Additive Compositionality in Urban Area Embeddings Based on Human Mobility Patterns

Understanding human mobility patterns in urban areas is crucial for a wide range of applications, including urban planning, commercial area analysis, tourism strategies, and disease control measures. In response to these diverse needs, several area embedding techniques have been actively researched, aiming to model mobility patterns for individual urban areas as vector representations within latent spaces. On the other hand, word embeddings are known to exhibit a property called additive compositionality, where arithmetic operations on embeddings correspond to meaningful semantic manipulations (e.g., ”king” - ”man” + ”woman” ≈ ”queen”). However, it remains unclear whether this property also holds in area embeddings, and if so, how it can be practically applied. Therefore, this study introduces and formulates the concept of additive compositionality from linguistics into area embeddings, defining it as a frequency-weighted average where the weights correspond to the frequency of occurrence for each area in the mobility dataset. Furthermore, we propose practical methods leveraging this property for flexible post-hoc transformations of area embeddings into different spatial shapes without retraining, and quantitative modeling of temporal mobility shifts as arithmetic operations between embeddings from different periods. Our results demonstrate that additive compositionality in area embeddings can effectively support operations on mobility patterns, spatial embedding transformations, and analysis of temporal mobility dynamics.