How the neighborhood amenity mix shapes urban vitality: An exploratory analysis from a rhythm perspective

Neighborhood amenities, essential components of the built environment that support everyday life, play a pivotal role in enhancing urban vitality and advancing sustainable development. However, how the spatial co-location of neighborhood amenities—conceptualized as neighborhood amenity mix (NAM) —shapes urban vitality through synergistic effects across spatially heterogeneous urban development modes remains underexplored. This study constructs a framework consisting of 12 indicators across 3 dimensions—configuration, supply pattern, and spatial arrangement—to quantify the synergistic effects and co-location characteristics of NAM. By identifying rhythms of urban vitality from time-series data, the study classifies urban space into three development types. Furthermore, interpretable machine learning models are employed to uncover nonlinear relationships and threshold effects between indicators and vitality intensity. The results show that the proposed indicators explain an average of 61.86 % of the variance. Configuration and supply patterns exhibit consistent and critical effects, while spatial arrangements demonstrate pronounced heterogeneity. Threshold variations across development types underscore the context-dependent nature of neighborhood amenity planning. These thresholds offer data-informed support for developing locally adapted planning strategies.