Abstract

Co-author: Shirshendu Chatterjee (CUNY)

One of the most common and crucial aspect of many network data sets is the dependence of network link structure on time or other attributes. There is a long history of researchers proposing networks for dynamic time-evolving formation of networks. Most complex networks, starting from biological networks like genetic or neurological networks to social, co-authorship and citation networks are time-varying. This has led the researchers to study dynamic, time-evolving networks. In this work, we consider the problem of finding a common clustering structure in time-varying networks. We consider three simple extension of spectral clustering methods to dynamic settings and give theoretical justification that the spectral clustering methods produce consistent community detection for such dynamic networks. We also propose an extension of the static version of nonparametric latent variable models to the dynamic setting and use a special case of the model to justify the spectral clusteri ng methods. We show the validity of the theoretical results via simulations too and apply the clustering methods to real-world dynamic biological networks.