JSTSP Volume 15 Issue 3

Optimal rank selection is an important issue in tensor decomposition problems, especially for Tensor Train (TT) and Tensor Ring (TR) (also known as Tensor Chain) decompositions. In this paper, a new rank selection method for TR decomposition has been proposed for automatically finding near-optimal TR ranks, which result in a lower storage cost, especially for tensors with inexact TT or TR structures.

The emergence of big data and the multidimensional nature of wireless communication signals present significant opportunities for exploiting the versatility of tensor decompositions in associated data analysis and signal processing. The uniqueness of tensor decompositions, unlike matrix-based methods, can be guaranteed under very mild and natural conditions. 

The papers in this special section focus on tensor decomposition for signal processing and machine learning. Tensor decomposition, also called tensor factorization, is useful for representing and analyzing multi-dimensional data. Tensor decompositions have been applied in signal processing applications (speech, acoustics, communications, radar, biomedicine), machine learning (clustering, dimensionality reduction, latent factor models, subspace learning), and well beyond.