Practical approximation algorithms for ℓ1-regularized sparse rank-1 approximation to higher-order tensors

Two approximation algorithms are proposed for ℓ 1 -regularized sparse rank-1 approximation to higher-order tensors. The algorithms are based on multilinear relaxation and sparsification, which are easily implemented and well scalable. In particular, the second one scales linearly with the size of th...

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Veröffentlicht in:Optimization letters Jg. 18; H. 3; S. 767 - 781
Hauptverfasser: Mao, Xianpeng, Yang, Yuning
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2024
Schlagworte:
Computational Intelligence
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Operations Research/Decision Theory
Optimization
Original Paper
Simulation
Rank-1 approximation
Sparse
Tensor
Approximation algorithm
Approximation bound
regularization
ISSN:1862-4472, 1862-4480
Online-Zugang:Volltext
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Beschreibung
Zusammenfassung:Two approximation algorithms are proposed for ℓ 1 -regularized sparse rank-1 approximation to higher-order tensors. The algorithms are based on multilinear relaxation and sparsification, which are easily implemented and well scalable. In particular, the second one scales linearly with the size of the input tensor. Based on a careful estimation of the ℓ 1 -regularized sparsification, theoretical approximation lower bounds are derived. Our theoretical results also suggest an explicit way of choosing the regularization parameters. Numerical examples are provided to verify the proposed algorithms.
ISSN:1862-4472
1862-4480
DOI:10.1007/s11590-023-02032-6