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Community Detection in Networks: Pruning and Picking Parameters

Peter J. Mucha, Dartmouth College
Tuesday April 22, 12-1pm
Zoom Link:听
In Person: 550 Sherbrooke, Room 189

Abstract:听Real-world networks are neither completely random nor fully regular, frequently containing essential structural features whose identification can help better understand the nature and purpose of a network. One common task is to seek out clusters in the data, sometimes described as "community detection". Numerous software packages are available and widely used for community detection, but many of these require parameters to be selected (or assume default values) that are not always obvious to application domain experts. For example, the best use of modularity-based methods includes setting a parameter to control the resolution. Moreover, most of the algorithms are pseudo-random heuristic approximations. As such, one frequently needs to reconcile numerous different partitions of nodes into communities while simultaneously exploring the parameter space. These problems are exacerbated when community detection is extended to multilayer networks, because of the addition of at least one parameter to specify the coupling between layers. To address these difficulties, we combine different theoretical and computational developments into a simple framework for pruning a set of partitions to a subset that are self-consistent by an equivalence with stochastic block model (SBM) inference. Implementing these pruning steps together typically highlights only a small number of "stable" (fixed point) partitions, making it easier for users to focus their attention on a smaller number of partitions. Our framework works for single networks and multilayer networks, as well as for restricting to a fixed number of communities when desired. Our intention is to make it relatively easy for application domain experts to use these methods, with code for implementing these procedures available at .

Biographical Sketch: Peter Mucha is the Jack Byrne Distinguished Professor in Mathematics at Dartmouth College. Born in Texas and raised in Minnesota, Mucha attended college at Cornell University where he majored in Engineering Physics. After a Churchill Scholarship studying in the Cavendish Laboratory at Cambridge with an M.Phil. in Physics, he returned to the States to study Applied and Computational Mathematics at Princeton, earning M.A. and Ph.D. degrees. Following a postdoctoral instructorship in applied mathematics at MIT and assistant professorship in Mathematics at Georgia Tech, he moved to UNC-Chapel Hill for 16 years, where he served as chair of the Department of Mathematics, the founding chair of the Department of Applied Physical Sciences, and the Director of the Chairs Leadership Program at the Institute for the Arts & Humanities. His awards include a DOE Early Career PI award, an NSF CAREER award, and recognition as an HHMI Gilliam Advisor. Mucha arrived at Dartmouth in 2021 as part of The Jack Byrne Academic Cluster in Mathematics and Decision Science.