Augmented Multi-Component Recurrent Graph Convolutional Network for Traffic Flow Forecasting
Abstract
:1. Introduction
- We propose an augmented multi-component module to capture the characteristics of the periodic temporal shift in traffic series by adding the temporal shift representations to the periodic representations.
- We propose the Temporal Correlation Learner (TCL) which incorporates one-dimensional convolution into LSTM and combine it with graph convolution in encoder–decoder architecture to handle the spatial–temporal correlations in the road network.
- Extensive experiments on two real-world traffic datasets, PEMSD4 and PEMSD8, verify that our AM-RGCN achieves state-of-the-art results compared with the existing approaches.
2. Related Work
2.1. Traffic Flow Forecasting
2.2. Graph Convolution Networks
3. Preliminaries
4. Methodology
4.1. Augmented Multi-Component Module for Periodic Temporal Shift
- (1)
- Recent component
- (2)
- Daily augmented component
- (3)
- Weekly augmented component
4.2. Encoder for Spatial–Temporal Correlations
4.2.1. Graph Convolution in Spatial Dimension
4.2.2. Temporal Correlation Learner (TCL) in Temporal Dimension
4.3. Decoder for Multi-Step Prediction
5. Experiment
5.1. Datasets
5.2. Model Parameter
5.3. Evaluation Metric
5.4. Baseline
- Historical Average (HA). We use the average of the past 12 time slices in the same period as a week ago to forecast the current time slice.
- ARIMA [2]. A typical traditional forecasting model for time series. We set the auto-regressive coefficient , difference coefficient , moving average coefficient .
- LSTM [22]. A special RNN model for time series prediction. We set historical traffic flow and the hidden size .
- Gated Recurrent Unit (GRU) network [23]. An improved RNN model for time series prediction. We set historical traffic flow and the hidden size as 64.
- STGCN [9]. The model employs one-dimensional convolution and graph convolution to extract spatial–temporal features, which are widely used in traffic flow forecasting. Both the graph convolution kernel size and temporal convolution kernel size are set to 3 in the experiments.
- MSTGCN [13]. A multi-component network for traffic flow forecasting. The best combinations adopted in this paper are , , and .
- ASTGCN [18]. A traffic flow forecasting model, which adds spatial–temporal attention to the MSTGCN. The best combinations adopted in this paper are , , and .
- STSGCN [28]. A traffic forecasting model which attempts to capture the complex localized spatial–temporal correlations in spatial–temporal data. The best setting consists of 4 STSGCLs, each STSGCM contains 3 graph convolutional operations with 64, 64, 64 filters, separately.
5.5. Results and Analysis
5.5.1. Baseline Comparison
5.5.2. Effects of Augmented Multi-Component Module
5.5.3. Effects of Temporal Correlation Learner
6. Conclusions and Future Work
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
