Modularity aided consistent attributed graph clustering via coarsening

TL;DR

This paper introduces a novel graph clustering method combining coarsening and modularity maximization, leveraging node features and adjacency information for improved accuracy, efficiency, and smaller community detection, with theoretical guarantees and strong empirical results.

Contribution

It proposes a new loss function and algorithm that integrate coarsening, modularity, and graph neural networks, providing theoretical consistency and superior clustering performance.

Findings

Achieves asymptotic error-free community detection under DC-SBM.

Outperforms state-of-the-art methods on benchmark datasets.

Seamlessly integrates with GNNs and VGAEs for enhanced feature learning.

Abstract

Graph clustering is an important unsupervised learning technique for partitioning graphs with attributes and detecting communities. However, current methods struggle to accurately capture true community structures and intra-cluster relations, be computationally efficient, and identify smaller communities. We address these challenges by integrating coarsening and modularity maximization, effectively leveraging both adjacency and node features to enhance clustering accuracy. We propose a loss function incorporating log-determinant, smoothness, and modularity components using a block majorization-minimization technique, resulting in superior clustering outcomes. The method is theoretically consistent under the Degree-Corrected Stochastic Block Model (DC-SBM), ensuring asymptotic error-free performance and complete label recovery. Our provably convergent and time-efficient algorithm seamlessly integrates with graph neural networks (GNNs) and variational graph autoencoders (VGAEs) to learn enhanced node features and deliver exceptional clustering performance. Extensive experiments on benchmark datasets demonstrate its superiority over existing state-of-the-art methods for both attributed and non-attributed graphs.