Robust Deep Signed Graph Clustering via Weak Balance Theory

Signed graph clustering is a critical technique for discovering community structures in graphs that exhibit both positive and negative relationships. We have identified two significant challenges in this domain: i) existing signed spectral methods are highly vulnerable to noise, which is prevalent in real-world scenarios; ii) the guiding principle ``an enemy of my enemy is my friend'', rooted in textitSocial Balance Theory, often narrows or disrupts cluster boundaries in mainstream signed graph neural networks. Addressing these challenges, we propose the underlineDeep underlineSigned underlineGraph underlineClustering framework (DSGC), which leverages textitWeak Balance Theory to enhance preprocessing and encoding for robust representation learning. First, DSGC introduces Violation Sign-Refine to denoise the signed network by correcting noisy edges with high-order neighbor information. Subsequently, Density-based Augmentation enhances semantic structures by adding positive edges within clusters and negative edges across clusters, following textitWeak Balance principles. The framework then utilizes textitWeak Balance principles to develop clustering-oriented signed neural networks to broaden cluster boundaries by emphasizing distinctions between negatively linked nodes. Finally, DSGC optimizes clustering assignments by minimizing a regularized clustering loss. Comprehensive experiments on synthetic and real-world datasets demonstrate DSGC consistently outperforms all baselines, establishing a new benchmark in signed graph clustering.