give three sufficient conditions for the three-way CANDECOMP/PARAFAC (CP) model which ensure uniqueness in one of the three modes (“uni-mode-uniqueness”). In this paper, we generalize these uniqueness conditions to n⩾3. Based on these conditions, a partial uniqueness condition is given which allows collinear loadings in only one mode.