Performance evaluation of nonnegative matrix factorization algorithms to estimate task-related neuronal activities from fMRI data

Nonnegative matrix factorization (NMF) is a blind source separation (BSS) algorithm which is based on the distinct constraint of nonnegativity of the estimated parameters as well as on the measured data. In this study, according to the potential feasibility of NMF for fMRI data, the four most popular NMF algorithms, corresponding to the following two types of (1) least-squares based update [i.e., alternating least-squares NMF (ALSNMF) and projected gradient descent NMF] and (2) multiplicative update (i.e., NMF based on Euclidean distance and NMF based on divergence cost function), were investigated by using them to estimate task-related neuronal activities. These algorithms were applied firstly to individual data from a single subject and, subsequently, to group data sets from multiple subjects. On the single-subject level, although all four algorithms detected task-related activation from simulated data, the performance of multiplicative update NMFs was significantly deteriorated when evaluated using visuomotor task fMRI data, for which they failed in estimating any task-related neuronal activities. In group-level analysis on both simulated data and real fMRI data, ALSNMF outperformed the other three algorithms. The presented findings may suggest that ALSNMF appears to be the most promising option among the tested NMF algorithms to extract task-related neuronal activities from fMRI data.