Identifying urban spatial clusters via flow dynamics: a coupled tensor-based method - Zilong Zhao; Zihan Kan; Mei-Po Kwan; Luliang Tang (International Journal of Digital Earth, 2025)
Revealing spatial clustering patterns among urban geographic units is crucial for synergistic regional development and integrated urban management. Existing clustering methods neglect the intrinsic relationships between different features and spatiotemporal interactions among units, leading to a biased comprehension of urban clusters. This study develops a Graph-Laplacian Coupled Non-negative Tucker Decomposition (GCNTD) model to recognize multi-scale urban clusters in planar and network urban spaces. First, we construct spatiotemporal feature tensors of mobility flows and spatially couple them to capture the intrinsic correlations among multi-view features. Then, we propose an enhanced gravity model to represent spatial interactions among geographic units under free and constrained flows, and embed it into the coupled tensors using Graph-Laplacian regularization. Based on the decomposed spatiotemporal factors, we analyze the dynamic characteristics of geographic units and utilize hierarchical clustering to identify urban spatial clusters. Using human flow data in China, the inter-city experiments revealed clustering patterns among 366 cities and extracted 11 urban clusters. The total flow within clusters accounted for 41.40% of national mobility, while inter-cluster flows represented 8.87%. Intra-city experiments were conducted in Wuhan, where 152 fine-grained nodes were categorized into 4 clusters representing stable volume-travel time, high daytime volume, high nighttime volume, and high travel time.