{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,18]],"date-time":"2025-10-18T15:14:09Z","timestamp":1760800449653,"version":"build-2065373602"},"reference-count":58,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,4,3]],"date-time":"2021-04-03T00:00:00Z","timestamp":1617408000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the Natural Science Foundation of Shandong Province, China","award":["ZR2020MD020"],"award-info":[{"award-number":["ZR2020MD020"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJGI"],"abstract":"<jats:p>Accurate prediction of citywide short-term metro passenger flow is essential to urban management and transport scheduling. Recently, an increasing number of researchers have applied deep learning models to passenger flow prediction. Nevertheless, the task is still challenging due to the complex spatial dependency on the metro network and the time-varying traffic patterns. Therefore, we propose a novel deep learning architecture combining graph attention networks (GAT) with long short-term memory (LSTM) networks, which is called the hybrid GLM (hybrid GAT and LSTM Model). The proposed model captures the spatial dependency via the graph attention layers and learns the temporal dependency via the LSTM layers. Moreover, some external factors are embedded. We tested the hybrid GLM by predicting the metro passenger flow in Shanghai, China. The results are compared with the forecasts from some typical data-driven models. The hybrid GLM gets the smallest root-mean-square error (RMSE) and mean absolute percentage error (MAPE) in different time intervals (TIs), which exhibits the superiority of the proposed model. In particular, in the TI 10 min, the hybrid GLM brings about 6\u201330% extra improvements in terms of RMSE. We additionally explore the sensitivity of the model to its parameters, which will aid the application of this model.<\/jats:p>","DOI":"10.3390\/ijgi10040222","type":"journal-article","created":{"date-parts":[[2021,4,3]],"date-time":"2021-04-03T22:03:36Z","timestamp":1617487416000},"page":"222","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["A Hybrid GLM Model for Predicting Citywide Spatio-Temporal Metro Passenger Flow"],"prefix":"10.3390","volume":"10","author":[{"given":"Yong","family":"Han","sequence":"first","affiliation":[{"name":"College of Information Science and Engineering, Ocean University of China, No. 238, Songling Road, Qingdao 266100, China"},{"name":"Laboratory for Regional Oceanography and Numerical Modeling, Qingdao National Laboratory for Marine Science and Technology, No. 1, Wenhai Road, Qingdao 266237, China"}]},{"given":"Tongxin","family":"Peng","sequence":"additional","affiliation":[{"name":"College of Information Science and Engineering, Ocean University of China, No. 238, Songling Road, Qingdao 266100, China"},{"name":"Laboratory for Regional Oceanography and Numerical Modeling, Qingdao National Laboratory for Marine Science and Technology, No. 1, Wenhai Road, Qingdao 266237, China"}]},{"given":"Cheng","family":"Wang","sequence":"additional","affiliation":[{"name":"Center of Grassroots Governance Led by the Chinese Communist Party in Shibei District, No. 161, Tailiu Road, Qingdao 266000, China"},{"name":"Big Data Development Bureau of Shibei District, No.161, Tailiu Road, Qingdao 266000, China"}]},{"given":"Zhihao","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Information Science and Engineering, Ocean University of China, No. 238, Songling Road, Qingdao 266100, China"},{"name":"Laboratory for Regional Oceanography and Numerical Modeling, Qingdao National Laboratory for Marine Science and Technology, No. 1, Wenhai Road, Qingdao 266237, China"}]},{"given":"Ge","family":"Chen","sequence":"additional","affiliation":[{"name":"College of Information Science and Engineering, Ocean University of China, No. 238, Songling Road, Qingdao 266100, China"},{"name":"Laboratory for Regional Oceanography and Numerical Modeling, Qingdao National Laboratory for Marine Science and Technology, No. 1, Wenhai Road, Qingdao 