On clustering network-valued data

TL;DR

This paper introduces methods for clustering multiple networks, either with or without node correspondence, using graphon estimates or feature vectors, supported by theoretical consistency results and empirical validation.

Contribution

It proposes novel clustering techniques for multiple networks, addressing both node correspondence scenarios, with theoretical guarantees and practical demonstrations.

Findings

Effective clustering of networks with node correspondence using graphon estimates.

Novel feature vector approach for networks without node correspondence.

Theoretical consistency of the proposed clustering methods.

Abstract

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. These networks may or may not have node correspondence. When node correspondence is present, we cluster networks by summarizing a network by its graphon estimate, whereas when node correspondence is not present, we propose a novel solution for clustering such networks by associating a computationally feasible feature vector to each network based on trace of powers of the adjacency matrix. We illustrate our methods using both simulated and real data sets, and theoretical justifications are provided in terms of consistency.