  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.
