Generalized Coupled Matrix Tensor Factorization Method Based on Normalized Mutual Information for Simultaneous EEG-fMRI Data Analysis

Abstract

Through the fusion of electroencephalogram (EEG) and functional magnetic resonance imaging (fMRI) data, the complementary properties of both modalities can be exploited. Thus, joint analysis of both modalities can be utilized in brain studies to estimate their shared and unshared components in brain activities. In this study, a comprehensive approach was proposed to jointly analyze EEG and fMRI datasets based on the advanced coupled matrix tensor factorization (ACMTF) method. The similarity of the components based on normalized mutual information (NMI) was defined to overcome the restrictive equality assumption of shared components in the common dimension of the ACMTF method. Because the mutual information (MI) measure is capable of identifying both linear and nonlinear relationships between the components, the proposed method can be viewed as a generalization of the ACMTF method; thus, it is called the generalized coupled matrix tensor factorization (GCMTF). The proposed GCMTF method was applied to simulated data, in which there was a nonlinear relationship between the components. The results demonstrate that the average match score increased by 23.46% compared to the ACMTF model, even with different noise levels. Furthermore, by applying this method to real data from an auditory oddball paradigm, it was demonstrated that three shared components with frequency responses in the alpha and theta bands were identified. The proposed MI-based method is not only capable of extracting shared components with any nonlinear or linear relationship but it is also able to identify more active brain areas corresponding to an auditory oddball paradigm compared to the ACMTF and other similar methods.