- Lv, Y.; Duan, Y.; Kang, W.; Li, Z.; Wang, F.Y. Traffic Flow Prediction with Big Data: A Deep Learning Approach. IEEE Trans. Intell. Transp. Syst. 2014, 16, 865–873. [Google Scholar] [CrossRef]
- Levin, M.; Tsao, Y.D. On Forecasting Freeway Occupancies and Volumes. Transp. Res. Rec. 1980, 173, 47–49. [Google Scholar]
- Okutani, I.; Stephanedes, Y.J. Dynamic Prediction of Traffic Volume through Kalman Filtering Theory. Transp. Res. Part B Methodol. 1984, 18, 1–11. [Google Scholar] [CrossRef]
- Wu, C.H.; Ho, J.M.; Lee, D.T. Travel-Time Prediction with Support Vector Regression. IEEE Trans. Intell. Transp. Syst. 2004, 5, 276–281. [Google Scholar] [CrossRef] [Green Version]
- Zhang, L.; Liu, Q.; Yang, W.; Wei, N.; Dong, D. An Improved K-nearest Neighbor Model for Short-Term Traffic Flow Prediction. Procedia-Soc. Behav. Sci. 2013, 96, 653–662. [Google Scholar] [CrossRef] [Green Version]
- Ma, X.; Tao, Z.; Wang, Y.; Yu, H.; Wang, Y. Long Short-Term Memory Neural Network for Traffic Speed Prediction Using Remote Microwave Sensor Data. Transp. Res. Part C 2015, 54, 187–197. [Google Scholar] [CrossRef]
- Rui, F.; Zuo, Z.; Li, L. Using LSTM and GRU Neural Network Methods for Traffic Flow Prediction. In Proceedings of the 2016 31st Youth Academic Annual Conference of Chinese Association of Automation (YAC), Wuhan, China, 11–13 November 2016; pp. 324–328. [Google Scholar] [CrossRef]
- Li, Y.; Yu, R.; Shahabi, C.; Liu, Y. Diffusion Convolutional Recurrent Neural Network: Data-Driven Traffic Forecasting. In Proceedings of the International Conference on Learning Representations (ICLR), Vancouver, BC, Canada, 30 April–3 May 2018. [Google Scholar]
- Yu, B.; Yin, H.; Zhu, Z. Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting. In Proceedings of the International Joint Conference on Artificial Intelligence, Stockholm, Sweden, 13–19 July 2018; pp. 3634–3640. [Google Scholar]
- Li, F.; Feng, J.; Yan, H.; Jin, G.; Jin, D.; Li, Y. Dynamic Graph Convolutional Recurrent Network for Traffic Prediction: Benchmark and Solution. arXiv 2021, arXiv:2104.14917. [Google Scholar]
- Yang, T.; Tang, X.; Liu, R. Dual Temporal Gated Multi-graph Convolution Network for Taxi Demand Prediction. Neural Comput. Appl. 2021, 1–16. [Google Scholar] [CrossRef]
- Zhang, J.; Zheng, Y.; Qi, D. Deep Spatio-Temporal Residual Networks for Citywide Crowd Flows Prediction. In Proceedings of the AAAI Conference on Artificial Intelligence, San Francisco, CA, USA, 4–9 February 2017; pp. 1655–1661. [Google Scholar]
- Feng, N.; Guo, S.; Song, C.; Zhu, Q.; Wan, H. Multi-component Spatial-Temporal Graph Convolution Networks for Traffic Flow Forecasting. J. Softw. 2019, 30, 759–769. [Google Scholar]
- Roy, A.; Roy, K.K.; Ahsan Ali, A.; Amin, M.A.; Rahman, A. SST-GNN: Simplified Spatio-Temporal Traffic Forecasting Model Using Graph Neural Network. In Proceedings of the Pacific-Asia Conference on Knowledge Discovery and Data Mining, Delhi, India, 11–14 May 2021; pp. 90–102. [Google Scholar]
- Chen, K.; Deng, M.; Shi, Y. A Temporal Directed Graph Convolution Network for Traffic Forecasting Using Taxi Trajectory Data. ISPRS Int. J. Geo-Inf. 2021, 10, 624. [Google Scholar] [CrossRef]
