  In this study, we propose using a neural embedding model-graph neural network
(GNN)- that leverages the heterogeneous features of urban areas and their
interactions captured by human mobility network to obtain vector
representations of these areas. Using large-scale high-resolution mobility data
sets from millions of aggregated and anonymized mobile phone users in 16
metropolitan counties in the United States, we demonstrate that our embeddings
encode complex relationships among features related to urban components (such
as distribution of facilities) and population attributes and activities. The
spatial gradient in each direction from city center to suburbs is measured
using clustered representations and the shared characteristics among urban
areas in the same cluster. Furthermore, we show that embeddings generated by a
model trained on a different county can capture 50% to 60% of the emergent
spatial structure in another county, allowing us to make cross-county
comparisons in a quantitative way. Our GNN-based framework overcomes the
limitations of previous methods used for examining spatial structures and is
highly scalable. The findings reveal non-linear relationships among urban
components and anisotropic spatial gradients in cities. Since the identified
spatial structures and gradients capture the combined effects of various
mechanisms, such as segregation, disparate facility distribution, and human
mobility, the findings could help identify the limitations of the current city
structure to inform planning decisions and policies. Also, the model and
findings set the stage for a variety of research in urban planning, engineering
and social science through integrated understanding of how the complex
interactions between urban components and population activities and attributes
shape the spatial structures in cities.
