Triangular Concordance Learning of Networks

Networks are widely used to describe relational data among objects in a complex system. As network data often exhibit clustering structures, research interest often focuses on discovering clusters of nodes. We develop a novel concordance-based method for node clustering in networks, where a linear model is imposed on the latent position of each node with respect to a node-specific center and its covariates via linear transformation. By maximizing a triangular concordance function with a concave pairwise penalty, the latent positions are estimated so that each node would be more likely to be close to its neighbors in contrast to non-neighbors and nodes are clustered by their node-specific centers. We develop an alternating direction method of multipliers algorithm for parameter estimation and an intimacy score between unlinked nodes for link prediction. Our method takes into account common characteristics of network data (i.e., assortativity, link pattern similarity, node heterogeneity and link transitivity), while it does not require the number of clusters to be known. The clustering effectiveness and link prediction accuracy of our method are demonstrated in simulated and real networks. Supplementary materials for this article are available online.