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

作者：Zhang, Ling^*; Huang, Ting-Zhu; Zhu, Qing-Fang; Feng, Lili

来源：Linear Algebra and Its Applications, 2013, 439(7): 1918-1928.

DOI：10.1016/j.laa.2013.05.023

• Uni-mode uniqueness
• Partial uniqueness
• CANDECOMP/PARAFAC
• PARALIND
• n-way arrays

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.

• 出版日期2013-10-1
• 单位重庆交通大学