Structure Amplification on Multi-layer Stochastic Block Models

Abstract

Much of the complexity of social, biological, and engineering systems arises from the complicated interactions among the entities in the corresponding networks. A number of network analysis tools have been successfully used to discover latent structures termed communities in such networks. However, some communities with relatively weak structures can be difficult to uncover because they are obscured by other stronger connections. To cope with this situation, our previous work proposes an algorithm called HICODE to detect and amplify the dominant and hidden community structures. In this work, we conduct a comprehensive and systematic theoretical analysis on the impact of hidden community structure and the efficacy of the HICODE algorithm, as well as provide illustrations of the detection process and results. Specifically, we define a multi-layer stochastic block model, and use this model to explain why the existence of hidden structure makes the detection of dominant structure harder than equivalent random noises, which can also explain why many community detection algorithms only focusing on the dominant structure do not work well as expected. We then provide theoretical analysis that the iterative reducing methods could help to enhance the discovery of hidden structure as well as the dominant structure in the multi-layer stochastic block model for the two cases of accurate and inaccurate detection. Finally, visual simulations and experimental results are presented to show the process of HICODE algorithm and the impact of different number of layers on the detection quality.