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Hierarchical Frequency-Decomposition Graph Neural Networks for Road Network Representation Learning

Jingtian Ma, Jingyuan Wang, Leong Hou U

TL;DR

This paper tackles the challenge of representing road networks by bridging spatial structure and frequency characteristics. It introduces HiFiNet, a hierarchical graph neural network that builds a three-level segment–locality–region hierarchy and a frequency-decomposition module that separately models and fuses low- and high-frequency signals via a topology-aware transformer. The authors provide theoretical justification showing that hierarchical projections act as a spectral low-pass filter, and they validate the approach with extensive experiments on three real-world datasets across four downstream tasks, achieving superior performance and generalization. Overall, HiFiNet advances road-network representation learning by unifying spatial and spectral perspectives and offers a general spatial–spectral paradigm for graph learning in spatio-temporal domains.

Abstract

Road networks are critical infrastructures underpinning intelligent transportation systems and their related applications. Effective representation learning of road networks remains challenging due to the complex interplay between spatial structures and frequency characteristics in traffic patterns. Existing graph neural networks for modeling road networks predominantly fall into two paradigms: spatial-based methods that capture local topology but tend to over-smooth representations, and spectral-based methods that analyze global frequency components but often overlook localized variations. This spatial-spectral misalignment limits their modeling capacity for road networks exhibiting both coarse global trends and fine-grained local fluctuations. To bridge this gap, we propose HiFiNet, a novel hierarchical frequency-decomposition graph neural network that unifies spatial and spectral modeling. HiFiNet constructs a multi-level hierarchy of virtual nodes to enable localized frequency analysis, and employs a decomposition-updating-reconstruction framework with a topology-aware graph transformer to separately model and fuse low- and high-frequency signals. Theoretically justified and empirically validated on multiple real-world datasets across four downstream tasks, HiFiNet demonstrates superior performance and generalization ability in capturing effective road network representations.

Hierarchical Frequency-Decomposition Graph Neural Networks for Road Network Representation Learning

TL;DR

This paper tackles the challenge of representing road networks by bridging spatial structure and frequency characteristics. It introduces HiFiNet, a hierarchical graph neural network that builds a three-level segment–locality–region hierarchy and a frequency-decomposition module that separately models and fuses low- and high-frequency signals via a topology-aware transformer. The authors provide theoretical justification showing that hierarchical projections act as a spectral low-pass filter, and they validate the approach with extensive experiments on three real-world datasets across four downstream tasks, achieving superior performance and generalization. Overall, HiFiNet advances road-network representation learning by unifying spatial and spectral perspectives and offers a general spatial–spectral paradigm for graph learning in spatio-temporal domains.

Abstract

Road networks are critical infrastructures underpinning intelligent transportation systems and their related applications. Effective representation learning of road networks remains challenging due to the complex interplay between spatial structures and frequency characteristics in traffic patterns. Existing graph neural networks for modeling road networks predominantly fall into two paradigms: spatial-based methods that capture local topology but tend to over-smooth representations, and spectral-based methods that analyze global frequency components but often overlook localized variations. This spatial-spectral misalignment limits their modeling capacity for road networks exhibiting both coarse global trends and fine-grained local fluctuations. To bridge this gap, we propose HiFiNet, a novel hierarchical frequency-decomposition graph neural network that unifies spatial and spectral modeling. HiFiNet constructs a multi-level hierarchy of virtual nodes to enable localized frequency analysis, and employs a decomposition-updating-reconstruction framework with a topology-aware graph transformer to separately model and fuse low- and high-frequency signals. Theoretically justified and empirically validated on multiple real-world datasets across four downstream tasks, HiFiNet demonstrates superior performance and generalization ability in capturing effective road network representations.

Paper Structure

This paper contains 37 sections, 4 theorems, 58 equations, 6 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Road Network Modeling.
  4. Graph Spectral Theory.
  5. Graph Neural Networks.
  6. Preliminaries
  7. Hierarchical Frequency-Decomposition Network
  8. Hierarchical Architecture Modeling
  9. Contextual Embedding for Road Segments.
  10. Locality Graph Construction.
  11. Region Graph Construction.
  12. Low-frequency Feature Propagation.
  13. Frequency Decomposition Modeling
  14. Decomposition Stage.
  15. Updating Stage.
  16. ...and 22 more sections

Key Result

Theorem 1

Let $A_{XY} \in \mathbb{R}^{N_Y \times N_X}$ denote an assignment matrix satisfying the equi-partition and row-normalization properties. Then, the projection of graph signals from the original graph $X$ to the coarsened graph $Y$ approximately preserves the low-frequency energy while attenuating hig

Figures (6)

  • Figure 1: The frequency decomposition of Fourier Transform and HiFiNet on traffic flow signals.
  • Figure 2: The overall framework of HiFiNet.
  • Figure 3: Ablation study of our model on Beijing dataset.
  • Figure 4: Parameter sensitivity of our model on Beijing dataset on label classification task.
  • Figure 5: The t-SNE visualization of road network representations under different frequency configurations.
  • ...and 1 more figures

Theorems & Definitions (13)

  • Definition 1: Road Network
  • Definition 2: Segment Signal
  • Definition 3: Locality
  • Definition 4: Region
  • Definition 5: Hierarchical Road Network
  • Definition 6: Road Network Representation Learning
  • Theorem 1
  • Lemma 1
  • proof
  • Lemma 2
  • ...and 3 more