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Scalable Multilevel and Memetic Signed Graph Clustering

Felix Hausberger, Marcelo Fonseca Faraj, Christian Schulz

TL;DR

This work tackles signed-graph clustering by minimizing the edge-cut, formalized as $C(\Pi)=\sum_{i<j}\omega(E_{ij})$ for a clustering $\Pi$ on a graph $G=(V,E)$ with $E=E^+\cup E^-$. It introduces two complementary methods: a scalable multilevel framework that coarsens by clustering and contraction and refines via label propagation and Fiduccia-Mattheyses (FM) moves, and a memetic algorithm built on the same multilevel backbone with recombination and mutation operating in an island-parallel setting. Empirical results show that the multilevel approach is competitive with state-of-the-art solvers while offering substantial speedups, and the memetic variant achieves the best edge-cut with dramatic runtime reductions, up to four orders of magnitude faster on large instances than GAEC+KLj. The combination provides a scalable tool for signed-graph clustering with potential applications in large, real-world networks and dynamic settings, with future work pointing to enhanced local search, dynamic graphs, and deeper multilevel parallelism.

Abstract

In this study, we address the complex issue of graph clustering in signed graphs, which are characterized by positive and negative weighted edges representing attraction and repulsion among nodes, respectively. The primary objective is to efficiently partition the graph into clusters, ensuring that nodes within a cluster are closely linked by positive edges while minimizing negative edge connections between them. To tackle this challenge, we first develop a scalable multilevel algorithm based on label propagation and FM local search. Then we develop a memetic algorithm that incorporates a multilevel strategy. This approach meticulously combines elements of evolutionary algorithms with local refinement techniques, aiming to explore the search space more effectively than repeated executions. Our experimental analysis reveals that this our new algorithms significantly outperforms existing state-of-the-art algorithms. For example, our memetic algorithm can reach solution quality of the previous state-of-the-art algorithm up to four orders of magnitude faster.

Scalable Multilevel and Memetic Signed Graph Clustering

TL;DR

This work tackles signed-graph clustering by minimizing the edge-cut, formalized as for a clustering on a graph with . It introduces two complementary methods: a scalable multilevel framework that coarsens by clustering and contraction and refines via label propagation and Fiduccia-Mattheyses (FM) moves, and a memetic algorithm built on the same multilevel backbone with recombination and mutation operating in an island-parallel setting. Empirical results show that the multilevel approach is competitive with state-of-the-art solvers while offering substantial speedups, and the memetic variant achieves the best edge-cut with dramatic runtime reductions, up to four orders of magnitude faster on large instances than GAEC+KLj. The combination provides a scalable tool for signed-graph clustering with potential applications in large, real-world networks and dynamic settings, with future work pointing to enhanced local search, dynamic graphs, and deeper multilevel parallelism.

Abstract

In this study, we address the complex issue of graph clustering in signed graphs, which are characterized by positive and negative weighted edges representing attraction and repulsion among nodes, respectively. The primary objective is to efficiently partition the graph into clusters, ensuring that nodes within a cluster are closely linked by positive edges while minimizing negative edge connections between them. To tackle this challenge, we first develop a scalable multilevel algorithm based on label propagation and FM local search. Then we develop a memetic algorithm that incorporates a multilevel strategy. This approach meticulously combines elements of evolutionary algorithms with local refinement techniques, aiming to explore the search space more effectively than repeated executions. Our experimental analysis reveals that this our new algorithms significantly outperforms existing state-of-the-art algorithms. For example, our memetic algorithm can reach solution quality of the previous state-of-the-art algorithm up to four orders of magnitude faster.
Paper Structure (10 sections, 3 figures, 3 tables)

This paper contains 10 sections, 3 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Multilevel Signed Graph Clustering
  4. Overall Multilevel Strategy.
  5. Uncoarsening.
  6. Distributed Memetic Signed Graph Clustering
  7. Notation, Population, and Fitness.
  8. Experimental Evaluation.
  9. Experimental Comparison.
  10. Conclusion

Figures (3)

  • Figure 1: Multilevel scheme.
  • Figure 2: In the recombination, the cut edges of both parents cannot be contracted during the first multilevel cycle to build an offspring.
  • Figure 3: Convergence plots for SCML and SCMLEvoPar. Both algorithms run in parallel using all cores of our machine for two minutes to compute a result. The plots show how the best solution computed by the algorithm decreases over time.