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Coupled Layer-wise Graph Convolution for Transportation Demand Prediction
Junchen Ye, Leilei Sun, Bowen Du, Yanjie Fu, Hui Xiong
TL;DR
Existing transportation GCNs often rely on heuristic adjacency matrices that inadequately represent real and multi-level spatial dependence. The paper proposes CCRNN, which learns coupled layer-wise graph structures and integrates them with recurrent temporal modeling. On NYC Citi Bike and NYC Taxi datasets, CCRNN achieves state-of-the-art results, including lower RMSE than Graph WaveNet.
Problem
Existing transportation GCNs commonly use heuristic adjacency matrices that cannot accurately reflect spatial relationships or adaptively capture multi-level demand dependence.
Method
CCRNN uses self-learned, layer-varying adjacency matrices coupled across layers, aggregates their representations, and integrates them with a gated recurrent unit.
Results
13.85% and 26.85% RMSE lower than Graph WaveNet on two datasets.
Takeaways & Limitations
CCRNN achieves the best performance across all evaluation metrics on NYC Citi Bike and NYC Taxi datasets.
Abstract
from arXiv · showhide
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.
Introduction
Transportation demand prediction is crucial for allocating transport resources, yet existing GCN-based approaches leave adaptive and hierarchical spatial dependence insufficiently addressed. The paper proposes CCRNN, combining self-learned layer-wise graph convolution, coupling, multi-level aggregation, and recurrent modeling.
- Precise regional demand forecasts can support advance resource allocation, rebalancing, and improved daily travel service.
- Existing transportation prediction research progressed from regional statistical analysis to deep learning models for spatio-temporal correlations.
- Most GCN approaches use heuristically fixed adjacency matrices and do not adequately model hierarchical spatial dependence.
- CCRNN introduces CGC with self-learned adjacency matrices that vary across layers to extract multi-level spatial dependence adaptively.
- A layer-wise coupling mechanism links upper- and lower-level topological structures while reducing computational costs.
- A unitary sequence-to-sequence framework integrates multi-level spatial hidden states with a gated recurrent unit for prediction.
Related Work
Related work spans statistical, deep learning, and graph convolutional approaches to transportation prediction. Existing graph methods improve non-Euclidean modeling but generally retain initial adjacency structures, limiting efficient multi-level dependence capture.
- Early transportation prediction methods combined data mining with empirical statistics but handled limited regions and missed simultaneous spatio-temporal correlations.
- GCNs generalize convolutional neural networks to non-Euclidean data and have attracted increasing research attention.
- Graph convolutional networks are commonly categorized into spatial-based and spectral-based methods.
- Spatial methods aggregate neighboring features, whereas spectral methods focus on graph-signal filtering and filter structure.
- Existing methods generally leverage an initial adjacency matrix or its variants, making efficient and accurate multi-level dependence capture difficult.
Preliminaries
The paper formalizes transportation systems as graphs and defines data-driven adjacency learning and multi-step demand forecasting. It then contrasts conventional fixed-structure propagation with CGC’s layer-varying self-learned representations.
- Station-based transportation maps stations to graph nodes, while station-less demand locations are treated as gathering around discrete places.
- Given historical graph signals, the adjacency matrix A is learned with a data-driven mapping to complete the transportation graph.
- Transportation demand prediction maps P historical graph-signal steps to the next Q forecast steps.
- The normalized adjacency matrix is defined as  = D^-1A, where D contains node degrees.
- Graph propagation uses a K-step diffusion process with filter parameters θ applied to input signals X.
- Conventional graph convolutions use an initial adjacency matrix and its powers, whereas CGC learns varying adjacency matrices across layers for hierarchical representations.
Methodology
CCRNN constructs transportation graphs from data-driven station similarities, then uses coupled layer-wise graph convolutions to model multi-level spatial dependence and a recurrent architecture to model temporal dynamics.
