Multi-curvature-based adaptive graph fusion for graph clustering

Abstract Graph clustering is a fundamental task in unsupervised learning. Most studies use graph neural networks to learn node embeddings and then adopt traditional clustering methods. However, they usually face the following problems: (1) noise and sparsity in original graph structures and attributes hinder clustering. (2) When the intrinsic structure of the data is complex, the linear properties of Euclidean space may not sufficiently capture the features between different semantics. (3) Node representations in multiple views fail to connect or capture the global clustering structure effectively. To address these issues, we propose Multi-Curvature-based Adaptive Graph Fusion for Clustering. Firstly, we design a shared-neighbor filtering module to enhance the adjacency matrix with second-order neighbor proximity and denoise attribute features using a graph Laplace filter. Secondly, we employ graph convolutional networks and multivariate curvature techniques to generate feature views and geometric attribute views in Euclidean and Riemannian spaces, creating heterogeneous node embeddings that better capture data complexity. Finally, an attention mechanism and learnable view sampling vectors dynamically adjust view weights to capture semantic information from different perspectives. Extensive experimental results on six benchmark datasets validate the effectiveness of our model.