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 extension of the generalized Dirichlet process, named the similarity-based generalized Dirichlet process (SGDP)-type distribution, 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 excess cluster production and incorporates pairwise similarity information to ensure accurate and meaningful clustering. The theoretical properties of the SGDP-type distribution are studied. Then, SGDP-type random partition is applied to a real-world dataset of hourly population flow in $500\text{m}^2$ meshes in the central part of Tokyo. In this empirical context, our method excels 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. The proposed random partition will significantly contribute to urban planning, transportation, and policy-making and will be a helpful tool for understanding population dynamics and their implications.

翻译：随机划分分布是基于模型聚类的关键工具。本研究在函数型空间数据背景下推进随机划分领域的发展，重点关注跨区域和日期的每小时人口数据所带来的挑战。我们提出广义狄利克雷过程的扩展，命名为基于相似性的广义狄利克雷过程（SGDP）型分布，以解决简单随机划分分布（例如由狄利克雷过程导出的分布）的局限性，如聚类数量过多。该模型防止产生过多聚类，并整合成对相似性信息以确保聚类结果的准确性和意义。本文研究了SGDP型分布的理论性质。随后，将SGDP型随机划分应用于东京市中心$500\text{m}^2$网格的每小时人口流动真实数据集。在此实证背景下，我们的方法在考虑空间细微差异的同时，能够出色地检测数据中的有意义模式。结果突显了该方法的适应性和实用性，展示了其揭示复杂时空动态的强大能力。所提出的随机划分方法将为城市规划、交通和政策制定做出重要贡献，并成为理解人口动态及其影响的有效工具。