Correntropy-Induced Hypergraph Spectral Clustering With Discrete Optimization

Abstract

Hypergraph clustering has garnered considerable attention in complex learning tasks due to its powerful capacity for modeling high-order relationships among samples. Nevertheless, existing methods encounter two fundamental challenges: 1) The need for an additional discretization step following low-dimensional spectral embedding, which introduces a suboptimal mismatch between continuous embeddings and discrete cluster assignments, thereby impairing clustering performance; and 2) the susceptibility to diverse and complex noise are commonly present in real-world scenarios, which significantly compromises clustering robustness. To address these issues, we propose a novel correntropy-induced hypergraph spectral clustering (CIHSC) model. Different from current spectral clustering methods, CIHSC integrates a correntropy-based framework to enable direct discrete spectral decomposition on hypergraphs, eliminating the need for post discretization and thereby enhancing clustering fidelity and robustness. To effectively address the non-convex optimization arising from the correntropy-induced objective, we develop a half-quadratic optimization strategy tailored to the CIHSC model. Extensive experiments conducted on both real-world and noise-contaminated datasets demonstrate that CIHSC consistently outperforms state-of-the-art clustering methods in terms of performance and robustness.