[Paper Review] Coupled Layer-wise Graph Convolution for Transportation Demand Prediction

Junchen Ye, Leilei Sun+3 more|arXiv (Cornell University)|Dec 15, 2020

Traffic Prediction and Management TechniquesEngineering34 references22 citations

TL;DR

This paper proposes CCRNN, a novel graph convolutional network for transportation demand prediction that uses self-learned, layer-wise adjacency matrices and a coupled layer-wise mechanism to capture multi-level spatial dependencies and temporal dynamics. The model achieves state-of-the-art performance, reducing RMSE by 13.85% and 26.85% over Graph WaveNet on NYC Citi Bike and NYC Taxi datasets, respectively.

ABSTRACT

Graph Convolutional Network (GCN) has been widely applied in transportation demand prediction due to its excellent ability to capture non-Euclidean spatial dependence among station-level or regional transportation demands. However, in most of the existing research, the graph convolution was implemented on a heuristically generated adjacency matrix, which could neither reflect the real spatial relationships of stations accurately, nor capture the multi-level spatial dependence of demands adaptively. To cope with the above problems, this paper provides a novel graph convolutional network for transportation demand prediction. Firstly, a novel graph convolution architecture is proposed, which has different adjacency matrices in different layers and all the adjacency matrices are self-learned during the training process. Secondly, a layer-wise coupling mechanism is provided, which associates the upper-level adjacency matrix with the lower-level one. It also reduces the scale of parameters in our model. Lastly, a unitary network is constructed to give the final prediction result by integrating the hidden spatial states with gated recurrent unit, which could capture the multi-level spatial dependence and temporal dynamics simultaneously. Experiments have been conducted on two real-world datasets, NYC Citi Bike and NYC Taxi, and the results demonstrate the superiority of our model over the state-of-the-art ones.

Motivation & Objective

• To address the limitation of fixed, heuristic adjacency matrices in existing GCNs that fail to capture real spatial relationships and multi-level dependencies in transportation demand.
• To model hierarchical spatial dependencies—such as global weather impacts versus localized traffic incidents—by enabling different adjacency matrices per network layer.
• To reduce parameter scale and computational cost through a layer-wise coupling mechanism that links upper and lower adjacency matrices.
• To integrate spatial representations with temporal dynamics using a gated recurrent unit for end-to-end spatio-temporal prediction.
• To demonstrate the superiority of self-learned adjacency matrices over distance-based or correlation-based initialization in real-world demand prediction.

Proposed method

• Proposes Coupled Layer-wise Graph Convolution (CGC), where each layer uses a distinct, trainable adjacency matrix instead of a fixed one.
• Introduces a layer-wise coupling mechanism that connects the upper-level adjacency matrix to the lower-level one via a learnable transformation, reducing parameter count.
• Employs a multi-level aggregation module to assign dynamic importance to representations from different layers based on their relevance.
• Fuses spatial hidden states from CGC with a gated recurrent unit (GRU) to model temporal dynamics and produce final demand predictions.
• Trains the entire model end-to-end with backpropagation, jointly optimizing adjacency matrices, graph convolutions, and prediction heads.
• Initializes adjacency matrices using adaptive embeddings (E₁⁰, E₂⁰) that are jointly learned during training, avoiding reliance on distance or correlation heuristics.

Experimental results

Research questions

• RQ1 Can self-learned, layer-specific adjacency matrices improve the modeling of multi-level spatial dependencies in transportation demand prediction?
• RQ2 Does a coupled layer-wise mechanism between adjacency matrices reduce parameter complexity while preserving or enhancing predictive performance?
• RQ3 How does the performance of CCRNN compare to state-of-the-art models like Graph WaveNet and DCRNN on real-world datasets?
• RQ4 To what extent do adaptive adjacency matrices outperform heuristic initialization methods such as spatial distance or Pearson correlation?
• RQ5 Can the integration of spatial representations with a GRU effectively model long-term temporal dynamics in demand patterns?

Key findings

• CCRNN achieves the lowest RMSE of 2.8382 on the NYC Citi Bike dataset and 9.5631 on the NYC Taxi dataset, outperforming all baselines.
• The model reduces RMSE by 13.85% and 26.85% compared to Graph WaveNet on the Citi Bike and Taxi datasets, respectively.
• The ablation study shows that random initialization of adjacency matrices leads to poor performance (PCC = 0.0204 on Citi Bike), confirming the necessity of proper initialization.
• Using PCC-based initialization yields a PCC of 0.7851 on Citi Bike and 0.9619 on Taxi, outperforming all baselines but still underperforming the full CCRNN model.
• The no-coupling variant achieves a PCC of 0.7702 on Citi Bike and 0.9594 on Taxi, indicating that coupling improves performance even when adjacency matrices are trainable.
• The complete CCRNN model achieves a PCC of 0.7934 on Citi Bike and 0.9648 on Taxi, demonstrating the effectiveness of the full architecture in capturing complex spatio-temporal dependencies.