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T-GCN: A Temporal Graph Convolutional Network for Traffic Prediction

Ling ZhaoYujiao SongChao ZhangYu LiuPu WangTao LinMin DengHaifeng Li

article2018IEEE Transactions on Intelligent Transportation Systems3,022 citations

Proposes a temporal graph convolutional network that integrates graph convolutions with gated recurrent units to simultaneously capture spatial road topology and dynamic temporal trends for accurate urban traffic forecasting.

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The paper introduces a neural network model called T-GCN to forecast traffic conditions such as speed on urban road networks. Traffic forecasting supports real-time management, congestion avoidance, and long-term planning in intelligent transportation systems, yet remains difficult because traffic volumes depend on both the fixed layout of connected roads and their changing patterns over time.

The work set out to build and test a single model that learns these spatial and temporal relationships together from historical data. The authors combined a graph convolutional network to encode the road network’s topology with a gated recurrent unit to track how conditions evolve, then trained and evaluated the resulting T-GCN on two real-world speed datasets: taxi trajectories covering 156 roads in Shenzhen’s Luohu district and loop-detector readings from 207 sensors on Los Angeles freeways. They compared results against five established baselines across 15- to 60-minute forecast horizons and conducted noise-injection tests to assess robustness.

The T-GCN produced the lowest errors on every horizon and metric, cutting root-mean-square error by roughly 3–58 percent relative to the next-best methods while raising accuracy by 1–41 percent. It maintained stable performance as the forecast window lengthened, unlike several baselines whose errors grew sharply. The model also proved more accurate than versions that used only spatial or only temporal components, confirming that joint modeling adds value. Finally, prediction quality held steady when Gaussian or Poisson noise was added to the input data.

These outcomes indicate that the approach can supply more reliable short- and medium-term speed estimates for traffic control centers and traveler information services, potentially reducing congestion-related delays and improving safety without requiring extensive new sensor infrastructure. Because the architecture is not limited to roads, it offers a practical template for other networked forecasting problems that combine graph structure with time series.

Further testing on additional cities, incident-rich periods, and multi-modal data would strengthen before large-scale deployment; the authors already note that peak-hour errors remain higher than average and suggest exploring richer loss functions or external covariates to address this. The reported gains rest on two mid-sized urban datasets and standard cross-validation, so results should be treated as promising but not yet definitive for every network type or data quality level.

Central South UniversityGeorgia Institute of TechnologyPeking UniversityZhejiang Universitygated recurrent unittemporal correlationstopological structuretemporal graph convolutional networktraffic predictionspatio-temporal traffic forecasting
arXiv: 1811.05320lehaifeng/T-GCN
Cover for T-GCN: A Temporal Graph Convolutional Network for Traffic Prediction

Abstract

Accurate and real-time traffic forecasting plays an important role in the Intelligent Traffic System and is of great significance for urban traffic planning, traffic management, and traffic control. However, traffic forecasting has always been considered an open scientific issue, owing to the constraints of urban road network topological structure and the law of dynamic change with time, namely, spatial dependence and temporal dependence. To capture the spatial and temporal dependence simultaneously, we propose a novel neural network-based traffic forecasting method, the temporal graph convolutional network (T-GCN) model, which is in combination with the graph convolutional network (GCN) and gated recurrent unit (GRU). Specifically, the GCN is used to learn complex topological structures to capture spatial dependence and the gated recurrent unit is used to learn dynamic changes of traffic data to capture temporal dependence. Then, the T-GCN model is employed to traffic forecasting based on the urban road network. Experiments demonstrate that our T-GCN model can obtain the spatio-temporal correlation from traffic data and the predictions outperform state-of-art baselines on real-world traffic datasets. Our tensorflow implementation of the T-GCN is available at this https URL.

Topics

gated recurrent unittemporal correlationstopological structureforecasting modelsattention mechanismconvolutional neural networks

Keywords

temporal graph convolutional networktraffic predictionspatio-temporal traffic forecastingshort-term traffic flow forecastingurban road networktravel time predictionspatio-temporal prediction

Table of Contents

  • I Introduction
  • II Related Work
  • III Methodology
  • III-A Problem Definition
  • III-B Overview
  • III-C Methodology
  • III-C1 Spatial Dependence Modeling
  • III-C2 Temporal Dependence Modeling
  • III-C3 Temporal Graph Convolutional Network
  • III-C4 Loss Function
  • IV Experiments
  • IV-A Data Description
  • IV-B Evaluation Metrics
  • IV-C Model Parameters Designing
  • IV-D Experimental Results
  • IV-E Perturbation Analysis and Robustness
  • IV-F Model Interpretation
  • V Conclusion
  • References

Knowls

  1. Knowl 1 — Spatio-Temporal Road Network Traffic Forecasting Formulation

    definition

    Urban road network traffic forecasting is formulated as predicting future network-wide traffic states over a time horizon TT given historical observations over nn preceding time steps on a topological road graph.

