Spectral Clustering for Dynamic Block Models

• Activity Number: 330 - Advances in Inference of Networks
• Type: Topic Contributed
• Date/Time: Tuesday, August 1, 2017 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Sharmodeep Bhattacharyya* and Shirshendu Chatterjee
• Companies: Oregon State University and City University of New York
• Keywords: Networks ; Spectral Clustering ; Dynamic Networks ; Time-evolving Networks

Abstract

One of the most common and crucial aspects of many network data sets is the dependence of network link structure on time. In this work, we consider the problem of finding clustering structure in time-varying networks. We also propose an extension of the static version of nonparametric latent variable models into the dynamic setting and use special cases of the dynamic models to justify the spectral clustering methods. We consider two extensions of spectral clustering methods to dynamic settings and give theoretical guarantee that the spectral clustering methods produce consistent community detection in case of both dynamic stochastic block model and dynamic degree-corrected block model. The methods are shown to work under sufficiently mild conditions on the number of time snapshots of networks and also if the networks at each time snapshot are sparse and networks at most time snapshots are below community detectability threshold. We show the validity of the theoretical results via simulations too.