Extreme Value Statistics of Community Detection in Complex Networks with Reduced Network Extremal Ensemble Learning (RenEEL)

TL;DR

This paper introduces RenEEL, a machine learning ensemble method for community detection in complex networks, analyzing how parameters influence the quality of the resulting partitions using extreme value statistics.

Contribution

The paper presents a novel ensemble approach, RenEEL, for community detection that leverages extreme value statistics to optimize parameters and improve partition quality.

Findings

Increasing ensemble size K improves partition quality more than increasing L.

RenEEL effectively finds high-modularity partitions in benchmark networks.

Extreme value statistics help understand the performance dependence on parameters.

Abstract

Arguably, the most fundamental problem in Network Science is finding structure within a complex network. One approach is to partition the nodes into communities that are more densely connected than one expects in a random network. "The" community structure then corresponds to the partition that maximizes Modularity, an objective function that quantifies this idea. Finding the maximizing partition, however, is a computationally difficult, NP-Complete problem. We explore using a recently introduced machine-learning algorithmic scheme to find the structure of benchmark networks. The scheme, known as RenEEL, creates an ensemble of $K$ partitions and updates the ensemble by replacing its worst member with the best of $L$ partitions found by analyzing a simplified network. The updating continues until consensus is achieved within the ensemble. We perform an empirical study of three real-world networks to explore how the Modularity of the consensus partition depends on the values of $K$ and $L$ and relate the results to the extreme value statistics of record-breaking. We find that increasing $K$ is generally more effective than increasing $L$ for finding the best partition.