Autonomous semantic community detection via adaptively weighted low-rank approximation

Identification of semantic community structures is important for understanding the interactions and sentiments of different groups of people and predicting the social emotion. A robust community detection method needs to autonomously determine the number of communities and community structure for a given network. Nonnegative matrix factorization (NMF), a component decomposition approach for latent sentiment discovery, has been extensively used for community detection. However, the existing NMF-based methods require the number of communities to be determined a priori, limiting their applicability in practice of affective computing. Here, we develop a novel NMF-based method to autonomously determine the number of semantic communities and community structure simultaneously. In our method, we use an initial number of semantic communities, larger than the actual number, in the NMF formulation, and then suppress some of the communities by introducing an adaptively weighted group-sparse low-rank regularization to derive the target number of communities and at the same time the corresponding community structure. Our method not only maintains the efficiency without increasing the complexity compared to the original NMF method but also can be straightforwardly extended to handle the non-network data. We thoroughly examine the new method, showing its superior performance over several competing methods on synthetic and large real-world social networks.