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Generic Multimodal Spatially Graph Network for Spatially Embedded Network Representation Learning

Xudong Fan, Jürgen Hackl

TL;DR

This work introduces GMu-SGCN, a Generic Multimodal Spatially Graph Convolutional Network designed for spatially embedded networks by fusing multimodal node and edge spatial features. It presents two variants, RSGCN and ESGCN, and a network reconstruction-based evaluation framework for edge existence prediction. Through case studies on river and power networks, GMu-SGCN consistently outperforms baselines, demonstrating the importance of incorporating multidimensional spatial features. The findings highlight modality-dependent effects on SEN topology and establish a scalable, memory-efficient approach for spatially informed network representation learning.

Abstract

Spatially embedded networks (SENs) represent a special type of complex graph, whose topologies are constrained by the networks' embedded spatial environments. The graph representation of such networks is thereby influenced by the embedded spatial features of both nodes and edges. Accurate network representation of the graph structure and graph features is a fundamental task for various graph-related tasks. In this study, a Generic Multimodal Spatially Graph Convolutional Network (GMu-SGCN) is developed for efficient representation of spatially embedded networks. The developed GMu-SGCN model has the ability to learn the node connection pattern via multimodal node and edge features. In order to evaluate the developed model, a river network dataset and a power network dataset have been used as test beds. The river network represents the naturally developed SENs, whereas the power network represents a man-made network. Both types of networks are heavily constrained by the spatial environments and uncertainties from nature. Comprehensive evaluation analysis shows the developed GMu-SGCN can improve accuracy of the edge existence prediction task by 37.1\% compared to a GraphSAGE model which only considers the node's position feature in a power network test bed. Our model demonstrates the importance of considering the multidimensional spatial feature for spatially embedded network representation.

Generic Multimodal Spatially Graph Network for Spatially Embedded Network Representation Learning

TL;DR

This work introduces GMu-SGCN, a Generic Multimodal Spatially Graph Convolutional Network designed for spatially embedded networks by fusing multimodal node and edge spatial features. It presents two variants, RSGCN and ESGCN, and a network reconstruction-based evaluation framework for edge existence prediction. Through case studies on river and power networks, GMu-SGCN consistently outperforms baselines, demonstrating the importance of incorporating multidimensional spatial features. The findings highlight modality-dependent effects on SEN topology and establish a scalable, memory-efficient approach for spatially informed network representation learning.

Abstract

Spatially embedded networks (SENs) represent a special type of complex graph, whose topologies are constrained by the networks' embedded spatial environments. The graph representation of such networks is thereby influenced by the embedded spatial features of both nodes and edges. Accurate network representation of the graph structure and graph features is a fundamental task for various graph-related tasks. In this study, a Generic Multimodal Spatially Graph Convolutional Network (GMu-SGCN) is developed for efficient representation of spatially embedded networks. The developed GMu-SGCN model has the ability to learn the node connection pattern via multimodal node and edge features. In order to evaluate the developed model, a river network dataset and a power network dataset have been used as test beds. The river network represents the naturally developed SENs, whereas the power network represents a man-made network. Both types of networks are heavily constrained by the spatial environments and uncertainties from nature. Comprehensive evaluation analysis shows the developed GMu-SGCN can improve accuracy of the edge existence prediction task by 37.1\% compared to a GraphSAGE model which only considers the node's position feature in a power network test bed. Our model demonstrates the importance of considering the multidimensional spatial feature for spatially embedded network representation.

Paper Structure

This paper contains 15 sections, 8 equations, 10 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related work and motivation
  3. Methods
  4. GMu-SGCN Model
  5. The variations of GMu-SGCN
  6. Link prediction task for SENs
  7. Model performance evaluation
  8. Case study
  9. River Network
  10. Power Network
  11. Results and Discussion
  12. Evaluation
  13. Prediction results of the River Network
  14. Reconstruction results of the Power Network
  15. Conclusion

Figures (10)

  • Figure 1: Spatially Embedded Networks ($x_v$ represents the node's point feature, $r_v$ represents the node's regional feature, $p_v^y, p_v^x$ represent the node's position feature, and $e_{v,u}$ represents the edge feature between node $u$, and $v$.)
  • Figure 2: GMu-SGCN layer illustration
  • Figure 3: Overall framework for link prediction
  • Figure 4: River Network Maps
  • Figure 5: A random subgraph sampled from Oregon River Network
  • ...and 5 more figures