Characterization of spatiotemporal evolutionary patterns of metro networks based on K-means DTW Barycenter Averaging Clustering

Abstract

Understanding metro development patterns is crucial for cities to design efficient and well-connected transit networks. However, the heterogeneity in network scale and variations in development timelines pose challenges in identifying universal evolutionary patterns. This study introduces a hybrid clustering approach that integrates K-means with Dynamic Time Warping (DTW) Barycenter Averaging to analyze unequal-length time series data, revealing the spatiotemporal evolution of metro networks. Drawing on 24 years of data from 34 Chinese cities, we classify metro network development into four distinct patterns: Nascent, Emerging, Developing, and Mature. First-tier cities with Mature networks prioritize optimizing connectivity and station interrelations, focusing on topological evolution rather than mere expansion. Additionally, we examine the role of key structural components in shaping network topology. Our findings highlight the significance of strengthening transfer stations as hubs to enhance overall topological potential, while ring lines improve network reliability and ridership. Notably, establishing core structures at an early stage is critical, as later modifications yield diminishing improvements in topological performance. These insights offer valuable guidance for urban metro planning and policymaking, supporting the development of more resilient and efficient transit systems.