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Modularity Based Community Detection in Hypergraphs

Bogumił Kamiński, Paweł Misiorek, Paweł Prałat, François Théberge

TL;DR

This paper proposes a scalable community detection algorithm using hypergraph modularity function, h–Louvain, an adaptation of the classical Louvain algorithm in the context of hypergraphs that yields improved results in various regimes.

Abstract

In this paper, we propose a scalable community detection algorithm using hypergraph modularity function, h-Louvain. It is an adaptation of the classical Louvain algorithm in the context of hypergraphs. We observe that a direct application of the Louvain algorithm to optimize the hypergraph modularity function often fails to find meaningful communities. We propose a solution to this issue by adjusting the initial stage of the algorithm via carefully and dynamically tuned linear combination of the graph modularity function of the corresponding two-section graph and the desired hypergraph modularity function. The process is guided by Bayesian optimization of the hyper-parameters of the proposed procedure. Various experiments on synthetic as well as real-world networks are performed showing that this process yields improved results in various regimes.

Modularity Based Community Detection in Hypergraphs

TL;DR

This paper proposes a scalable community detection algorithm using hypergraph modularity function, h–Louvain, an adaptation of the classical Louvain algorithm in the context of hypergraphs that yields improved results in various regimes.

Abstract

In this paper, we propose a scalable community detection algorithm using hypergraph modularity function, h-Louvain. It is an adaptation of the classical Louvain algorithm in the context of hypergraphs. We observe that a direct application of the Louvain algorithm to optimize the hypergraph modularity function often fails to find meaningful communities. We propose a solution to this issue by adjusting the initial stage of the algorithm via carefully and dynamically tuned linear combination of the graph modularity function of the corresponding two-section graph and the desired hypergraph modularity function. The process is guided by Bayesian optimization of the hyper-parameters of the proposed procedure. Various experiments on synthetic as well as real-world networks are performed showing that this process yields improved results in various regimes.
Paper Structure (20 sections, 6 equations, 8 figures, 4 tables, 2 algorithms)

This paper contains 20 sections, 6 equations, 8 figures, 4 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Modularity Functions
  3. Hypergraphs Used in Our Experiments
  4. Synthetic Hypergraph Model: h--ABCD
  5. Real-world Hypergraphs
  6. Hypergraph Modularity Optimization Algorithm: h--Louvain
  7. Louvain Algorithm
  8. Challenges with Adjusting the Algorithm to Hypergraphs
  9. Our Approach to Hypergraph Modularity Optimization
  10. Parameters of the h--Louvain Algorithm
  11. Bayesian Optimization: Selecting the Parameters
  12. Experiments
  13. Selecting the Modularity Function to Optimize
  14. Synthetic h--ABCD Hypergraphs
  15. More Challenging Case---Synthetic Hypergraphs with Localized Noise
  16. ...and 5 more sections

Figures (8)

  • Figure 1: Quality of h--Louvain on h--ABCD as a function of parameters $p_b, p_c$. Optimal combinations of the two parameters depend on the choice of h--ABCD variant and hypergraph modularity function: strict, large level of noise (left), majority, large level of noise (middle), or linear, small level of noise (right).
  • Figure 2: Visualization of the Bayesian optimization approach optimizing the modularity function returned by the h--Louvain algorithm.
  • Figure 3: Results with h--ABCD hypergraphs with strict model for the community edge composition, ( strict_5 and strict_2to5) showing AMI difference between 2-section communities and the considered algorithms. Positive values indicate increase of AMI for a given algorithm.
  • Figure 4: Results with h--ABCD hypergraphs with linear model for the community edge composition, ( linear_5 and linear_2to5) showing AMI difference between 2-section communities and the considered algorithms. Positive values indicate increase of AMI for a given algorithm.
  • Figure 5: Results with h--ABCD hypergraphs with majority model for the community edge composition, ( majority_5 and majority_2to5) showing AMI difference between 2-section communities and the considered algorithms. Positive values indicate increase of AMI for a given algorithm.
  • ...and 3 more figures