Weighted Graph Clustering via Scale Contraction and Graph Structure Learning

TL;DR

This work tackles weighted graph clustering under noise by introducing CeeGCN, which combines a cluster-oriented graph contraction module to shrink graphs while preserving clustering structure and an edge-weight-aware sparse graph attention network with $\alpha$-entmax to suppress noisy edges. The model jointly optimizes clustering with edge weights through a dual-loss objective: a modularity-based loss $L_M$ and a graph-structure contrastive loss $L_G$, enabling robust representation learning. Empirical results on three real-world datasets show superior clustering performance and notable efficiency gains due to contraction, with strong resilience to added noisy edges. Overall, the approach advances scalable, noise-robust weighted graph clustering by integrating structure learning, edge weight information, and fuzzy clustering.

Abstract

Graph clustering aims to partition nodes into distinct clusters based on their similarity, thereby revealing relationships among nodes. Nevertheless, most existing methods do not fully utilize these edge weights. Leveraging edge weights in graph clustering tasks faces two critical challenges. (1) The introduction of edge weights may significantly increase storage space and training time, making it essential to reduce the graph scale while preserving nodes that are beneficial for the clustering task. (2) Edge weight information may inherently contain noise that negatively impacts clustering results. However, few studies can jointly optimize clustering and edge weights, which is crucial for mitigating the negative impact of noisy edges on clustering task. To address these challenges, we propose a contractile edge-weight-aware graph clustering network. Specifically, a cluster-oriented graph contraction module is designed to reduce the graph scale while preserving important nodes. An edge-weight-aware attention network is designed to identify and weaken noisy connections. In this way, we can more easily identify and mitigate the impact of noisy edges during the clustering process, thus enhancing clustering effectiveness. We conducted extensive experiments on three real-world weighted graph datasets. In particular, our model outperforms the best baseline, demonstrating its superior performance. Furthermore, experiments also show that the proposed graph contraction module can significantly reduce training time and storage space.

Figures (7)

• Figure 1: An illustrative example of graph clustering on a noisy weighted graph.
• Figure 1: Two-dimensional visualization of clustering results on Vessel01.
• Figure 2: The architecture of CeeGCN, including (a) Cluster-oriented graph contraction module, (b) EWSGAT, and (c) Inference and training objective.
• Figure 3: Analysis of $\varepsilon$ on model performance.
• Figure 4: Analysis of $\alpha$ and $\eta$ on model performance.