Graph Clustering with Graph Neural Networks (2006.16904v3)

Abstract: Graph Neural Networks (GNNs) have achieved state-of-the-art results on many graph analysis tasks such as node classification and link prediction. However, important unsupervised problems on graphs, such as graph clustering, have proved more resistant to advances in GNNs. Graph clustering has the same overall goal as node pooling in GNNs - does this mean that GNN pooling methods do a good job at clustering graphs? Surprisingly, the answer is no - current GNN pooling methods often fail to recover the cluster structure in cases where simple baselines, such as k-means applied on learned representations, work well. We investigate further by carefully designing a set of experiments to study different signal-to-noise scenarios both in graph structure and attribute data. To address these methods' poor performance in clustering, we introduce Deep Modularity Networks (DMoN), an unsupervised pooling method inspired by the modularity measure of clustering quality, and show how it tackles recovery of the challenging clustering structure of real-world graphs. Similarly, on real-world data, we show that DMoN produces high quality clusters which correlate strongly with ground truth labels, achieving state-of-the-art results with over 40% improvement over other pooling methods across different metrics.

Graph Clustering with Graph Neural Networks: An Overview

This paper addresses the challenge of unsupervised graph clustering using Graph Neural Networks (GNNs), an area where existing approaches have not fully capitalized on the potential of GNN architectures to reveal latent cluster structures. The authors introduce Deep Modularity Networks (DMoN), presenting it as a robust alternative for clustering tasks in graph-based data, demonstrating its advantage over current methods.

Key Contributions and Findings

The paper presents significant advances by proposing a novel mechanism, DMoN, which is rooted in the modularity measure for clustering quality. This unsupervised pooling method is engineered to extract meaningful cluster structures effectively, outperforming traditional pooling techniques used in GNNs, such as DiffPool and MinCutPool. The critical advancement here is a purported 40% improvement over existing pooling methods across multiple metrics, demonstrating DMoN's ability to align closely with ground truth classifications in real-world scenarios.

Key results are founded on a comprehensive series of experiments that manipulate signal-to-noise ratios in graph structures and node attributes. The paper asserts that conventional GNNs perform suboptimally in clustering tasks primarily because their design originally aimed at supervised or semi-supervised tasks. In contrast, DMoN can optimize cluster assignments in an end-to-end differentiable manner, an advantage for performance in unsupervised settings.

Methodological Insights

DMoN's design is underscored by two core advancements: an end-to-end differentiable clustering module and a novel regularization approach to collapse regularization. By leveraging the modularity matrix in a spectral relaxation framework, DMoN effectively tunes GNNs to capture both intrinsic graph structural properties and node attributes simultaneously. Crucially, DMoN incorporates a Frobenius norm-based regularizer to ensure balanced cluster sizes, which enhances model robustness against trivial clustering solutions.

A particular highlight is the scalability and refined performance of DMoN compared to its counterparts. This improvement is achievable by strategically reformulating the modularity optimization to reduce computational complexity significantly, making it feasible for sparse graph datasets.

Theoretical and Practical Implications

The theoretical contribution solidifies with a proof of strong and weak consistency of DMoN under the Degree-Corrected Stochastic Block Model. Such consistency guarantees are crucial as they demonstrate that DMoN's performance metrics are reliable and expected to hold in practical settings where the underlying graph models adhere to recognized generative assumptions.

Practically, the implications are twofold. First, DMoN's superior clustering ability can significantly impact various domains such as social network analysis, bioinformatics, and recommendation systems, where understanding community structure is vital. Second, the modular design could inspire further exploration into GNN architectures optimized specifically for unsupervised learning paradigms, pushing the boundary of how GNNs are utilized beyond their traditional applications.

Future Directions

The work naturally points towards several promising future research avenues. One such direction involves extending the DMoN approach to accommodate overlapping community structures, which more complex datasets frequently exhibit. Another potential exploration could delve into the integration of temporal or dynamic graph features to bolster the performance of GNNs in evolving network contexts.

In conclusion, the paper articulates a detailed and methodologically robust solution to a longstanding challenge in graph analytics. By effectively marrying spectral clustering principles with the flexibility of GNNs, DMoN presents a compelling case for the evolution of unsupervised learning frameworks in the AI community. The insights gained from this paper could be instrumental in refining future GNN applications across diverse fields.