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.

中文翻译：

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张量奇异值分解的张量神经网络模型

近年来，张量分解变得越来越普遍。传统上，使用CANDECOMP / PARAFAC，Tucker模型或它们的某些变体将张量表示或分解为一阶外部乘积之和。这些分解的动机是找到给定张量的近似表示。本文的主要建议是针对给定的三阶张量开发两个神经网络模型，以找到基于t乘积的近似值。理论分析表明，每个神经网络模型都能确保收敛性能。计算机仿真结果进一步证实了该模型可以有效地找到左右奇异张量子空间。