Co-Hub Node-Based Multiview Graph Learning

In many applications, learning the graph structure from nodal observations, is a significant task. Existing approaches are mostly limited to single graph learning assuming that the observed data are homogeneous. In many applications, data sets are heterogeneous and involve multiple related graphs, i.e., multiview graphs. Recent work on multiview graph learning ensures the similarity through edge-based similarity between the views. In this paper, we take a node-based approach instead of assuming that similarities across views are driven by individual edges, providing a more intuitive interpretation. In particular, we focus on a co-hub node model, where the different views are assumed to share a set of hub nodes. The corresponding optimization framework is formulated by imposing structured sparsity on the connectivities of the co-hub nodes. The proposed approach is evaluated on synthetic graph data and functional magnetic resonance imaging (fMRI) time series data across multiple subjects.