266237, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,4,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"783","DOI":"10.1080\/13658816.2017.1413192","article-title":"Inferring spatial interaction patterns from sequential snapshots of spatial distributions","volume":"32","author":"Zhu","year":"2018","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1016\/j.trc.2011.06.009","article-title":"Forecasting the short-term metro passenger flow with empirical mode decomposition and neural networks","volume":"21","author":"Wei","year":"2012","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Dhall, D., Kaur, R., and Juneja, M. (,  2019). Machine Learning: A Review of the Algorithms and Its Applications. Proceedings of the ICRIC 2019, Cham, Switzerland.","DOI":"10.1007\/978-3-030-29407-6_5"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"15232","DOI":"10.1109\/ACCESS.2020.2964680","article-title":"RNN-Based Subway Passenger Flow Rolling Prediction","volume":"8","author":"Sha","year":"2020","journal-title":"IEEE Access"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Yang, D., Yang, H., Wang, P., and Li, S. (2019, January 21\u201323). Multi-Step Traffic Flow Prediction Using Recurrent Neural Network. Proceedings of the 2019 IEEE International Conferences on Ubiquitous Computing & Communications (IUCC) and Data Science and Computational Intelligence (DSCI) and Smart Computing, Networking and Services (SmartCNS), Shenyang, China.","DOI":"10.1109\/IUCC\/DSCI\/SmartCNS.2019.00163"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2150042","DOI":"10.1142\/S0217984921500421","article-title":"Short-term traffic flow prediction based on 1DCNN-LSTM neural network structure","volume":"35","author":"Qiao","year":"2020","journal-title":"Mod. Phys. Lett. B"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"802","DOI":"10.1080\/13658816.2019.1652303","article-title":"A hybrid integrated deep learning model for the prediction of citywide spatio-temporal flow volumes","volume":"34","author":"Ren","year":"2020","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_8","unstructured":"Guo, S., Lin, Y., Feng, N., Song, C., and Wan, H. (February, January 27). Attention Based Spatial-Temporal Graph Convolutional Networks for Traffic Flow Forecasting. Proceedings of the AAAI Conference on Artificial Intelligence, Honolulu, HI, USA."},{"key":"ref_9","unstructured":"Lv, M., Hong, Z., Chen, L., Chen, T., Zhu, T., and Ji, S. (2020). Temporal Multi-Graph Convolutional Network for Traffic Flow Prediction. IEEE Trans. Intell. Transp., 1\u201312."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Ye, J., Zhao, J., Ye, K., and Xu, C. (2020, January 19\u201324). Multi-STGCnet: A Graph Convolution Based Spatial-Temporal Framework for Subway Passenger Flow Forecasting. Proceedings of the 2020 International Joint Conference on Neural Networks (IJCNN), Glasgow, UK.","DOI":"10.1109\/IJCNN48605.2020.9207049"},{"key":"ref_11","unstructured":"Defferrard, M., Bresson, X., and Vandergheynst, P. (2016, January 5\u201310). Convolutional neural networks on graphs with fast localized spectral filtering. Proceedings of the 30th International Conference on Neural Information Processing Systems, Barcelona, Spain."},{"key":"ref_12","unstructured":"Velickovic, P., Cucurull, G., Casanova, A., Romero, A., Li\u00f2, P., and Bengio, Y. (2017). Graph Attention Networks. arXiv."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"012065","DOI":"10.1088\/1742-6596\/1792\/1\/012065","article-title":"Research on Forecast of Rail Traffic Flow Based on ARIMA Model","volume":"1792","author":"Liu","year":"2021","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1111\/gean.12026","article-title":"A Dynamic Spatial Weight Matrix and Localized Space\u2014Time Autoregressive Integrated Moving Average for Network Modeling","volume":"46","author":"Cheng","year":"2014","journal-title":"Geogr. Anal."