I. Introduction
FUNCTIONAL magnetic resonance imaging (fMRI) provides a non-invasive, high-resolution technique for observing the low-frequency fluctuation in blood-oxygenation-level-dependent (BOLD) signals to characterize the metabolism of the human brain. Recent evidence [1]–[3] suggests that multiple fMRI datasets contain complementary information and can predict individual variations in behavioral and cognitive traits better than using a single dataset. Numerous data fusion methods have been developed to integrate multiple paradigms of fMRI. For instance, ICA-based approaches [4], [5] were proposed by Calhoun et al. and Sui et al. to analyze the joint information from multiple fMRI paradigms. Jie et al. [6] and Zhu et al. [7] proposed manifold regularized multi-task learning models to describe the subject-subject and the response-response relationships. These models were further extended by Xiao et al. [8], [9] to incorporate the relation information both within and between modalities. These approaches are typically based on linear models without considering complex nonlinear relationship between these data.