HEProOE: A hyperedge enhanced probabilistic optimal estimation method for detecting spatial fuzzy communities.

Identifying spatial communities with human mobility data has emerged as a key approach to understanding urban spatial structure. However, relying solely on human mobility data to partition spatial communities ignores the semantic information and may fragment large, semantic consistent Indivisible Regions (IRs) such as college campuses. Furthermore, individual spatial units often belong simultaneously to multiple IRs, creating membership uncertainty, while the spatial stochasticity of human movements inherently introduces ambiguity to the boundaries of spatial fuzzy communities. To address these challenges, we proposed the Hyperedge-Enhanced Probabilistic Optimal Estimation method (HEProOE) that integrated the hyperedge into spatial fuzzy community detection, representing IRs as semantic consistent regions. First, IRs were represented as hyperedges, where each spatial unit holds a probabilistic community membership. Second, a novel distance-weighted Jensen-Shannon (JS) divergence metric was introduced to measure the semantic consistency within each hyperedge. Finally, this metric was converted into a new likelihood component and seamlessly integrated with the mobility-based ProOE model, yielding a unified framework that simultaneously optimizes for both mobility patterns and semantic consistency. Experimental results demonstrated that HEProOE uncovers spatial fuzzy communities with significantly higher semantic consistency, providing an effective tool for a more authentic understanding of urban spatial structures.