Stefano De Sabbata, Andrea Ballatore, Pengyuan Liu and Nicholas J. Tate

Exploring urban form through graph neural networks

Graph theory has long provided the basis for the computational modelling of urban flows and networks and, thus, for the study of urban form. The development of graph-convolutional neural networks offers the opportunity to explore new applications of deep learning approaches in urban studies. In this project, we explore the use of an unsupervised graph representation learning framework for analysing urban street networks (see methods and code below).

Our preliminary results (see results and supplementary materials below) illustrate how a model trained on a 1% random sample of street junctions in the UK can be used to explore the urban form of the city of Leicester, generating embeddings which are similar but distinct from classic metrics and able to capture key aspects such as the shift from urban to suburban structures.

Data

We used the Global Urban Street Networks data made available by Geoff Boeing, which include simplified street networks of 138 cities in the UK derived from OpenStreetMap.

Create storage as a subfolder of the main directory, which will be used to store large data files not to be syncronised with the GitHub repo. Download the Global Urban Street Networks GraphML files of interest into the storage and unzip them.

mkdir storage
mkdir storage/osmnx
mkdir storage/osmnx/zip
mkdir storage/osmnx/graphml
wget -O storage/osmnx/zip/united_kingdom-GBR_graphml.zip https://dataverse.harvard.edu/api/access/datafile/4287573
unzip storage/osmnx/zip/united_kingdom-GBR_graphml.zip -d storage/osmnx/graphml

Environment

The conda environment used for the project is described in this yml file (please see this README file as well).

Methods and code

We developed a graph autoencoder model using PyTorch Geometric. The encoder (see gnnuf_models_pl.py) is composed of five steps: one MLP projects the input node attributes into a large 256-dimensional space, three steps using modified graph isomorphism operators designed to incorporate the edge attributes in the aggregation step of the convolution, using 256 hidden features; and a final MLP layer, which reduces the 256 hidden features to 2 embeddings. The decoder is a standard inner product operator.

To train our model (see gnnuf_train_model_v0-12.py), we randomly sampled 1% of the nodes from 139 cities in the UK.

To evaluate the model, we used it to generate embeddings for all street junctions in Leicester -- see gnnuf_embedding_model_v0-12_Leicester.py for node embeddings and gnnuf_embedding_model_v0-12_Leicester_pool.py for embeddings pooled at node ego-graph level -- and Glasgow -- see gnnuf_embedding_model_v0-12_Glasgow.py for node embeddings and gnnuf_embedding_model_v0-12_Glasgow_pool.py for embeddings pooled at node ego-graph level,

In our preliminary analysis (see results and supplementary materials below), we qualitatively explore the expressiveness of the model through a series of plots and maps, and we quantitatively compare the embeddings with closeness and betweenness centrality, both based on the whole city graph and based on the node's ego-graph (see osmnx_stats_node_centrality_with_egograph_Leicester.py), as well as basic statistics (as provided by OSMnx) for each node's ego-graph (see osmnx_stats_egograph_basic_Leicester.py).

Results and supplementary materials

The pages below present the main results obtained from our analysis as a jupyter notebook compiled to html, alongside an additional quarto document.

• Exploratory analyses of the results obtained for Leicester
  • additional correlations pairs-plot created in R
• Exploratory analyses of the results obtained for Glasgow

Future work

Our preliminary results illustrate the potential of GNNs to develop an unsupervised framework to capture and explore urban form, but a more thorough exploration of the design space is necessary.

In our future work, we aim to expand the use of our framework in three aspects. First, we aim to explore the adaptability and usefulness of our approach through space, time and scale, testing how models behave when using a continental or global dataset for training, including past street networks or limiting the training to cities of the same scale as the target one(s). Second, we will explore how to encode places beyond junctions, including buildings or points of interest. Third, we will explore how to encode flows beyond networks, including commuting or communications.

Acknowledgements

The authors acknowledge the work of OpenStreetMap contributors and Geoff Boeing in creating the data that made this work possible. This research used the ALICE High Performance Computing Facility at the University of Leicester.