},{"key":"ref_15","first-page":"1113","article-title":"SARIMA modelling approach for railway passenger flow forecasting","volume":"33","author":"Melichar","year":"2018","journal-title":"Transp. Vilnius"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1016\/S0968-090X(02)00009-8","article-title":"Comparison of parametric and nonparametric models for traffic flow forecasting","volume":"10","author":"Smith","year":"2002","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"9717582","DOI":"10.1155\/2016\/9717582","article-title":"Three Revised Kalman Filtering Models for Short-Term Rail Transit Passenger Flow Prediction","volume":"2016","author":"Jiao","year":"2016","journal-title":"Math. Probl. Eng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1054","DOI":"10.1109\/TITS.2017.2711046","article-title":"Using an ARIMA-GARCH Modeling Approach to Improve Subway Short-Term Ridership Forecasting Accounting for Dynamic Volatility","volume":"19","author":"Ding","year":"2018","journal-title":"IEEE Trans. Intell. Transp."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"120937","DOI":"10.1109\/ACCESS.2019.2937114","article-title":"Short-Term Passenger Flow Prediction in Urban Public Transport: Kalman Filtering Combined K-Nearest Neighbor Approach","volume":"7","author":"Liang","year":"2019","journal-title":"IEEE Access"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Suthaharan, S. (2016). Support Vector Machine. Machine Learning Models and Algorithms for Big Data Classification: Thinking with Examples for Effective Learning, Springer.","DOI":"10.1007\/978-1-4899-7641-3"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"3189238","DOI":"10.1155\/2018\/3189238","article-title":"Forecasting of Short-Term Metro Ridership with Support Vector Machine Online Model","volume":"2018","author":"Wang","year":"2018","journal-title":"J. Adv. Transp."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1080\/18128600902823216","article-title":"Traffic forecasting using least squares support vector machines","volume":"5","author":"Zhang","year":"2009","journal-title":"Transportmetrica"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/j.neucom.2015.03.085","article-title":"A novel wavelet-SVM short-time passenger flow prediction in Beijing subway system","volume":"166","author":"Sun","year":"2015","journal-title":"Neurocomputing"},{"key":"ref_24","first-page":"5","article-title":"The Use of Ls-Svm for Short-Term Passenger Flow Prediction","volume":"26","author":"Chen","year":"2011","journal-title":"Transp. Vilnius"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1186\/s13638-020-01881-4","article-title":"Short-term passenger flow forecast for urban rail transit based on multi-source data","volume":"2021","author":"Li","year":"2021","journal-title":"Eurasip. J. Wirel. Commun. Netw."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Cao, C., and Xu, J. (2007, January 22\u201324). Short-Term Traffic Flow Predication Based on PSO-SVM. Proceedings of the First International Conference on Transportation Engineering, Chengdu, China.","DOI":"10.1061\/40932(246)28"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Roos, J., Bonnevay, S., and Gavin, G. (2016, January 18\u201320). Short-Term Urban Rail Passenger Flow Forecasting: A Dynamic Bayesian Network Approach. Proceedings of the 2016 15th IEEE International Conference on Machine Learning and Applications (ICMLA), Anaheim, CA, USA.","DOI":"10.1109\/ICMLA.2016.0187"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"4515","DOI":"10.1007\/s12652-018-1135-2","article-title":"Applying a multistage of input feature combination to random forest for improving MRT passenger flow prediction","volume":"10","author":"Liu","year":"2019","journal-title":"J. Ambient. Intell. Humaniz. Comput."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"012002","DOI":"10.1088\/1742-6596\/1656\/1\/012002","article-title":"A prediction model of buses passenger flow based on neural networks","volume":"1656","author":"Zhang","year":"2020","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_30","first-page":"1695","article-title":"Short-Term Passenger Flow Forecast in Urban Rail Transit Based on Enhanced K-Nearest Neighbor Approach","volume":"2019","author":"Bai","year":"2019","journal-title":"CICTP"},{"key":"ref_31","unstructured":"Paul, S., and Singh, L. (2015, January 14\u201317). A review on advances in deep learning. Proceedings of the 2015 IEEE Workshop on Computational Intelligence: Theories, Applications and Future Directions (WCI), Kanpur, India."