Data-driven methods based on independent component analysis (ICA) and its extensions, have been attractive for data fusion as they minimize the assumptions placed on the data. Two widely used extensions of ICA, joint ICA (jICA) and multiset canonical correlation analysis prior to joint ICA (MCCA-jICA) fuse data from different datasets by assuming identical mixing matrices. However, these methods typically only take the common features into account within the linked datasets by disregarding the available distinct features, thus limiting their usefulness. In this paper, we propose a new method for fusion based on ICA and canonical correlation analysis (CCA), disjoint subspace framework using ICA (DS-ICA), to identify and extract not only the common but also distinct features, to yield results that better reveal the underlying relationships between the datasets. Separate analyses on the common and distinct subspaces provide flexibility of choosing suitable algorithm and order for each subspace, ensuring more robust results than the competitive methods. We perform and demonstrate performance advantage of DS-ICA through both simulations and application to multiset functional magnetic resonance imaging (fMRI) data collected from healthy controls, as well as patients of schizophrenia performing an auditory odd ball task (AOD).