A Unified Framework for Deep Hypergraph Clustering Beyond Homophily

Deep hypergraph clustering has shown strong potential in learning node representations by modeling high-order relationships. However, most existing methods rely on fixed propagation mechanisms that implicitly assume homophily, where connected nodes tend to be similar. This assumption often fails in real-world scenarios, especially in heterophilic settings, leading to degraded clustering performance. To bridge this gap, we propose a \textbf{Uni}fied Framework for \textbf{D}eep \textbf{H}ypergraph \textbf{C}lustering (Uni-DHC). Specifically, we introduce a learnable high-order hypergraph propagation scheme that aggregates information from multiple propagation orders and adaptively learns their importance from data. To stabilize unsupervised training and prevent structural redundancy introduced by high-order aggregation, we further impose consistency at the node level and decorrelation at the hyperedge level. From a spectral perspective, we show that conventional HGNN-style propagation corresponds to a fixed low-pass filter, while the proposed approach induces a learnable polynomial spectral filter. Extensive experiments on homophilic and heterophilic benchmarks demonstrate that Uni-DHC consistently outperforms state-of-the-art methods, with particularly strong gains in heterophilic settings.