Tensor Networks for Latent Variable Analysis: Higher Order Canonical Polyadic Decomposition.

The canonical polyadic decomposition (CPD) is a convenient and intuitive tool for tensor factorization; however, for higher order tensors, it often exhibits high computational cost and permutation of tensor entries, and these undesirable effects grow exponentially with the tensor order. Prior compression of tensor in-hand can reduce the computational cost of CPD, but this is only applicable when the rank R of the decomposition does not exceed the tensor dimensions. To resolve these issues, we present a novel method for CPD of higher order tensors, which rests upon a simple tensor network of representative inter-connected core tensors of orders not higher than 3.