Parallelization scheme for canonical polyadic decomposition of large-scale high-order tensors

A B S T R A C T Modeling multidimensional data using tensor models, particularly through the Canonical Polyadic (CP) model, can be found in large numbers of timely and important signal-based applications. However, the computational complexity in the case of high-order and large-scale tensors remains a challenge that prevents the implementation of the CP model in practice. While some algorithms in the literature deal with large-scale problems, others target high-order tensors. Nevertheless, these algorithms encounter major issues when both problems are present. In this paper, we propose a parallelizable strategy based on the tensor network theory, to deal simultaneously with both high-order and large-scale problems. We show the usefulness of the proposed strategy in reducing the computation time on a realistic electroencephalography data set.(c) 2022 Elsevier B.V. All rights reserved.