Identification of 71 factors influencing urban vitality and examination of their spatial dependence: A comprehensive validation applying multiple machine-learning models

The COVID-19 outbreak has renewed debate on urban vitality and the factors influencing it. Urban informatization leads to increasingly complex connotations of vitality; however, linear models have difficulty describing complex relationships, and machine learning tends to ignore spatial heterogeneity. Nanjing is used as an example to establish the urban information box storing 71 indicators in six categories and dividing vitality into social, economic, cyberspace, and cultural-tourism dimensions. The variables' spatial-dependence decay laws were analyzed to build a spatial machine-learning model (SML). Comprehensive validation of comparisons and cross-identification of key influences used gradient-boosted regression trees, random forests, and support vector regression. Results show that 1) SML has a better goodness-of-fit than ordinary least squares, spatial error, spatial lag, and basic machine-learning model. 2) Spatial dependence generally reaches its peak at the 2.5 km² reach; subsequently, different variables' rates decayed differently. Vitality relies on important spatial dependences: transportation, morphology, function, and geography. 3) Key factors influencing urban vitality differed significantly, with only points of interest density in common. This study provides a generalizable research framework, advancing urban research by considering spatial heterogeneity. Identifying the factors that influence urban vitality provides theoretical guidance for spatial optimization to enhance urban vitality and promote sustainable urban development.