- Ou, J.; Sun, J.; Zhu, Y.; Jin, H.; Liu, Y.; Zhang, F.; Huang, J.; Wang, X. STP-Trellisnets: Spatial-Temporal Parallel Trellisnets for Metro Station Passenger Flow Prediction. In Proceedings of the 29th ACM International Conference on Information & Knowledge Management, Online. 19–23 October 2020; pp. 1185–1194. [Google Scholar]
- An, J.; Guo, L.; Liu, W.; Fu, Z.; Ren, P.; Liu, X.; Li, T. IGAGCN: Information Geometry and Attention-based Spatiotemporal Graph Convolutional Networks for Traffic Flow Prediction. Neural Netw. 2021, 143. [Google Scholar] [CrossRef]
- Guo, S.; Lin, Y.; Feng, N.; Song, C.; Wan, H. Attention Based Spatial-Temporal Graph Convolutional Networks for Traffic Flow Forecasting. In Proceedings of the AAAI Conference on Artificial Intelligence, Hilton Hawaiian Village, HI, USA, 27 January–1 February 2019; Volume 33, pp. 922–929. [Google Scholar]
- Miglani, A.; Kumar, N. Deep Learning Models for Traffic Flow Prediction in Autonomous Vehicles: A Review, Solutions, and Challenges. Veh. Commun. 2019, 20, 100184. [Google Scholar] [CrossRef]
- Zheng, L.; Yang, J.; Chen, L.; Sun, D.; Liu, W. Dynamic Spatial-Temporal Feature Optimization with ERI Big Data for Short-Term Traffic Flow Prediction. Neurocomputing 2020, 412, 339–350. [Google Scholar] [CrossRef]
- Oliveira, D.D.; Rampinelli, M.; Tozatto, G.Z.; Andreão, R.V.; Müller, S.M. Forecasting Vehicular Traffic Flow using MLP and LSTM. Neural Comput. Appl. 2021, 33, 17245–17256. [Google Scholar] [CrossRef]
- Hochreiter, S.; Schmidhuber, J. Long Short-Term Memory. Neural Comput. 1997, 9, 1735–1780. [Google Scholar]
- Chung, J.; Gulcehre, C.; Cho, K.; Bengio, Y. Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling. arXiv 2014, arXiv:1412.3555. [Google Scholar]
- Ma, X.; Zhuang, D.; Zhengbing, H.; Jihui, M.; Yong, W.; Yunpeng, W. Learning Traffic as Images: A Deep Convolutional Neural Network for Large-Scale Transportation Network Speed Prediction. Sensors 2017, 17, 818. [Google Scholar] [CrossRef] [Green Version]
- Yu, H.; Zhihai, W.; Shuqin, W.; Yunpeng, W.; Xiaolei, M. Spatiotemporal Recurrent Convolutional Networks for Traffic Prediction in Transportation Networks. Sensors 2017, 17, 1501. [Google Scholar] [CrossRef] [Green Version]
- Kipf, T.N.; Welling, M. Semi-Supervised Classification with Graph Convolutional Networks. In Proceedings of the International Conference on Learning Representations (ICLR), Toulon, France, 24–26 April 2017. [Google Scholar]
- Zhao, L.; Song, Y.; Zhang, C.; Liu, Y.; Wang, P.; Lin, T.; Deng, M.; Li, H. T-GCN: A Temporal Graph Convolutional Network for Traffic Prediction. IEEE Trans. Intell. Transp. Syst. 2019, 21, 3848–3858. [Google Scholar] [CrossRef] [Green Version]
- Song, C.; Lin, Y.; Guo, S.; Wan, H. Spatial-Temporal Synchronous Graph Convolutional Networks: A New Framework for Spatial-Temporal Network Data Forecasting. In Proceedings of the AAAI Conference on Artificial Intelligence, New York, NY, USA, 7–12 February 2020; Volume 34, pp. 914–921. [Google Scholar]
