On estimating a mixture on graphons

Soumendu Sundar Mukherjee, Purnamrita Sarkar, Lizhen Lin

Published 2016-06-08Version 1

Community detection, which focuses on clustering nodes or detecting communities in (mostly) a single network, is a problem of considerable practical interest and has received a great deal of attention in the research community. While being able to cluster within a network is important, there are emerging needs to be able to cluster multiple networks. This is largely motivated by the routine collection of network data that are generated from potentially different populations, such as brain networks of subjects from different disease groups, genders, or biological networks generated under different experimental conditions, etc. We propose a simple and general framework for clustering multiple networks based on a mixture model on graphons. Our clustering method employs graphon estimation as a first step and performs spectral clustering on the matrix of distances between estimated graphons. This is illustrated through both simulated and real data sets, and theoretical justification of the algorithm is given in terms of consistency.