    The road network is defined as an unweighted graph G=(V,E)G = (V, E), where V={v1,v2,…,vN}V = \{v_1, v_2, \dots, v_N\} is the set of NN road segments (nodes) and EE is the set of edges. The network topology is represented by a binary adjacency matrix A∈{0,1}N×NA \in \{0, 1\}^{N \times N}, where Aij=1A_{ij} = 1 denotes a direct topological connection between road viv_i and road vjv_j, and Aij=0A_{ij} = 0 denotes no connection.

    Traffic attributes (such as speed, flow, or density) across the network are represented by a feature matrix X∈RN×PX \in \mathbb{R}^{N \times P}, where PP is the length of the time series history, and Xt∈RNX_t \in \mathbb{R}^N denotes the vector of traffic measurements across all NN nodes at time step tt. The objective of spatio-temporal forecasting is to learn a mapping function ff conditioned on GG:

    [Xt+1,Xt+2,…,Xt+T]=f(G;(Xt−n+1,…,Xt−1,Xt))[X_{t+1}, X_{t+2}, \dots, X_{t+T}] = f\left(G; (X_{t-n+1}, \dots, X_{t-1}, X_t)\right)

  2. Knowl 2 — Spatial Graph Convolution Operator for Road Networks

    equation

    To capture non-Euclidean spatial dependencies dictated by road network topology, a 2-layer Graph Convolutional Network (GCN) feature mapping f(Xt,A)f(X_t, A) is defined using first-order localized spectral graph convolutions:

    f(Xt,A)=σ(A^ ReLU(A^XtW0)W1)f(X_t, A) = \sigma\left( \hat{A} \, \text{ReLU}\left( \hat{A} X_t W_0 \right) W_1 \right)

    where Xt∈RN×dinX_t \in \mathbb{R}^{N \times d_{\text{in}}} is the node attribute feature matrix at time step tt, A∈RN×NA \in \mathbb{R}^{N \times N} is the adjacency matrix, and A^\hat{A} is the symmetrically normalized adjacency matrix with added self-loops:

    A^=D~−12A~D~−12\hat{A} = \tilde{D}^{-\frac{1}{2}} \tilde{A} \tilde{D}^{-\frac{1}{2}}

    A~=A+IN\tilde{A} = A + I_N

    D~ii=∑jA~ij\tilde{D}_{ii} = \sum_{j} \tilde{A}_{ij}

    Here INI_N is the identity matrix of size NN, D~\tilde{D} is the diagonal degree matrix of A~\tilde{A}, W0W_0 and W1W_1 are trainable parameter weight matrices for the first and second graph convolutional layers, ReLU(⋅)=max⁡(0,⋅)\text{ReLU}(\cdot) = \max(0, \cdot) is the rectified linear activation function, and σ(⋅)\sigma(\cdot) is the activation function.

  3. Knowl 3 — Temporal Graph Convolutional Network (T-GCN) Cell Architecture

    model/method

    The Temporal Graph Convolutional Network (T-GCN) integrates graph convolutional operations into a Gated Recurrent Unit (GRU) cell to simultaneously model spatial topology and temporal dynamics in traffic data.

    At time step tt, given the input traffic feature matrix XtX_t, the graph adjacency matrix AA, and the previous hidden state ht−1h_{t-1}, the T-GCN cell computes gate activations and updates the hidden state as follows:

    ut=σ(Wu[f(A,Xt),ht−1]+bu)u_t = \sigma\left(W_u [f(A, X_t), h_{t-1}] + b_u\right)

    rt=σ(Wr[f(A,Xt),ht−1]+br)r_t = \sigma\left(W_r [f(A, X_t), h_{t-1}] + b_r\right)

    ct=tanh⁡(Wc[f(A,Xt),(rt∗ht−1)]+bc)c_t = \tanh\left(W_c [f(A, X_t), (r_t * h_{t-1})] + b_c\right)

    ht=ut∗ht−1+(1−ut)∗cth_t = u_t * h_{t-1} + (1 - u_t) * c_t

    where f(A,Xt)f(A, X_t) is the 2-layer graph convolution mapping; [f(A,Xt),ht−1][f(A, X_t), h_{t-1}] denotes matrix concatenation along the feature dimension; ∗* represents the Hadamard (element-wise) product; utu_t is the update gate controlling how much previous hidden state information is carried over; rtr_t is the reset gate controlling how much historical information is ignored; ctc_t is the candidate hidden state (memory content) at time tt; hth_t is the updated hidden state output; Wu,Wr,WcW_u, W_r, W_c are learnable weight matrices; bu,br,bcb_u, b_r, b_c are learnable bias vectors; σ(⋅)\sigma(\cdot) is the sigmoid function; and tanh⁡(⋅)\tanh(\cdot) is the hyperbolic tangent activation function.

