Post-Processing Partitions to Identify Domains of Modularity Optimization

We introduce the Convex Hull of Admissible Modularity Partitions (CHAMP) algorithm to prune and prioritize different network community structures identified across multiple runs of possibly various computational heuristics. Given a set of partitions, CHAMP identifies the domain of modularity optimiz...

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Main Authors: William H. Weir, Scott Emmons, Ryan Gibson, Dane Taylor, Peter J. Mucha
Format: Article
Language:English
Published: MDPI AG 2017-08-01
Series:Algorithms
Subjects:
Online Access:https://www.mdpi.com/1999-4893/10/3/93
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spelling doaj-ca992258a1424ac2890df9fddec5043e2020-11-24T21:59:21ZengMDPI AGAlgorithms1999-48932017-08-011039310.3390/a10030093a10030093Post-Processing Partitions to Identify Domains of Modularity OptimizationWilliam H. Weir0Scott Emmons1Ryan Gibson2Dane Taylor3Peter J. Mucha4Carolina Center for Interdisciplinary Applied Mathematics, Department of Mathematics, University of North Carolina, Chapel Hill, NC 27599, USACarolina Center for Interdisciplinary Applied Mathematics, Department of Mathematics, University of North Carolina, Chapel Hill, NC 27599, USACarolina Center for Interdisciplinary Applied Mathematics, Department of Mathematics, University of North Carolina, Chapel Hill, NC 27599, USACarolina Center for Interdisciplinary Applied Mathematics, Department of Mathematics, University of North Carolina, Chapel Hill, NC 27599, USACarolina Center for Interdisciplinary Applied Mathematics, Department of Mathematics, University of North Carolina, Chapel Hill, NC 27599, USAWe introduce the Convex Hull of Admissible Modularity Partitions (CHAMP) algorithm to prune and prioritize different network community structures identified across multiple runs of possibly various computational heuristics. Given a set of partitions, CHAMP identifies the domain of modularity optimization for each partition—i.e., the parameter-space domain where it has the largest modularity relative to the input set—discarding partitions with empty domains to obtain the subset of partitions that are “admissible” candidate community structures that remain potentially optimal over indicated parameter domains. Importantly, CHAMP can be used for multi-dimensional parameter spaces, such as those for multilayer networks where one includes a resolution parameter and interlayer coupling. Using the results from CHAMP, a user can more appropriately select robust community structures by observing the sizes of domains of optimization and the pairwise comparisons between partitions in the admissible subset. We demonstrate the utility of CHAMP with several example networks. In these examples, CHAMP focuses attention onto pruned subsets of admissible partitions that are 20-to-1785 times smaller than the sets of unique partitions obtained by community detection heuristics that were input into CHAMP.https://www.mdpi.com/1999-4893/10/3/93networkscommunity detectionmodularityresolution parametermultilayer networks
collection DOAJ
language English
format Article
sources DOAJ
author William H. Weir
Scott Emmons
Ryan Gibson
Dane Taylor
Peter J. Mucha
spellingShingle William H. Weir
Scott Emmons
Ryan Gibson
Dane Taylor
Peter J. Mucha
Post-Processing Partitions to Identify Domains of Modularity Optimization
Algorithms
networks
community detection
modularity
resolution parameter
multilayer networks
author_facet William H. Weir
Scott Emmons
Ryan Gibson
Dane Taylor
Peter J. Mucha
author_sort William H. Weir
title Post-Processing Partitions to Identify Domains of Modularity Optimization
title_short Post-Processing Partitions to Identify Domains of Modularity Optimization
title_full Post-Processing Partitions to Identify Domains of Modularity Optimization
title_fullStr Post-Processing Partitions to Identify Domains of Modularity Optimization
title_full_unstemmed Post-Processing Partitions to Identify Domains of Modularity Optimization
title_sort post-processing partitions to identify domains of modularity optimization
publisher MDPI AG
series Algorithms
issn 1999-4893
publishDate 2017-08-01
description We introduce the Convex Hull of Admissible Modularity Partitions (CHAMP) algorithm to prune and prioritize different network community structures identified across multiple runs of possibly various computational heuristics. Given a set of partitions, CHAMP identifies the domain of modularity optimization for each partition—i.e., the parameter-space domain where it has the largest modularity relative to the input set—discarding partitions with empty domains to obtain the subset of partitions that are “admissible” candidate community structures that remain potentially optimal over indicated parameter domains. Importantly, CHAMP can be used for multi-dimensional parameter spaces, such as those for multilayer networks where one includes a resolution parameter and interlayer coupling. Using the results from CHAMP, a user can more appropriately select robust community structures by observing the sizes of domains of optimization and the pairwise comparisons between partitions in the admissible subset. We demonstrate the utility of CHAMP with several example networks. In these examples, CHAMP focuses attention onto pruned subsets of admissible partitions that are 20-to-1785 times smaller than the sets of unique partitions obtained by community detection heuristics that were input into CHAMP.
topic networks
community detection
modularity
resolution parameter
multilayer networks
url https://www.mdpi.com/1999-4893/10/3/93
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