Tensor neural network models for tensor singular value decompositions

Xuezhong Wang (), Maolin Che () and Yimin Wei ()
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Xuezhong Wang: Hexi University
Maolin Che: Southwestern University of Finance and Economics
Yimin Wei: Fudan University

Computational Optimization and Applications, 2020, vol. 75, issue 3, No 8, 753-777

Abstract: Abstract Tensor decompositions have become increasingly prevalent in recent years. Traditionally, tensors are represented or decomposed as a sum of rank-one outer products using either the CANDECOMP/PARAFAC, the Tucker model, or some variations thereof. The motivation of these decompositions is to find an approximate representation for a given tensor. The main propose of this paper is to develop two neural network models for finding an approximation based on t-product for a given third-order tensor. Theoretical analysis shows that each of the neural network models ensures the convergence performance. The computer simulation results further substantiate that the models can find effectively the left and right singular tensor subspace.

Keywords: Tensor decomposition; Singular value decomposition; Tensor singular value decomposition; Tensor neural networks; Asymptotic stability; 15A18; 15A69; 65F15; 65F10 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10589-020-00167-1

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