Tensor decomposition is now being used for data analysis, information compression, and knowledge recovery. However, the mathematical property of tensor decomposition is not yet fully clarified because it is one of singular learning machines. In this paper, we give the upper bound of its real log canonical threshold (RLCT) of the tensor decomposition by using an algebraic geometrical method and derive its Bayesian generalization error theoretically. We also give considerations about its mathematical property through numerical experiments.

翻译：张量分解目前已被用于数据分析、信息压缩和知识恢复。然而，由于其属于奇异学习机器之一，张量分解的数学性质尚未完全阐明。本文利用代数几何方法给出了张量分解实对数正则阈值（RLCT）的上限，并从理论上推导了其贝叶斯泛化误差。此外，我们还通过数值实验对其数学性质进行了探讨。