Document Type
Article - post-print
Publication Date
2013
Abstract
The study of network structure is pervasive in sociology, biology, computer science, and many other disciplines. One of the most important areas of network science is the algorithmic detection of cohesive groups of nodes called “communities.” One popular approach to finding communities is to maximize a quality function known as modularity to achieve some sort of optimal clustering of nodes. In this paper, we interpret the modularity function from a novel perspective: we reformulate modularity optimization as a minimization problem of an energy functional that consists of a total variation term and an $\ell_2$ balance term. By employing numerical techniques from image processing and $\ell_1$ compressive sensing---such as convex splitting and the Merriman--Bence--Osher (MBO) scheme---we develop a variational algorithm for the minimization problem. We present our computational results using both synthetic benchmark networks and real data.
Original Publication Citation
H. Hu, T. Laurent, M. A. Porter and A. L. Bertozzi. A Method Based on Total Variation for Network Modularity Optimization using the MBO Scheme. SIAM J. Appl. Math., 73(6), pp. 2224-2246, 2013. DOI:10.1137/130917387.
Publisher Statement
This is an author-manuscript of an article accepted for publication in SIAM Journal on Applied Mathematics following peer review. The version of record: H. Hu, T. Laurent, M. A. Porter and A. L. Bertozzi. A Method Based on Total Variation for Network Modularity Optimization using the MBO Scheme. SIAM J. Appl. Math., 73(6), pp. 2224-2246, 2013. is available online at: DOI:10.1137/130917387.
Digital Commons @ LMU & LLS Citation
Hu, Huiyi; Laurent, Thomas; Porter, Mason A.; and Bertozzi, Andrea L., "A Method Based on Total Variation for Network Modularity Optimization using the MBO Scheme" (2013). Mathematics, Statistics and Data Science Faculty Works. 90.
https://digitalcommons.lmu.edu/math_fac/90
