Community detection using fast low-cardinality semidefinite programming

• URL: http://arxiv.org/abs/2012.02676v1
• Date: Fri, 4 Dec 2020 15:46:30 GMT
• Title: Community detection using fast low-cardinality semidefinite programming
• Authors: Po-Wei Wang, J. Zico Kolter
• Abstract summary: We propose a new low-cardinality algorithm that generalizes the local update to maximize a semidefinite relaxation derived from Leiden-k-cut. This proposed algorithm is scalable, outperforms state-of-the-art algorithms, and outperforms in real-world time with little additional cost.
• Score: 94.4878715085334
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Modularity maximization has been a fundamental tool for understanding the community structure of a network, but the underlying optimization problem is nonconvex and NP-hard to solve. State-of-the-art algorithms like the Louvain or Leiden methods focus on different heuristics to help escape local optima, but they still depend on a greedy step that moves node assignment locally and is prone to getting trapped. In this paper, we propose a new class of low-cardinality algorithm that generalizes the local update to maximize a semidefinite relaxation derived from max-k-cut. This proposed algorithm is scalable, empirically achieves the global semidefinite optimality for small cases, and outperforms the state-of-the-art algorithms in real-world datasets with little additional time cost. From the algorithmic perspective, it also opens a new avenue for scaling-up semidefinite programming when the solutions are sparse instead of low-rank.

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