Network Embedding-based Directed Community Detection with Unknown Community Number

Community detection of network analysis plays an important role in numerous application areas, in which estimating the number of communities is a fundamental issue. However, many existing methods focus on undirected networks ignoring the directionality of edges or unrealistically assume that the number of communities is known a priori. In this article, we develop a data-dependent community detection method for the directed network to determine the number of communities and recover community structures simultaneously, which absorbs the ideas of network embedding and penalized fusion by embedding the out- and in-nodes into low-dimensional vector space and forcing the embedding vectors toward its center. The asymptotic consistency properties of the proposed method are established in terms of network embedding, directed community detection, and estimation of the number of communities. The proposed method is applied on synthetic networks and real brain functional networks, which demonstrate the superior performance of the proposed method against a number of competitors. Supplementary materials for this article are available online.