Exploring urban form
through deep unsupervised
graph representation learning


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

sdesabbata.github.io/gnn-urban-form

Learning urban form representations

  • Deep neural network model on street network graphs
    • Graph Neural Networks (GNNs)
    • see e.g. Bruna et al. (2014), Gilmer et al. (2017), Hamilton (2020)
  • Learn effective representations of urban form from data
    • Arribas-Bel and Fleischmann (2022) define urban form as what a space “looks like” compared to urban function, which focuses on “what it is used for”
  • Enable down-stream urban analytics models


Message passing GNN framework

\[ h_{u}^{(l+1)} = {\scriptstyle UPDATE}^{(l)} \left( h_{u}^{(l)}\ ,\ {\scriptstyle AGGREGATE}^{(l)} \left( \bigl\{ h_{v}^{(l)}\ ,\ \forall v \in N(u) \bigl\} \right) \right) \]

Graph AutoEncoder

Unsupervised learning of nodes representations (Kipf and Welling 2016)

  • by optimising a dimensionality reduction model
  • encoder: uses graph-convolution and linear layers
  • decoder: commonly an inner product of the embeddings
  • loss: binary cross entropy for positive and negative sampled edges

Results

Street network data by OpenStreetMap, under ODbL, and by Boeing (2020), under CC0 1.0

 

Results (Glasgow)

 

Street network data by OpenStreetMap, under ODbL, and by Boeing (2020), under CC0 1.0

Conclusions

GNNs can be used as an unsupervised framework to explore urban form

  • still at exploratory phase
    • the design space is vast
    • a systematic approach is necessary
  • testing can be particularly challenging
    • no “ground-truth” labels

Future work

  • adaptability and usefulness through space, time and scale
  • encoding places beyond junctions, including buildings or points of interest
  • encoding flows beyond networks, including commuting or communications.

Thank you for your attention

Check out our GitHub repo

sdesabbata.github.io/gnn-urban-form

Stef De Sabbata
University of Leicester, UK
s.desabbata@leicester.ac.uk

Andrea Ballatore
King’s College London, UK
andrea.ballatore@kcl.ac.uk

Pengyuan Liu
Singapore-ETH Centre, Singapore
(moving to Glasgow in Jan 2025) pengyuan.liu@sec.ethz.ch

Nicholas J. Tate
University of Leicester, UK
njt9@leicester.ac.uk

Graph AutoEncoder (some details)

Pre-processing

  • random 1% of nodes from 138 UK cities
  • an ego-graph for each node
    • 500m network distance (min 8 nodes)
    • junctions as nodes
      • num. of segments as an attribute
      • bounded min-max (1 to 4)
    • street segments as edges
      • length as an edge attribute
      • bounded min-max (50m to 500m)

Model

  • PyTorch Geometric
  • five-step encoder
    • one MLP
      • 1 attribute to 256 features
    • three GINE (Hu et al. 2020) layers
      • 256 hidden features
    • one MLP
      • 256 features to 2 embeddings
  • trained for 1000 epochs
    • AdamW optimiser
    • random 70% + 10% val of ego-graphs
  • tested on remaining 20%

Case study

Leicester (UK)

  • Population: 368,600 at the 2021 UK Census, increased by 11.8% since 2011
  • Minority-majority city: 43.4% identify as Asian, 33.2% are White British
  • Area: about 73 km2 (28 sq mi)
  • Simplified OSM street network data by Boeing (2020)

Baselines comparison

Node embeddings Ego-graph emb.
Measure Fist dimension Second dimension Fist dimension Second dimension
Node in city
closeness centrality 0.134*** -0.249*** 0.260*** -0.310***
betweenness centrality 0.106*** -0.203*** 0.188*** -0.100***
Ego-graph
count of nodes 0.003*** -0.126*** 0.049*** -0.258***
count of edges -0.032*** -0.085*** -0.002. -0.194***
average node degree -0.179*** 0.218*** -0.257*** 0.305***
total edge length 0.017** 0.134*** 0.070*** 0.108***
average edge length 0.092*** 0.439*** 0.134*** 0.690***
average count of streets per node 0.230*** 0.256*** 0.429*** 0.354***
count of intersections 0.064*** -0.038*** 0.158** -0.129***
total street segment length 0.077*** 0.117*** 0.165*** 0.085***
count of street segments 0.035*** -0.083*** 0.108*** -0.192***
average street segment length 0.074*** 0.428*** 0.101*** 0.672***
average street circuity -0.075*** 0.001. -0.140*** -0.003.

Results (embedding clustering)

Street network data by OpenStreetMap, under ODbL, and by Boeing (2020), under CC0 1.0

 

Results (ego-graph pooled)

Street network data by OpenStreetMap, under ODbL, and by Boeing (2020), under CC0 1.0

 

References

Arribas-Bel, Daniel, and Martin Fleischmann. 2022. “Spatial Signatures - Understanding (Urban) Spaces Through Form and Function.” Habitat International 128: 102641. https://doi.org/10.1016/j.habitatint.2022.102641.
Boeing, Geoff. 2020. “Global Urban Street Networks GraphML.” Harvard Dataverse. https://doi.org/10.7910/DVN/KA5HJ3.
Bruna, Joan, Wojciech Zaremba, Arthur Szlam, and Yann LeCun. 2014. “Spectral Networks and Locally Connected Networks on Graphs.” https://arxiv.org/abs/1312.6203.
Gilmer, Justin, Samuel S. Schoenholz, Patrick F. Riley, Oriol Vinyals, and George E. Dahl. 2017. “Neural Message Passing for Quantum Chemistry.” In Proceedings of the 34th International Conference on Machine Learning, edited by Doina Precup and Yee Whye Teh, 70:1263–72. Proceedings of Machine Learning Research. PMLR. https://proceedings.mlr.press/v70/gilmer17a.html.
Hamilton, William L. 2020. Graph Representation Learning. Morgan & Claypool Publishers.
Hu, Weihua, Bowen Liu, Joseph Gomes, Marinka Zitnik, Percy Liang, Vijay Pande, and Jure Leskovec. 2020. “Strategies for Pre-training Graph Neural Networks.” arXiv. https://doi.org/10.48550/arXiv.1905.12265.
Kipf, Thomas N., and Max Welling. 2016. “Variational Graph Auto-Encoders.” https://arxiv.org/abs/1611.07308.