Random partition distribution is a crucial tool for model-based clustering. This study advances the field of random partition in the context of functional spatial data, focusing on the challenges posed by hourly population data across various regions and dates. We propose an extended generalized Dirichlet process, named the similarity-based generalized Dirichlet process (SGDP), to address the limitations of simple random partition distributions (e.g., those induced by the Dirichlet process), such as an overabundance of clusters. This model prevents producing excess clusters as well as incorporates pairwise similarity information to ensure a more accurate and meaningful grouping. The theoretical properties of SGDP are studied. Then, SGDP is applied to a real-world dataset of hourly population flows in 500$\rm{m}^2$ meshes in the central part of Tokyo. In this empirical context, SGDP excelled at detecting meaningful patterns in the data while accounting for spatial nuances. The results underscore the adaptability and utility of the method, showcasing its prowess in revealing intricate spatiotemporal dynamics. This study's findings contribute significantly to urban planning, transportation, and policy-making by providing a helpful tool for understanding population dynamics and their implications.

翻译：随机划分分布是基于模型的聚类分析中的关键工具。本研究在函数型空间数据的背景下推进了随机划分领域的发展，重点解决了不同区域和日期的小时级人口数据所带来的挑战。我们提出了一种扩展的广义狄利克雷过程，即基于相似性的广义狄利克雷过程（SGDP），以解决简单随机划分分布（例如由狄利克雷过程诱导的分布）的局限性，如聚类数量过多的问题。该模型不仅能够防止生成过多的聚类，还能整合成对相似性信息，从而确保更准确、更有意义的分组。本文研究了SGDP的理论性质，并将其应用于东京中心区域500$\rm{m}^2$网格中小时级人口流量的真实数据集。在此实证背景下，SGDP在考虑空间细微差异的同时，擅长检测数据中的有意义模式。结果凸显了该方法的适应性和实用性，展示了其在揭示复杂时空动态方面的优势。本研究的发现通过提供一种理解人口动态及其影响的有效工具，为城市规划、交通和政策制定做出了重要贡献。