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1109\/72.279188","article-title":"Recurrent neural networks and robust time series prediction","volume":"5","author":"Connor","year":"1994","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"147653","DOI":"10.1109\/ACCESS.2019.2941987","article-title":"Cluster-Based LSTM Network for Short-Term Passenger Flow Forecasting in Urban Rail Transit","volume":"7","author":"Zhang","year":"2019","journal-title":"IEEE Access"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Cho, K., Merrienboer, B.V., Gulcehre, C., Ba Hdanau, D., Bougares, F., Schwenk, H., and Bengio, Y. (2014). Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation. arXiv.","DOI":"10.3115\/v1\/D14-1179"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1049\/iet-its.2016.0208","article-title":"LSTM network: A deep learning approach for short-term traffic forecast","volume":"11","author":"Zhao","year":"2017","journal-title":"IET Intell. Transp. Syst."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"578","DOI":"10.1049\/iet-its.2017.0313","article-title":"Combining Weather Condition Data to Predict Traffic Flow: A GRU Based Deep Learning Approach","volume":"12","author":"Zhang","year":"2018","journal-title":"IET Intell. Transp. Syst."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Han, Y., Wang, C., Ren, Y., Wang, S., Zheng, H., and Chen, G. (2019). Short-Term Prediction of Bus Passenger Flow Based on a Hybrid Optimized LSTM Network. ISPRS Int. J. Geo-Inf., 8.","DOI":"10.3390\/ijgi8090366"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Lin, S., and Tian, H. (2020, January 12\u201314). Short-Term Metro Passenger Flow Prediction Based on Random Forest and LSTM. Proceedings of the 2020 IEEE 4th Information Technology, Networking, Electronic and Automation Control Conference (ITNEC), Chongqing, China.","DOI":"10.1109\/ITNEC48623.2020.9084974"},{"key":"ref_39","first-page":"1097","article-title":"ImageNet Classification with Deep Convolutional Neural Networks","volume":"25","author":"Krizhevsky","year":"2012","journal-title":"Commun. ACM"},{"key":"ref_40","unstructured":"Zhang, J., Zheng, Y., Qi, D., Li, R., and Yi, X. (November, January 31). DNN-based prediction model for spatio-temporal data. Proceedings of the 24th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems, Burlingame, CA, USA."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1016\/j.artint.2018.03.002","article-title":"Predicting citywide crowd flows using deep spatio-temporal residual networks","volume":"259","author":"Zhang","year":"2018","journal-title":"Artif. Intell."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Yu, F., Wei, D., Zhang, S., and Shao, Y. (2019, January 5\u20137). 3D CNN-based Accurate Prediction for Large-scale Traffic Flow. Proceedings of the 2019 4th International Conference on Intelligent Transportation Engineering (ICITE), Singapore.","DOI":"10.1109\/ICITE.2019.8880210"},{"key":"ref_43","unstructured":"Bruna, J., Zaremba, W., Szlam, A., and Lecun, Y. (2013). Spectral Networks and Locally Connected Networks on Graphs. arXiv."},{"key":"ref_44","unstructured":"Kipf, T.N., and Welling, M. (2016). Semi-supervised classification with graph convolutional networks. arXiv."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Yu, B., Yin, H., and Zhu, Z. (2017). Spatio-temporal graph convolutional networks: A deep learning framework for traffic forecasting. arXiv.","DOI":"10.24963\/ijcai.2018\/505"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"3848","DOI":"10.1109\/TITS.2019.2935152","article-title":"T-GCN: A Temporal Graph Convolutional Network for Traffic Prediction","volume":"21","author":"Zhao","year":"2020","journal-title":"IEEE Trans. Intell. Transp."