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Tensor decomposition is now being used for data analysis, informationcompression, and knowledge recovery. However, the mathematical property oftensor decomposition is not yet fully clarified because it is one of singularlearning machines. In this paper, we give the upper bound of its real logcanonical threshold (RLCT) of the tensor decomposition by using an algebraicgeometrical method and derive its Bayesian generalization error theoretically.We also give considerations about its mathematical property through numericalexperiments.

Upper Bound of Real Log Canonical Threshold of Tensor Decomposition and its Application to Bayesian Inference