    Final traffic speed predictions across the desired forecasting horizon are generated by passing the recurrent state sequence through a fully connected output layer.

  4. Knowl 4 — T-GCN Loss Function with Regularization

    equation

    The T-GCN model is trained by minimizing a loss function that balances speed prediction error against an L2L_2 weight regularization term to prevent overfitting:

    loss=∥Yt−Y^t∥+λLreg\text{loss} = \| Y_t - \hat{Y}_t \| + \lambda L_{\text{reg}}

    where YtY_t is the matrix of ground-truth traffic speeds on the road network at target time step tt, Y^t\hat{Y}_t is the corresponding predicted speed matrix, ∥⋅∥\| \cdot \| is the prediction error norm, LregL_{\text{reg}} denotes the L2L_2 weight penalty on the model's trainable parameters, and λ\lambda is a regularization hyperparameter.

  5. Knowl 5 — Evaluation Metrics for Multi-Step Traffic Forecasting

    definition

    To assess spatio-temporal traffic speed forecasting accuracy across all network nodes over nn evaluation samples between actual values YY and predictions Y^\hat{Y}, five evaluation metrics are employed:

    1. Root Mean Squared Error (RMSE): RMSE=1n∑i=1n(Yi−Y^i)2\text{RMSE} = \sqrt{\frac{1}{n} \sum_{i=1}^n \left(Y_i - \hat{Y}_i\right)^2}

    2. Mean Absolute Error (MAE): MAE=1n∑i=1n∣Yi−Y^i∣\text{MAE} = \frac{1}{n} \sum_{i=1}^n \left| Y_i - \hat{Y}_i \right|

    3. Accuracy: Accuracy=1−∥Y−Y^∥F∥Y∥F\text{Accuracy} = 1 - \frac{\| Y - \hat{Y} \|_F}{\| Y \|_F} where ∥⋅∥F\| \cdot \|_F denotes the Frobenius norm.

    4. Coefficient of Determination (R2R^2): R2=1−∑i=1n(Yi−Y^i)2∑i=1n(Yi−Yˉ)2R^2 = 1 - \frac{\sum_{i=1}^n (Y_i - \hat{Y}_i)^2}{\sum_{i=1}^n (Y_i - \bar{Y})^2} where Yˉ\bar{Y} is the sample mean of YY.

    5. Explained Variance Score (var\text{var}): var=1−Var{Y−Y^}Var{Y}\text{var} = 1 - \frac{\text{Var}\{Y - \hat{Y}\}}{\text{Var}\{Y\}}

  6. Knowl 6 — Experimental Setup and Traffic Datasets: SZ-taxi and Los-loop

    experimental setup

    T-GCN is evaluated on two real-world traffic speed datasets:

    • SZ-taxi: Taxi trajectory speed data from Shenzhen, China, spanning Jan. 1 to Jan. 31, 2015, on N=156N = 156 major roads in Luohu District. Road spatial connectivity is defined by a 156×156156 \times 156 binary adjacency matrix. Speed measurements are aggregated in 15-minute intervals.
    • Los-loop: Highway traffic speed data collected by N=207N = 207 loop detector sensors in Los Angeles County from Mar. 1 to Mar. 7, 2012. Speeds are aggregated into 5-minute intervals, missing values are imputed via linear interpolation, and the adjacency matrix is computed based on network distances between sensors.

    For both datasets, features are normalized to [0,1][0, 1]. The first 80% of chronological data is allocated for training and the remaining 20% for testing. Predictions are evaluated at horizons of 15, 30, 45, and 60 minutes. The model is trained using the Adam optimizer with a learning rate of 0.0010.001, a batch size of 6464, and 30003000 training epochs.

