A Continuous View of Urban Space: Neural Dirichlet Random Measures for Urban Spatial Learning

Urban regions aggregate different information depending on specific partitions, but existing data-driven urban region representations are typically learned on a fixed spatial partition, limiting their applicability. To address this limitation, we propose a neural Dirichlet random measure: instead of learning representations for regions in a fixed partition, we learn a continuous intensity field over the entire spatial domain. Thus, integrating the field over any region gives its quantitative representation while ensuring conservation. Moreover, this continuous representation can also be learned directly from observations on different urban partitions, leading to a more flexible and generalizable way. We conduct experiments from both perspectives: as a predictor on arbitrary partitions, and as a learner of partition-agnostic urban spatial embeddings. As a predictor, experiments on ten major U.S. cities with widely used urban spatial embeddings show that our method guarantees quantitative conservation and also yields generally better predictive quality than conventional direct prediction. As a learner, cross-city transfer validation shows that our method learns partition-agnostic embeddings directly from observations on different partitions, and that these embeddings transfer to unseen cities and generally outperform those trained in the conventional fixed-partition way. These indicate that it is feasible to remove the dependence on fixed spatial partitions, which provides a new direction for urban representation learning.