- Adjacency Matrix Generation: CCRNN generates adjacency matrices from compact station representations obtained by decomposing graph-signal data with SVD.The station-wise representation Xs captures compact, high-level station features, and pairwise similarity determines adjacency edge weights.
- Transportation Graph Construction: The framework uses a unified graph formalization for station-based and station-less transportation.Station nodes represent fixed infrastructure, while concentrated pickup and drop-off locations can form virtual stations.
- Coupled Layer-wise Graph Convolution: CGC assigns different adjacency matrices to different graph-convolution layers to capture multi-level spatial dependence.The layer outputs are recursively connected, with A(m) varying across layers.
- Coupled Layer-wise Graph Convolution: A coupled mapping constructs upper-level adjacency matrices from lower-level matrices and reduces parameterization through shared low-dimensional node embeddings.The mapping parameters are shared between E1 and E2, with each coupled mapping using L × (L + 1) parameters.
- Coupled Layer-wise Graph Convolution: The first-layer adjacency matrix is initialized from the original graph structure and optimized with stochastic gradient descent to discover spatial relationships.This replaces purely random initialization while retaining end-to-end adaptation.
- Temporal Dependence Modeling: Attention aggregates representations from all graph-convolution layers before feeding the result into CCGRU for sequence-to-sequence forecasting.The recurrent unit uses reset and update gates, while scheduled sampling supports multi-step prediction.
Experiments
Experiments evaluate CCRNN on NYC Citi Bike and NYC Taxi against multiple baselines and across forecast horizons. CCRNN achieves the strongest reported overall and multi-step results, while ablations support adaptive, coupled adjacency learning.
- Experimental Setup: Experiments use NYC Citi Bike and NYC Taxi datasets, comparing CCRNN with seven forecasting baselines.The baselines include HA, XGBoost, FC-LSTM, DCRNN, STGCN, STG2Seq, and Graph WaveNet.
- Experimental Setup: The study retains 250 bike stations and clusters taxi orders into 266 virtual stations within an 8.42km × 14.45km region.Demand is modeled with half-hour time steps, using the first two of the last four weeks for validation and the last two for testing.
- Main Results: CCRNN achieves the best performance on all evaluation metrics across both NYC datasets.Models are evaluated on multi-step outputs, and each baseline is trained 10 times for an average result.
- Main Results: 13.85% and 26.85% lower RMSE than Graph WaveNet on the two datasets indicates more accurate and efficient transportation-demand dependency capture.Graph WaveNet remains competitive because it learns an adaptive adjacency matrix.
- Multi-step Demand Prediction: Across selected 0.5-, 2.5-, 4.5-, and 6.0-hour horizons, CCRNN achieves the lowest RMSE and highest PCC despite sequence-to-sequence performance decline.Graph WaveNet is stable across horizons but has lower short-term accuracy, while DCRNN declines as forecast time increases.
- Ablation Study: The complete CCRNN outperforms its ablated variants, while distance- and PCC-initialized variants still outperform all Table 1 baselines.Randomly initializing the embedding matrices produces PCC below 0.1, indicating that proper adjacency initialization is necessary for training.
Conclusion
The paper concludes that CCRNN combines layer-specific self-learned graph structures, layer-wise coupling, multi-level aggregation, and recurrent prediction for transportation demand forecasting. Experiments on taxi and bike datasets achieve state-of-the-art results.
- Conclusion: CCRNN uses CGC with self-learned adjacency matrices that vary across layers to capture multi-level spatial dependence.A layer-wise coupling mechanism bridges upper- and lower-level graph structures and reduces model parameter scale.
- Conclusion: A multi-level aggregation module weights extracted representations before a unitary network fuses them for final predictions.The paper frames this architecture as integrating spatial representations with recurrent prediction.
- Conclusion: Experiments on real-world taxi and sharing-bike datasets report state-of-the-art results for CCRNN.The paper presents the model as a new perspective on graph convolution with layer-wise adjacency matrices.