A Unified Framework for Deep Hypergraph Clustering Beyond Homophily

Deep hypergraph clustering exhibits compelling capacity for node representation learning via modeling high-order relationships. However, most existing methods adopt fixed propagation mechanisms and implicitly assume homophily, which presumes that adjacent nodes possess similar characteristics. This assumption might deviate from real-world situations, particularly under heterophilic conditions, thereby degrading clustering performance. To address this limitation, we propose a Unified Framework for Deep Hypergraph Clustering (Uni-DHC). Specifically, we design a learnable high-order hypergraph propagation strategy that fuses multi-order information and adaptively learns their importance derived from raw data. To stabilize unsupervised training and eliminate structural redundancy caused by high-order aggregation, we additionally enforce node-level consistency and hyperedge-level decorrelation constraints. From the spectral perspective, we demonstrate that conventional HGNN-style propagation corresponds to a fixed low-pass filter, whereas our designed method induces a learnable polynomial spectral filter. Extensive experiments on homophilic and heterophilic datasets illustrate that Uni-DHC consistently outperforms state-of-the-art methods, achieving prominent performance improvement in heterophilic settings.