  7. Knowl 7 — Effect of Hidden Unit Dimensionality on T-GCN Performance

    empirical result

    Varying the number of hidden units in the T-GCN cell across candidate values {8,16,32,64,100,128}\{8, 16, 32, 64, 100, 128\} demonstrates an inverted U-shaped relationship with model precision:

    • For the SZ-taxi dataset (156156 road segments), prediction error (RMSE and MAE) decreases as hidden units increase from 8 to 100, while Accuracy, R2R^2, and Explained Variance (var\text{var}) reach their peaks at 100 hidden units. Increasing to 128 units degrades performance due to increased model complexity and training difficulty. Thus, 100 hidden units is the optimal configuration.
    • For the Los-loop dataset (207207 sensors), prediction accuracy, R2R^2, and extvar ext{var} reach maximum values, and RMSE/MAE reach minimum values, when using 64 hidden units.

  8. Knowl 8 — Multi-Horizon Benchmark Performance of T-GCN across Datasets

    data/table

    The performance of T-GCN and baseline models—History Average (HA), ARIMA, Support Vector Regression (SVR), Graph Convolutional Network (GCN), and Gated Recurrent Unit (GRU)—across 15, 30, 45, and 60-minute prediction horizons on the SZ-taxi and Los-loop datasets is reported below. The symbol ∗* denotes values that are near-zero or negligible.

    TT Metric SZ-taxi Los-loop
    HA ARIMA SVR GCN GRU T-GCN HA ARIMA SVR GCN GRU T-GCN
    15min RMSE 7.9198 8.2151 7.5368 9.2717 4.0483 3.9162 7.4427 10.0439 6.0084 7.7922 5.2182 5.1264
    MAE 5.4969 6.2192 4.9269 7.2606 2.6814 2.7061 4.0145 7.6832 3.7285 5.3525 3.0602 3.1802
    Accuracy 0.6807 0.4278 0.6961 0.6433 0.7178 0.7306 0.8733 0.8275 0.8977 0.8673 0.9109 0.9127
    R2R^2 0.7914 0.0842 0.8111 0.6147 0.8498 0.8541 0.7121 * 0.8123 0.6843 0.8576 0.8634
    var 0.7914 * 0.8121 0.6147 0.8499 0.8626 0.7121 * 0.8146 0.6844 0.8577 0.8634
    30min RMSE 7.9198 8.2123 7.4747 9.3450 4.0769 3.9617 7.4427 9.3450 6.9588 8.3353 6.2802 6.0598
    MAE 5.4969 6.2144 4.9819 7.3211 2.7009 2.7452 4.0145 7.6891 3.7248 5.6118 3.6505 3.7466
    Accuracy 0.6807 0.4281 0.6987 0.6405 0.7158 0.7275 0.8733 0.8275 0.8815 0.8581 0.8931 0.8968
    R2R^2 0.7914 0.0834 0.8142 0.6086 0.8477 0.8523 0.7121 * 0.7492 0.6402 0.7957 0.8098
    var 0.7914 * 0.8144 0.6086 0.8477 0.8523 0.7121 * 0.7523 0.6404 0.7958 0.8100
    45min RMSE 7.9198 8.2132 7.4755 9.4023 4.1002 3.9950 7.4427 10.0508 7.7504 8.8036 7.0343 6.7065
    MAE 5.4969 6.2154 5.0332 7.3704 2.7207 2.7666 4.0145 7.6924 4.1288 5.9534 4.0915 4.1158
    Accuracy 0.6807 0.4280 0.6986 0.6383 0.7142 0.7252 0.8733 0.8273 0.8680 0.8500 0.8801 0.8857
    R2R^2 0.7914 0.0837 0.8141 0.6038 0.8460 0.8509 0.7121 * 0.6899 0.5999 0.7446 0.7679
    var 0.7914 * 0.8142 0.6039 0.8459 0.8509 0.7121 * 0.6947 0.6001 0.7451 0.7684
    60min RMSE 7.9198 8.2063 7.4883 9.4504 4.1241 4.0141 7.4427 10.0538 8.4388 9.2657 7.6621 7.2677
    MAE 5.4969 6.2118 5.0714 7.4120 2.7431 2.7889 4.0145 7.6952 4.5036 6.2892 4.5186 4.6021
    Accuracy 0.6807 0.4282 0.6981 0.6365 0.7125 0.7238 0.8733 0.8273 0.8562 0.8421 0.8694 0.8762
    R2R^2 0.7914 0.0825 0.8135 0.5998 0.8442 0.8503 0.7121 * 0.6336 0.5583 0.6980 0.7283
    var 0.7914 * 0.8136 0.5999 0.8321 0.8504 0.7121 * 0.5593 0.5593 0.6984 0.7290

    T-GCN achieves the lowest RMSE and highest Accuracy, R2R^2, and Explained Variance across all horizons on both datasets, reducing prediction error by approximately 1.5%–57.8% compared to baseline models. Methods incorporating temporal recurrent units (T-GCN, GRU) substantially outperform purely spatial GCN models, while T-GCN's spatial graph convolutions further improve upon GRU across all horizons (e.g., reducing 15-min RMSE on SZ-taxi by 3.3% relative to GRU and 57.8% relative to GCN).

