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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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 |
work_keys_str_mv |
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