  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 excess cluster production as well as incorporates pairwise
similarity information to ensure accurate and meaningful grouping. The
theoretical properties of the SGDP are studied. Then, SGDP-based 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 SGDP will significantly contribute to urban planning,
transportation, and policy-making and will be a helpful tool for understanding
population dynamics and their implications.
