Multiview Graph Learning With Consensus Graph

Abstract

Graph topology inference is a significant task in many application domains. Existing approaches are mostly limited to learning a single graph assuming that the observed data is homogeneous. This is problematic because many modern datasets are heterogeneous and involve multiple related graphs, i.e., multiview graphs. Prior work in multiview graph learning ensures the similarity of learned view graphs through pairwise regularization, which has several limitations. First, most of the existing work focuses on the Gaussian Graphical Models (GGM) which learns precision matrices rather than the actual graph structures. Second, these methods do not infer the consensus structure across views, which may be useful in certain applications for summarizing the group level connectivity patterns. Finally, the number of pairwise constraints increases quadratically with the number of views. To address these issues, we propose a consensus graph-based multiview graph model, where each view is assumed to be a perturbed version of an underlying consensus graph. The proposed framework assumes that the observed graph data is smooth over the multiview graph and learns the graph Laplacians. A generalized optimization framework to jointly learn the views and the consensus graph is proposed, where different regularization functions can be incorporated into the formulation based on the structure of the underlying consensus graph and the perturbation model. Experiments with simulated data show that the proposed method has better performance than existing GGM-based methods and requires less run time than pairwise regularization-based methods. The proposed framework is also employed to infer the functional brain connectivity networks of multiple subjects from their electroencephalogram (EEG) recordings, revealing both the consensus structure and the individual variation across subjects.