Can graph convolution network learn spatial relations ?

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This document discusses using graph convolutional networks to learn spatial relations from geographic data represented as graphs. It presents experiments on (1) detecting alignments between linear geographic features and (2) selecting roads from a generalized network that should be kept or erased at a target map scale. For alignment detection, proximity criteria were used to modify the graph and convolutional networks with attribute features predicted alignments with 72% accuracy. For road selection, features like length and importance were used and the method classified 72% of sections correctly with 73% precision and 83% recall. The document concludes graph convolutional networks show promise for learning spatial relations from graph-represented geographic data.

Technology

Can Graph
ConvolutionNetworks
LearnSpatial Relations ?
Azelle Courtial, Guillaume Touya , Xiang Zhang
LASTIG, Univ Gustave Eiffel, ENSG, IGN, France
1

Plan
• Introduction
• Motivation : Graph modelisation of geographic information.
• Definitions : Graph and deep learning principle.
• Methods : Graph convolution network.
• Alignement detection
• Road selection
• Conclusion
2

Graph modelisation of geographic
information
3
(Mackaness and
Beard, 1993)
(Zhang et al., 2013)
(Bader et al., 2013)

Graph modelisation of geographic
information
Some geographic objects have a direct
representationas a graph:
transportationand hydrographic
networks.
Spatialrelationbetween
geographic object can be
model in a graph.
The vector shape of
object can be encoding as
edge and node.
(Yan et al., 2020)
4

Learning about graph
Node attribute prediction
Graph classification
Link prediction
7

Deep learning principles
Input
examples Graph convolution
Target
examples
Prediction
Comparison
8
Weight adjustement

Deep learning principles
Input
examples Graph convolution
Target
examples
Prediction
Comparison
9
Weight adjustement

Graph convolution
10
Deep series of informationencoding and decoding layer.
Attribut
matrix
× Adjacency matrix
× Weight

Alignement detection
Experiment
1 2
3 4
13

Alignement detection
Proximity structures
Proximity criteria
Remove edge with a distanceabove
a threshold.
Add edge with a low weight
comparing to the weight of
the shortest path between its nodes.
Criteria from (Bader et al., 2005)
14

Alignement detection
Attributes
17
Elongation difference Area difference
Orientationdifference
Facing ratio
(Wang et al., 2019)

Alignement detection
Results
18
Annotation /
Prediction
Curvilinear
alignements
Straight
alignements
No
alignements
Total
Curvilinear
alignements
1125 34 1412 2571
Straight
alignements
66 1196 2662 3924
No
alignement
819 1746 9919 12484
Total 2010 2976 13993 18979

Road selection
21
Generalised road network (for 1:50k)
Detailedroad network (for 1:25k)

Road selection
Structure change cases
22
Erased at target scale
Kept at target scale
Annotation

Road selection
Attributes
23
Edge length Importance Sinuosity
Betweness centrality Face size Stroke length

Road selection
Results
25
Annotation
/ Prediction
Deleted Kept Total
Deleted 3098 1280 4378
Kept 2313 6246 8559
Total 5411 7526 12937
72% of section are well classified
Precision: 73%
Recall : 83%

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