On Kruskal’s uniqueness condition for the Candecomp/Parafac decomposition
Copyright policy )On Kruskal’s uniqueness condition for the Candecomp/Parafac decomposition
The Candecomp/Parafac-decomposition of the real valued three-way array \(X\) is written as \(X=\underline{Y}^{(1)} + \ldots + \underline{Y}^{(R)} +\underline{E}\), where \(\underline{Y}^{(r)}\) are rank one arrays defined as outer products of three specified vectors and \(\underline E\) is a rest term. The question of uniqueness for this decomposition is provided by the theorem of \textit{J. B. Kruskal} [Linear Algebra Appl. 18, 95-138 (1977; Zbl 0364.15021)]. The authors obtain an accessible and more simple proof of Kruskal theorem, which can be easily adopted to the complex case.
Parafac, Numerical Analysis, Vector spaces, linear dependence, rank, lineability, Algebra and Number Theory, CP-decomposition, uniqueness, Candecomp, Kruskal-rank condition, RANK, ARRAYS, Discrete Mathematics and Combinatorics, Uniqueness, three-way arrays, Geometry and Topology, Three-way arrays
Parafac, Numerical Analysis, Vector spaces, linear dependence, rank, lineability, Algebra and Number Theory, CP-decomposition, uniqueness, Candecomp, Kruskal-rank condition, RANK, ARRAYS, Discrete Mathematics and Combinatorics, Uniqueness, three-way arrays, Geometry and Topology, Three-way arrays
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