Coupled Nonnegative Matrix/Tensor Factorization in Brain Imaging Data

Abstract

Continuous advancement of brain imaging techniques has witnessed data analysis methods evolving from matrix component analysis to tensor component analysis, from individual analysis to group analysis regarding the analysis of brain data with multi-set/multi-modal, multi-coupling and multi-way characteristics. Coupled matrix/tensor factorization is robust in merging the advantages of analysis methods, including multi-way retainability, flexible coupling settings, mild uniqueness conditions, and applicability of various constraints, which is relatively difficult for most existing methods. Therefore, this dissertation aims to develop efficient coupled nonnegative matrix/tensor factorization algorithms, which can be used for the analysis of brain imaging data at the group level. First, aiming at constrained group analysis of data from multiple sources, we design a flexible model of coupled nonnegative matrix factorization with sparse regularization and adopt alternating direction method of multipliers (ADMM) for optimization. Then, to reduce the high computational cost of largescale problems, we propose three efficient coupled nonnegative tensor factorization algorithms, which are respectively based on fast hierarchical alternating least squares (fHALS), alternating proximal gradient (APG) and a combination of APG and low-rank approximation. Experiments using synthetic and real-world data are conducted to demonstrate the performances of the proposed algorithms. Specifically, for multi-subject simulated functional magnetic resonance imaging data, the proposed ADMMbased algorithm can achieve better performance than its competitors and extract both common and individual patterns while correcting the disorders of common patterns. For multi-subject ongoing electroencephalography data, the proposed fHALS-based algorithm can effectively extract brain activities of interest associated with the musical stimulus. For multi-subject event-related potential data, the proposed APG-based algorithms can obtain higher decomposition accuracy and more robust multi-domain feature extraction stability, and low-rank approximation can greatly improve computation efficiency without losing the accuracy. Overall, according to data characteristics , we have developed efficient coupled nonnegative matrix/tensor decomposition algorithms, which have been successfully applied to the group analysis of brain imaging data. Keywords: Brain imaging data, coupled constraint, group analysis, nonnegative matrix/tensor factorization, sparse regularization