Tensor Decompositions: A New Concept in Brain Data Analysis?

TL;DR

This paper reviews emerging tensor decomposition models and their applications in brain data analysis, focusing on blind source separation, feature extraction, and classification tasks.

Contribution

It introduces new tensor decomposition models and approaches specifically tailored for brain data analysis and related applications.

Findings

Tensor decompositions are effective for multiway BSS and ICA.

New models like constrained Tucker and CP improve analysis.

Tensor methods enhance feature extraction and classification.

Abstract

Matrix factorizations and their extensions to tensor factorizations and decompositions have become prominent techniques for linear and multilinear blind source separation (BSS), especially multiway Independent Component Analysis (ICA), NonnegativeMatrix and Tensor Factorization (NMF/NTF), Smooth Component Analysis (SmoCA) and Sparse Component Analysis (SCA). Moreover, tensor decompositions have many other potential applications beyond multilinear BSS, especially feature extraction, classification, dimensionality reduction and multiway clustering. In this paper, we briefly overview new and emerging models and approaches for tensor decompositions in applications to group and linked multiway BSS/ICA, feature extraction, classification andMultiway Partial Least Squares (MPLS) regression problems. Keywords: Multilinear BSS, linked multiway BSS/ICA, tensor factorizations and decompositions, constrained Tucker and CP models, Penalized Tensor Decompositions (PTD), feature extraction, classification, multiway PLS and CCA.