Learning urban form through unsupervised graph-convolutional neural networks


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

sdesabbata.github.io/gnn-urban-form

Urban form (and function)

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”.

Urban form

  • the analysis of urban infrastructure
    • street network connectivity and structure
    • building structure and arrangement

Urban function

  • the study of urban activities and agents
    • land use
    • presence and diversity of points of interest
    • accessibility measures

Graph neural networks

Conceptually akin to Convolutional Neural Networks (CNNs) used in image processing

  • apply convolutional operations to graph structures within a deep learning process
  • Kipf and Welling (2017) defined a graph convolutional network (GCN) layer for a node \(v\) with weights (\(W^{(l)}\)), activation function (\(\sigma\)) as

\[ h_{v}^{(l)} = \sigma \left( W^{(l)} \sum_{u \in N(v)} \frac{1}{|N(v)|} h_{u}^{(l-1)} \right) \]

  • Hamilton, Ying, and Leskovec (2017) then proposed a generalisation

\[ h_{v}^{(l)} = \sigma \left( W^{(l)} \ {\scriptstyle COMBINE} \left( h_{v}^{l-1}, {\scriptstyle AGGREGATE} \left( \bigl\{ h_{u}^{(l-1)}, \forall u \in N(v) \bigl\} \right) \right) \right) \]


► Research Question: Can we use them to study urban form (and function)?

Graph AutoEncoder

Unsupervised learning of nodes representations

  • 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

Graph AutoEncoder (some details)

Pre-processing

  • random 1% of nodes from 137 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
  • three-layer encoder
    • two GINE (Hu et al. 2020) layers
      • 64 hidden features
    • one linear layer
      • 64 features to 2 embeddings
  • trained for 1000 epochs
    • AdamW optimiser
    • 0.0001 learning rate
    • random 80% 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)

Results

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

 

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

 

Baselines comparison

Node embeddings Ego-graph emb.
Measure Fist dimension Second dimension Fist dimension Second dimension
Node in city
closeness centrality 0.262*** -0.194*** 0.365*** -0.337***
betweenness centrality 0.242*** -0.026*** 0.117*** -0.155***
Ego-graph
count of nodes -0.033*** -0.104*** -0.138*** -0.226***
count of edges 0.013* -0.101*** -0.068*** -0.213***
average node degree 0.261*** 0.005 0.377*** 0.037***
total edge length 0.210*** -0.131*** 0.208*** -0.246***
average edge length 0.370*** -0.045*** 0.580*** -0.022***
average count of streets per node 0.280*** -0.232*** 0.431*** -0.421***
count of intersections 0.047*** -0.144*** -0.019*** -0.302***
total street segment length 0.192*** -0.163*** 0.190*** -0.315***
count of street segments 0.009 -0.134*** -0.070*** -0.285***
average street segment length 0.365*** -0.044*** 0.589*** -0.015*
average street circuity -0.028*** 0.131*** -0.066*** 0.225***

Conclusions

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

  • merely a first exploratory study
    • 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

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

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
Nanjing University of Information Science and Technology, China
003732@nuist.edu.cn

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

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.
Hamilton, Will, Zhitao Ying, and Jure Leskovec. 2017. “Inductive Representation Learning on Large Graphs.” In Advances in Neural Information Processing Systems, edited by I. Guyon, U. Von Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett. Vol. 30. Curran Associates, Inc. https://proceedings.neurips.cc/paper_files/paper/2017/file/5dd9db5e033da9c6fb5ba83c7a7ebea9-Paper.pdf.
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. 2017. “Semi-Supervised Classification with Graph Convolutional Networks.” https://arxiv.org/abs/1609.02907.