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"1210","DOI":"10.1049\/iet-its.2019.0873","article-title":"Multi-graph convolutional network for short-term passenger flow forecasting in urban rail transit","volume":"14","author":"Zhang","year":"2020","journal-title":"IET Intell. Transp. Syst."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Zhang, J., Chen, F., Cui, Z., Guo, Y., and Zhu, Y. (2020). Deep Learning Architecture for Short-Term Passenger Flow Forecasting in Urban Rail Transit. IEEE Trans. Intell. Transp., 1\u201311.","DOI":"10.1109\/TITS.2020.3000761"},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Huang, Y., Bi, H., Li, Z., Mao, T., and Wang, Z. (November, January 27). STGAT: Modeling Spatial-Temporal Interactions for Human Trajectory Prediction. Proceedings of the 2019 IEEE\/CVF International Conference on Computer Vision (ICCV), Seoul, Korea.","DOI":"10.1109\/ICCV.2019.00637"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"1735","DOI":"10.1162\/neco.1997.9.8.1735","article-title":"Long Short-Term Memory","volume":"9","author":"Hochreiter","year":"1997","journal-title":"Neural Comput."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"107346","DOI":"10.1016\/j.apacoust.2020.107346","article-title":"A novel demodulation system for base band digital modulation signals based on the deep long short-term memory model","volume":"166","author":"Daldal","year":"2020","journal-title":"Appl. Acoust."},{"key":"ref_52","unstructured":"Goodfellow, I., Bengio, Y., Courville, A., and Bengio, Y. (2016). Deep Learning, MIT Press."},{"key":"ref_53","first-page":"2775","article-title":"Introduction to linear regression analysis","volume":"40","author":"Ober","year":"2010","journal-title":"J. R. Stat. Soc."},{"key":"ref_54","doi-asserted-by":"crossref","unstructured":"Xu, Y., and Li, D. (2019). Incorporating Graph Attention and Recurrent Architectures for City-Wide Taxi Demand Prediction. ISPRS Int. J. Geo-Inf., 8.","DOI":"10.3390\/ijgi8090414"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"653","DOI":"10.1016\/j.sbspro.2013.08.076","article-title":"An Improved K-nearest Neighbor Model for Short-term Traffic Flow Prediction","volume":"96","author":"Zhang","year":"2013","journal-title":"Procedia Soc. Behav. Sci."},{"key":"ref_56","doi-asserted-by":"crossref","unstructured":"Ma, X., Dai, Z., He, Z., Ma, J., Wang, Y., and Wang, Y. (2017). Learning Traffic as Images: A Deep Convolutional Neural Network for Large-Scale Transportation Network Speed Prediction. Sensors, 17.","DOI":"10.3390\/s17040818"},{"key":"ref_57","doi-asserted-by":"crossref","unstructured":"Han, Y., Wang, S.K., Ren, Y.B., Wang, C., Gao, P., and Chen, G. (2019). Predicting Station-Level Short-Term Passenger Flow in a Citywide Metro Network Using Spatiotemporal Graph Convolutional Neural Networks. ISPRS Int. J. Geo-Inf., 8.","DOI":"10.3390\/ijgi8060243"},{"key":"ref_58","doi-asserted-by":"crossref","unstructured":"Landassuri-Moreno, V.M., Bustillo-Hern\u00e1ndez, C.L., Carbajal-Hern\u00e1ndez, J.J., and Fern\u00e1ndez, L.P.S. (2013, January 20\u201323). Single-Step-Ahead and Multi-Step-Ahead Prediction with Evolutionary Artificial Neural Networks. Proceedings of the Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications, Havana, Cuba.","DOI":"10.1007\/978-3-642-41822-8_9"}],"container-title":["ISPRS International Journal of Geo-Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2220-9964\/10\/4\/222\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T13:58:16Z","timestamp":1760363896000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2220-9964\/10\/4\/222"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,4,3]]},"references-count":58,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2021,4]]}},"alternative-id":["ijgi10040222"],"URL":"https:\/\/doi.org\/10.3390\/ijgi10040222","relation":{},"ISSN":["2220-9964"],"issn-type":[{"type":"electronic","value":"2220-9964"}],"subject":[],"published":{"date-parts":[[2021,4,3]]}}}