GENERIC UNIQUENESS CONDITIONS FOR THE CANONICAL POLYADIC DECOMPOSITION AND INDSCAL

被引：53
作者：
Domanov, Ignat [1 ,2 ,3 ]
De lathauwer, Lieven [1 ,2 ,3 ]
机构：
[1] KU Leuven Kulak, Grp Sci Engn & Technol, B-8500 Kortrijk, Belgium
[2] Katholieke Univ Leuven, Dept Elect Engn ESAT STADIUS, B-3001 Leuven Heverlee, Belgium
[3] Katholieke Univ Leuven, ESAT STADIUS, iMinds Med IT, B-3001 Leuven, Belgium
来源：
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 2015年 / 36卷 / 04期
基金：
欧洲研究理事会;
关键词：
canonical polyadic decomposition; CANDECOMP/PARAFAC decomposition; INDSCAL; third-order tensor; uniqueness; algebraic geometry; TENSOR DECOMPOSITIONS; IDENTIFIABILITY; RANK; TERMS;
D O I：
10.1137/140970276
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We find conditions that guarantee that a decomposition of a generic third-order tensor in a minimal number of rank-1 tensors (canonical polyadic decomposition (CPD)) is unique up to a permutation of rank-1 tensors. Then we consider the case when the tensor and all its rank-1 terms have symmetric frontal slices (INDSCAL). Our results complement the existing bounds for generic uniqueness of the CPD and relax the existing bounds for INDSCAL. The derivation makes use of algebraic geometry. We stress the power of the underlying concepts for proving generic properties in mathematical engineering.
引用
收藏
页码：1567 / 1589
页数：23
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