- Bai, J.; Zhu, J.; Song, Y.; Zhao, L.; Hou, Z.; Du, R.; Li, H. A3T-GCN: Attention Temporal Graph Convolutional Network for Traffic Forecasting. ISPRS Int. J. Geo-Inf. 2021, 10, 485. [Google Scholar] [CrossRef]
- Chen, W.; Chen, L.; Xie, Y.; Cao, W.; Gao, Y.; Feng, X. Multi-Range Attentive Bicomponent Graph Convolutional Network for Traffic Forecasting. In Proceedings of the AAAI Conference on Artificial Intelligence, New York, NY, USA, 7–12 February 2020; pp. 3529–3536. [Google Scholar] [CrossRef]
- Zheng, C.; Fan, X.; Wang, C.; Qi, J. Gman: A Graph Multi-Attention Network for Traffic Prediction. In Proceedings of the AAAI Conference on Artificial Intelligence, New York, NY, USA, 7–12 February 2020; Volume 34, pp. 1234–1241. [Google Scholar] [CrossRef]
- Zhang, X.; Huang, C.; Xu, Y.; Xia, L. Spatial-Temporal Convolutional Graph Attention Networks for Citywide Traffic Flow Forecasting. In Proceedings of the 29th ACM International Conference on Information & Knowledge Management, Online. 19–23 October 2020; pp. 1853–1862. [Google Scholar] [CrossRef]
- Yao, H.; Tang, X.; Wei, H.; Zheng, G.; Li, Z. Revisiting Spatial-Temporal Similarity: A Deep Learning Framework for Traffic Prediction. In Proceedings of the AAAI Conference on Artificial Intelligence, Hilton Hawaiian Village, HI, USA, 27 January–1 February 2019; Volume 33, pp. 5668–5675. [Google Scholar]
- Hamilton, W.; Ying, Z.; Leskovec, J. Inductive Representation Learning on Large Graphs. In Proceedings of the 31st International Conference on Neural Information Processing Systems, Long Beach, CA, USA, 4–9 December 2017; pp. 1025–1035. [Google Scholar]
- Veličković, P.; Cucurull, G.; Casanova, A.; Romero, A.; Lio, P.; Bengio, Y. Graph Attention Networks. In Proceedings of the International Conference on Learning Representations (ICLR), Toulon, France, 24–26 April 2017. [Google Scholar]
- Bruna, J.; Zaremba, W.; Szlam, A.; LeCun, Y. Spectral Networks and Locally Connected Networks on Graphs. In Proceedings of the International Conference on Learning Representations (ICLR), Banff, AB, Canada, 14–16 April 2014. [Google Scholar]
- Defferrard, M.; Bresson, X.; Vandergheynst, P. Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering. Adv. Neural Inf. Process. Syst. 2016, 29, 3844–3852. [Google Scholar]
- Shi, X.; Chen, Z.; Wang, H.; Yeung, D.Y.; Wong, W.K.; Woo, W.c. Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting. Adv. Neural Inf. Process. Syst. 2015, 28, 802–810. [Google Scholar]
- Kingma, D.P.; Ba, J. Adam: A Method for Stochastic Optimization. arXiv 2014, arXiv:1412.6980. [Google Scholar]
- Srivastava, N.; Hinton, G.; Krizhevsky, A.; Sutskever, I.; Salakhutdinov, R. Dropout: A Simple Way to Prevent Neural Networks from Overfitting. J. Mach. Learn. Res. 2014, 15, 1929–1958. [Google Scholar]
Datasets | Nodes | Edges | Interval | Time Range | Time Steps |
---|---|---|---|---|---|
PEMSD4 | 307 | 340 | 5 min | 1 January 2018–28 February 2018 | 16,992 |
