Title: Geometry-Aware Generative Modeling for Graph Clustering via Hyperspherical Diffusion
Primary area: learning on graphs and other geometries & topologies
Keywords: Graph Representation Learning, Graph Clustering, Generative Modeling

Abstract: Unsupervised graph clustering is fundamental for uncovering latent structures in graph-structured data, particularly in scenarios where labeled data is limited or unavailable. However, existing approaches often struggle to simultaneously achieve cluster-discriminative representations and geometric consistency. Conventional variational graph autoencoders rely on unimodal Gaussian priors in Euclidean space, often leading to overlapping latent clusters, while contrastive approaches depend on heuristic augmentations that may disrupt essential structural information. To overcome these limitations, we propose Hyperspherical Contrastive Diffusion (HCD), a novel unsupervised graph clustering framework that jointly leverages hyperspherical geometry and diffusion-based generative modeling. HCD constrains node embeddings to lie on a unit hypersphere and refines them via a multi-step temporal denoising diffusion process. It integrates a Product-of-Experts aggregation strategy, a von Mises–Fisher KL divergence to regularize angular latent distributions, a spherical contrastive loss to enforce discriminative alignment, and a cluster compactness-separation regularizer based on Student-t assignments and entropy minimization. These objectives collectively shape a latent space that preserves graph structure while promoting tight intra-cluster cohesion and clear inter-cluster separation. Comprehensive experiments across diverse benchmarks and multiple clinically and biologically significant real-world tissue clustering scenarios (ranging from complex neuroanatomical region identification to cancer tissue segmentation under varied conditions) demonstrate that HCD consistently achieves state-of-the-art performance in clustering accuracy, robustness, and stability.