A Riemannian gossip approach to subspace learning on Grassmann manifold

Group-Wise Hub Identification by Learning Common Graph Embeddings on Grassmannian Manifold

Human brain is a complex yet economically organized system, where a small portion of critical hub regions support the majority of brain functions. The identification of common hub nodes in a population of networks is often simplified as a voting procedure on the set of identified hub nodes across individual brain networks, which ignores the intrinsic data geometry and partially lacks the reproducible findings in neuroscience. Hence, we propose a first-ever group-wise hub identification method to identify hub nodes that are common across a population of individual brain networks. Specifically, the backbone of our method is to learn common graph embedding that can represent the majority of local topological profiles. By requiring orthogonality among the graph embedding vectors, each graph embedding as a data element is residing on the Grassmannian manifold. We present a novel Grassmannian manifold optimization scheme that allows us to find the common graph embeddings, which not only identify the most reliable hub nodes in each network but also yield a population-based common hub node map. Results of the accuracy and replicability on both synthetic and real network data show that the proposed manifold learning approach outperforms all hub identification methods employed in this evaluation.