PEMSD8 | 170 | 295 | 5 min | 1 July 2016–31 August 2016 | 17,856 |
Data | Method | 15 min | 30 min | 1 h | |||
---|---|---|---|---|---|---|---|
RMSE | MAE | RMSE | MAE | RMSE | MAE | ||
PEMSD8 | HA | 40.14 | 23.15 | 41.49 | 24.64 | 46.37 | 29.20 |
ARIMA [2] | 28.96 | 27.77 | 30.38 | 29.59 | 48.33 | 44.25 | |
LSTM [22] | 26.02 | 17.95 | 28.35 | 19.68 | 32.56 | 22.61 | |
GRU [23] | 25.92 | 17.97 | 28.35 | 19.71 | 31.80 | 22.18 | |
STGCN [9] | 24.58 | 16.33 | 27.31 | 17.91 | 31.24 | 20.85 | |
MSTGCN [13] | 22.38 | 15.15 | 23.90 | 16.09 | 25.46 | 17.11 | |
ASTGCN [18] | 21.81 | 14.76 | 23.33 | 15.71 | 24.40 | 16.33 | |
STSGCN [28] | 21.93 | 14.20 | 23.71 | 15.28 | 26.05 | 16.67 | |
AM-RGCN | 20.43 | 13.54 | 21.77 | 14.58 | 22.87 | 15.03 | |
PEMSD4 | HA | 45.40 | 28.88 | 46.96 | 30.40 | 53.20 | 35.59 |
ARIMA [2] | 36.91 | 33.71 | 46.65 | 41.36 | 52.32 | 47.74 | |
LSTM [22] | 34.00 | 22.02 | 35.81 | 23.34 | 38.81 | 25.58 | |
GRU [23] | 34.17 | 22.05 | 35.88 | 23.45 | 38.84 | 25.83 | |
STGCN [9] | 32.77 | 21.34 | 34.07 | 21.78 | 37.42 | 24.32 | |
MSTGCN [13] | 28.97 | 19.40 | 30.61 | 20.49 | 32.71 | 22.01 | |
ASTGCN [18] | 29.19 | 19.59 | 30.26 | 20.32 | 32.37 | 21.83 | |
STSGCN [28] | 29.74 | 18.52 | 31.52 | 19.73 | 33.63 | 21.06 | |
AM-RGCN | 27.22 | 18.00 | 28.25 | 18.65 | 29.79 | 19.82 |
Method | Multi-Component | 1 h | |||
---|---|---|---|---|---|
RMSE | MAE | ||||
AM-RGCN | ✓ | 36.61 | 25.08 | ||
✓ | 34.80 | 22.34 | |||
✓ | 25.03 | 17.00 | |||
✓ | ✓ | 32.91 | 22.13 | ||
✓ | ✓ | 24.56 | 16.85 | ||
✓ | ✓ | 24.53 | 16.71 | ||
✓ | ✓ | ✓ | 22.87 | 15.03 |
Method | Augmented Multi-Component | ||
---|---|---|---|
RMSE | MAE | Dataset | |
AM-CNN-GCN | 24.31 | 16.00 | |
AM-LSTM-GCN | 26.85 | 18.19 | PEMSD8 |
AM-RGCN | 22.87 | 15.03 |
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Zhang, C.; Zhou, H.-Y.; Qiu, Q.; Jian, Z.; Zhu, D.; Cheng, C.; He, L.; Liu, G.; Wen, X.; Hu, R. Augmented Multi-Component Recurrent Graph Convolutional Network for Traffic Flow Forecasting. ISPRS Int. J. Geo-Inf. 2022, 11, 88. https://doi.org/10.3390/ijgi11020088
Zhang C, Zhou H-Y, Qiu Q, Jian Z, Zhu D, Cheng C, He L, Liu G, Wen X, Hu R. Augmented Multi-Component Recurrent Graph Convolutional Network for Traffic Flow Forecasting. ISPRS International Journal of Geo-Information. 2022; 11(2):88. https://doi.org/10.3390/ijgi11020088
Chicago/Turabian StyleZhang, Chi, Hong-Yu Zhou, Qiang Qiu, Zhichun Jian, Daoye Zhu, Chengqi Cheng, Liesong He, Guoping Liu, Xiang Wen, and Runbo Hu. 2022. "Augmented Multi-Component Recurrent Graph Convolutional Network for Traffic Flow Forecasting" ISPRS International Journal of Geo-Information 11, no. 2: 88. https://doi.org/10.3390/ijgi11020088
APA StyleZhang, C., Zhou, H.-Y., Qiu, Q., Jian, Z., Zhu, D., Cheng, C., He, L., Liu, G., Wen, X., & Hu, R. (2022). Augmented Multi-Component Recurrent Graph Convolutional Network for Traffic Flow Forecasting. ISPRS International Journal of Geo-Information, 11(2), 88. https://doi.org/10.3390/ijgi11020088