Nonlinear PageRank Problem for Local Graph Partitioning
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917101076217856 |
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| author | Kodsi, Costy Pasadakis, Dimosthenis |
| author_facet | Kodsi, Costy Pasadakis, Dimosthenis |
| contents | A nonlinear generalisation of the PageRank problem involving the Moore-Penrose inverse of an incidence matrix is developed for local graph partitioning purposes. The Levenberg-Marquardt method with a full rank Jacobian variant provides a strategy for obtaining a numerical solution to the generalised problem. Sets of vertices are formed according to the ranking supplied by the solution, and a conductance criterion decides upon the set that best represents the cluster around a starting vertex. Experiments on both synthetic and real-world inspired graphs demonstrate the capability of the approach to not only produce low conductance sets, but to also recover local clusters with an accuracy that consistently surpasses state-of-the-art algorithms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_01834 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nonlinear PageRank Problem for Local Graph Partitioning Kodsi, Costy Pasadakis, Dimosthenis Numerical Analysis 05C50 (Primary), 65K05, 90C35, 90C90 (Secondary) G.1.3; G.1.6; G.2.2 A nonlinear generalisation of the PageRank problem involving the Moore-Penrose inverse of an incidence matrix is developed for local graph partitioning purposes. The Levenberg-Marquardt method with a full rank Jacobian variant provides a strategy for obtaining a numerical solution to the generalised problem. Sets of vertices are formed according to the ranking supplied by the solution, and a conductance criterion decides upon the set that best represents the cluster around a starting vertex. Experiments on both synthetic and real-world inspired graphs demonstrate the capability of the approach to not only produce low conductance sets, but to also recover local clusters with an accuracy that consistently surpasses state-of-the-art algorithms. |
| title | Nonlinear PageRank Problem for Local Graph Partitioning |
| topic | Numerical Analysis 05C50 (Primary), 65K05, 90C35, 90C90 (Secondary) G.1.3; G.1.6; G.2.2 |
| url | https://arxiv.org/abs/2409.01834 |