# Tensor Decompositions: A New Concept in Brain Data Analysis?

arXiv: https://arxiv.org/abs/1305.0395 · HTML: https://mlsanity.com/paper/1305.0395/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 May 2013.

## Built on by (most cited first, 4 of 4)

- [Tensor decomposition of higher-order correlations by nonlinear Hebbian plasticity](https://mlsanity.com/paper/2106.15685/) (2021)
- [Tensor Decomposition of Large-scale Clinical EEGs Reveals Interpretable Patterns of Brain Physiology](https://mlsanity.com/paper/2211.13793/) (2022)
- [Fast Learnings of Coupled Nonnegative Tensor Decomposition Using Optimal Gradient and Low-rank Approximation](https://mlsanity.com/paper/2302.05119/) (2023)
- [A weighted subspace exponential kernel for support tensor machines](https://mlsanity.com/paper/2302.08134/) (2023)

## Abstract (arXiv)

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.