A Comprehensive Overview of the Traffic Flow Prediction Model Considering Spatial Correlation of Non-Neighboring Nodes

A Comprehensive Overview of the Traffic Flow Prediction Model Considering Spatial Correlation of Non-Neighboring Nodes

Introduction

Traffic flow prediction is a fundamental research area in intelligent transportation systems, aiming to forecast future traffic conditions based on historical road information. Accurate traffic prediction is crucial for urban traffic management and smart mobility applications. However, existing models often struggle to explicitly capture the spatial correlations between non-neighboring nodes, which limits their predictive performance.

Traditional traffic prediction approaches can be categorized into statistical models, machine learning models, and deep learning models. Statistical models, such as autoregressive integrated moving average (ARIMA) and Kalman filters, are simple and computationally efficient but perform poorly on nonlinear and complex traffic data. Machine learning models, including support vector machines (SVM) and k-nearest neighbors (KNN), improved prediction accuracy but still required extensive feature engineering. With the advancement of deep learning, models like recurrent neural networks (RNN) and convolutional neural networks (CNN) have been widely adopted due to their strong nonlinear modeling capabilities.

However, most deep learning models are designed for Euclidean data, such as images, whereas traffic data is inherently non-Euclidean, distributed over road networks. To address this, graph neural networks (GNNs) have been introduced to model spatial dependencies by aggregating information from neighboring nodes. Models such as STGCN and DCRNN demonstrated the effectiveness of GNNs in traffic prediction. Further improvements incorporated attention mechanisms and adaptive graph structures to enhance temporal and spatial feature extraction.

Despite these advancements, conventional graph-based models are limited to pairwise relationships, making it difficult to capture higher-order spatial correlations among non-neighboring nodes. For instance, traffic sensors located near similar functional areas (e.g., shopping districts) may exhibit correlated patterns even without direct physical connections. To overcome this limitation, hypergraph theory has been introduced, allowing hyperedges to connect multiple nodes simultaneously, thereby modeling complex spatial relationships beyond pairwise connections.

This paper proposes a novel Double Attention Hypergraph Convolutional Neural Network (A2HGCN) to explicitly model spatiotemporal correlations, particularly among non-neighboring nodes. The model constructs hyperedges based on node similarity and connectivity, then employs hypergraph convolution and line graph convolution to capture multi-node spatial relationships. Additionally, a convolutional long short-term memory (ConvLSTM) network with a dual attention mechanism is used to extract temporal features. Experimental results on real-world datasets demonstrate that A2HGCN outperforms baseline models across various prediction horizons.

Background and Related Work

Graph and Hypergraph Theory

Traffic networks are typically represented as graphs, where nodes denote sensors and edges denote connections between them. The adjacency matrix encodes pairwise relationships, where a value of 1 indicates a direct connection and 0 otherwise. However, graphs are limited in capturing higher-order relationships among multiple nodes.

Hypergraphs extend this concept by allowing hyperedges to connect multiple nodes simultaneously. A hypergraph is defined by its node set and hyperedge set, represented via an incidence matrix. Unlike traditional graphs, hypergraphs can model complex spatial dependencies among non-neighboring nodes, making them suitable for traffic prediction tasks where multiple sensors may exhibit correlated behavior.

Hypergraph Learning in Traffic Prediction

Recent studies have explored hypergraph neural networks (HGNNs) for traffic prediction. Early models like HGNN applied graph convolution to hypergraphs, while subsequent works introduced dynamic hypergraphs and attention mechanisms. However, existing approaches either ignore hyperedge-to-hyperedge relationships or rely on distance-based hypergraph construction, which may be sensitive to parameter choices.

To address these limitations, A2HGCN integrates hypergraph convolution with line graph convolution, enabling the model to capture both node-level and hyperedge-level spatial dependencies. Additionally, the dual attention mechanism enhances temporal feature extraction, improving prediction accuracy.

Methodology

Hypergraph Construction

The proposed model constructs hyperedges by identifying nodes with similar traffic patterns using Pearson correlation coefficients. Nodes with a correlation above a threshold (e.g., 0.6) are grouped into hyperedges. The final hypergraph combines these similarity-based hyperedges with the original road network adjacency matrix to ensure both local and global spatial relationships are captured.