  9. Knowl 9 — Noise Robustness under Gaussian and Poisson Perturbations

    empirical result

    The robustness of T-GCN against real-world data collection noise was evaluated by injecting two types of synthetic random noise into normalized traffic data:

    1. Gaussian noise: N(0,σ2)\mathcal{N}(0, \sigma^2) with σ∈{0.2,0.4,0.8,1.0,2.0}\sigma \in \{0.2, 0.4, 0.8, 1.0, 2.0\}.
    2. Poisson noise: P(λ)\mathcal{P}(\lambda) with λ∈{1,2,4,8,16}\lambda \in \{1, 2, 4, 8, 16\}.

    All noise-perturbed input matrices were normalized back to [0,1][0, 1]. Across all test noise levels σ\sigma and λ\lambda on both the SZ-taxi and Los-loop datasets, the evaluation metrics (RMSE, MAE, Accuracy, R2R^2, and var\text{var}) displayed minimal variation, indicating that T-GCN possesses strong noise immunity and maintains stable forecasting precision under sensor noise.

  10. Knowl 10 — Peak-Value Smoothing and Low-Flow Sensitivity Limitations in T-GCN

    limitation

    Visual inspection of road-level traffic speed predictions across time horizons reveals two primary limitations of the T-GCN model:

    1. Over-smoothing at Sharp Peaks: T-GCN predicts traffic speeds less accurately at extreme peak moments (rush hours). This is attributed to the GCN component defining smooth filters in the Fourier domain that operate over localized graph neighborhoods, which spatially smooths rapid local fluctuations and flattens acute peaks.
    2. Relative Error Discrepancies during Zero/Low-Traffic Periods: In instances where road segments experience absence of vehicular probes (yielding zero-value records), or when traffic speeds are very low, small absolute deviations in predictions result in disproportionately large relative errors.

Coverage note — None was omitted; all core architectural components, mathematical formulations, experimental configurations, empirical benchmark tables, perturbation findings, and stated model limitations are fully represented.

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Citation

MLA
Zhao, L., et al. “T-GCN: A Temporal Graph Convolutional Network for Traffic Prediction”. IEEE Transactions on Intelligent Transportation Systems, vol. 21, no. 9, 2020, pp. 3848–58, https://doi.org/10.1109/TITS.2019.2935152.
APA
Zhao, L., Song, Y., Zhang, C., Liu, Y., Wang, P., Lin, T., Deng, M., & Li, H. (2020). T-GCN: A Temporal Graph Convolutional Network for Traffic Prediction. IEEE Transactions on Intelligent Transportation Systems, 21(9), 3848–3858. https://doi.org/10.1109/TITS.2019.2935152
Chicago
Zhao, L., Y. Song, C. Zhang, et al. 2020. “T-GCN: A Temporal Graph Convolutional Network for Traffic Prediction”. IEEE Transactions on Intelligent Transportation Systems 21 (9): 3848–58. https://doi.org/10.1109/TITS.2019.2935152.
Harvard
Zhao, L. et al. (2020) “T-GCN: A Temporal Graph Convolutional Network for Traffic Prediction”, IEEE Transactions on Intelligent Transportation Systems, 21(9), pp. 3848–3858. Available at: https://doi.org/10.1109/TITS.2019.2935152.
Vancouver
1. Zhao L, Song Y, Zhang C, Liu Y, Wang P, Lin T, Deng M, Li H (2020) T-GCN: A Temporal Graph Convolutional Network for Traffic Prediction. IEEE Transactions on Intelligent Transportation Systems 21:3848–3858

BibTeX

@article{Zhao_2020, title={T-GCN: A Temporal Graph Convolutional Network for Traffic Prediction}, volume={21}, ISSN={1558-0016}, url={http://dx.doi.org/10.1109/TITS.2019.2935152}, DOI={10.1109/tits.2019.2935152}, number={9}, journal={IEEE Transactions on Intelligent Transportation Systems}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Zhao, Ling and Song, Yujiao and Zhang, Chao and Liu, Yu and Wang, Pu and Lin, Tao and Deng, Min and Li, Haifeng}, year={2020}, month=Sept, pages={3848–3858} }
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