Optimization-Based Algorithms for Tensor Decompositions: Canonical Polyadic Decomposition, Decomposition in Rank-$(L_r,L_r,1)$ Terms, and a New Generalization

The canonical polyadic and rank-$(L_r,L_r,1)$ block term decomposition (CPD and BTD, respectively) are two closely related tensor decompositions. The CPD and, recently, BTD are important tools in psychometrics, chemometrics, neuroscience, and signal processing. We present a decomposition that genera...

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Vydané v:SIAM journal on optimization Ročník 23; číslo 2; s. 695 - 720
Hlavní autori: Sorber, Laurent, Van Barel, Marc, De Lathauwer, Lieven
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Philadelphia Society for Industrial and Applied Mathematics 01.01.2013
Predmet:
Algorithms
Compounding
Compounds
Computation
Computer engineering
Decomposition
Least squares method
Mathematical analysis
Memory
Optimization
Optimization techniques
ISSN:1052-6234, 1095-7189
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Shrnutí:The canonical polyadic and rank-$(L_r,L_r,1)$ block term decomposition (CPD and BTD, respectively) are two closely related tensor decompositions. The CPD and, recently, BTD are important tools in psychometrics, chemometrics, neuroscience, and signal processing. We present a decomposition that generalizes these two and develop algorithms for its computation. Among these algorithms are alternating least squares schemes, several general unconstrained optimization techniques, and matrix-free nonlinear least squares methods. In the latter we exploit the structure of the Jacobian's Gramian to reduce computational and memory cost. Combined with an effective preconditioner, numerical experiments confirm that these methods are among the most efficient and robust currently available for computing the CPD, rank-$(L_r,L_r,1)$ BTD, and their generalized decomposition. [PUBLICATION ABSTRACT]
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ISSN:1052-6234
1095-7189
DOI:10.1137/120868323