Spatial Feature Extraction

Hypergraph Convolution

Hypergraph convolution operates by propagating node features through hyperedges, aggregating information from multiple connected nodes. The process involves computing the hypergraph Laplacian, which encodes node relationships, and applying spectral convolution to extract spatial features. The model simplifies the convolution operation to reduce computational complexity while maintaining expressive power.

Line Graph Convolution

To capture relationships between hyperedges, the model transforms the hypergraph into a line graph, where each node represents a hyperedge, and edges denote shared nodes between hyperedges. Graph convolution is then applied to the line graph, enabling the model to learn higher-order spatial dependencies.

Temporal Feature Extraction

A ConvLSTM network enhanced with a dual attention mechanism is employed to model temporal patterns. The attention mechanism consists of feature aggregation and feature distribution steps, where global features are first aggregated and then adaptively distributed to each node based on local relevance. This approach strengthens the model’s ability to capture long-term dependencies and dynamic traffic patterns.

Model Training and Optimization

The model is trained using the Adam optimizer with an initial learning rate of 0.001 and early stopping to prevent overfitting. The loss function is mean absolute error (MAE), and evaluation metrics include MAE, mean absolute percentage error (MAPE), and root mean square error (RMSE).

Experimental Results

Datasets

Experiments were conducted on two real-world traffic datasets:
• PEMS-BAY: Contains traffic speed data from 325 sensors in California, collected from January to June 2017.

• PEMSM: Includes traffic speed data from 228 sensors in California, collected from May to June 2012.

The datasets were split into training (70%), validation (10%), and test (20%) sets, with input data normalized using Z-score standardization.

Baseline Models

The proposed A2HGCN was compared against several state-of-the-art models, including:
• HA (Historical Average): A simple statistical baseline.

• LSTNet: Combines CNN and LSTM for multivariate time-series prediction.

• STGCN: Uses Chebyshev polynomial-based graph convolution.

• DCRNN: Integrates diffusion convolution with RNN.

• Graph WaveNet: Learns adaptive adjacency matrices.

• GMAN: Uses spatiotemporal attention blocks.

• MTGNN: Employs mixed-hop propagation for spatial dependencies.

• AGCRN: Incorporates node-adaptive parameter learning.

• SAGCN-SST: Integrates self-attention with GCN.

Performance Comparison

A2HGCN achieved superior performance across all prediction horizons (15, 30, and 60 minutes). Key findings include:
• On PEMS-BAY, A2HGCN reduced MAE by 7.5% (15 min), 6.2% (30 min), and 4.3% (60 min) compared to the best baseline.

• On PEMSM, the model improved MAE by 7.6% (15 min), 7.8% (30 min), and 3.4% (60 min) over SAGCN-SST.

• The model consistently outperformed adaptive graph-based approaches (e.g., MTGNN, AGCRN), demonstrating the effectiveness of hypergraph-based spatial modeling.

Ablation Study

Ablation experiments confirmed the contributions of each component:
• Removing the dual attention mechanism (HGCN) degraded long-term prediction performance.

• Using only hypergraph convolution (A2sHGCN) or line graph convolution (A2LGCN) reduced accuracy, highlighting the importance of capturing both node-level and hyperedge-level relationships.

Case Study

Visualizations of predicted vs. actual traffic speeds demonstrated that A2HGCN accurately captured peak and trough patterns, even in highly dynamic scenarios. While some time lag was observed during rapid fluctuations, the model’s predictions remained closer to ground truth compared to baselines.

Conclusion

The A2HGCN model addresses a critical limitation in traffic prediction by explicitly modeling spatial correlations among non-neighboring nodes using hypergraph theory. By combining hypergraph convolution, line graph convolution, and a dual attention-enhanced ConvLSTM, the model effectively captures complex spatiotemporal dependencies. Experimental results on real-world datasets validate its superiority over existing approaches.

Future work will explore dynamic hypergraph construction and directional hypergraphs to further enhance spatial modeling. Additionally, integrating Transformer-based architectures may improve long-term forecasting capabilities. The proposed framework can also be extended to other spatiotemporal prediction tasks, such as crowd flow forecasting and air quality prediction.

doi.org/10.19734/j.issn.1001-3695.2024.07.0261

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