Title: Optimization-based algorithms for tensor decompositions: canonical polyadic decomposition, decomposition in rank-$(L_r,L_r,1)$ terms and a new generalization
Authors: Sorber, Laurent ×
Van Barel, Marc
De Lathauwer, Lieven #
Issue Date: 18-Apr-2013
Publisher: The Society of Industrial and Applied Mathematics
Series Title: SIAM Journal on Optimization vol:23 issue:2 pages:695-720
Abstract: 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.
ISSN: 1052-6234
Publication status: published
KU Leuven publication type: IT
Appears in Collections:ESAT - STADIUS, Stadius Centre for Dynamical Systems, Signal Processing and Data Analytics
NUMA, Numerical Analysis and Applied Mathematics Section
Electrical Engineering (ESAT), Campus Kulak Kortrijk
Electrical Engineering - miscellaneous
× corresponding author
# (joint) last author

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