Title: Tensor Networks for Latent Variable Analysis: Higher Order Canonical Polyadic Decomposition,
Abstract: 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, 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. For rigour, we
develop an exact conversion scheme from the core tensors to the factor matrices
in CPD, and an iterative algorithm with low complexity to estimate these factor
matrices for the inexact case. Comprehensive simulations over a variety of
scenarios support the approach.