In this paper, we propose a new unified optimization algorithm for general tensor decomposition which is formulated as an inverse problem for low-rank tensors in the general linear observation models. The proposed algorithm supports three basic loss functions ($\ell_2$-loss, $\ell_1$-loss and KL divergence) and various low-rank tensor decomposition models (CP, Tucker, TT, and TR decompositions). We derive the optimization algorithm based on hierarchical combination of the alternating direction method of multiplier (ADMM) and majorization-minimization (MM). We show that wide-range applications can be solved by the proposed algorithm, and can be easily extended to any established tensor decomposition models in a {plug-and-play} manner.

翻译：本文提出了一种新的统一优化算法，用于广义张量分解，该问题被表述为一般线性观测模型下低秩张量的逆问题。所提算法支持三种基本损失函数（$\ell_2$损失、$\ell_1$损失和KL散度）以及多种低秩张量分解模型（CP、Tucker、TT和TR分解）。我们基于交替方向乘子法（ADMM）和最小化-最大化（MM）的层次化组合推导了该优化算法。研究表明，该算法可解决广泛的应用问题，并能够以“即插即用”的方式轻松扩展至任何现有的张量分解模型。