Tensor Decompositions: A New Concept in Brain Data Analysis?
It addresses data analysis challenges in neuroscience, but is incremental as it reviews existing techniques.
The paper overviews tensor decomposition models for tackling problems in brain data analysis, such as blind source separation and feature extraction, but does not report specific results or numbers.
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.