{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:02:43Z","timestamp":1760144563436,"version":"build-2065373602"},"reference-count":45,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2024,4,30]],"date-time":"2024-04-30T00:00:00Z","timestamp":1714435200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Beijing Natural Science Foundation","award":["L211026","12171462"],"award-info":[{"award-number":["L211026","12171462"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["L211026","12171462"],"award-info":[{"award-number":["L211026","12171462"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Spatiotemporal information on individual trajectories in urban rail transit is important for operational strategy adjustment, personalized recommendation, and emergency command decision-making. However, due to the lack of journey observations, it is difficult to accurately infer unknown information from trajectories based only on AFC and AVL data. To address the problem, this paper proposes a spatiotemporal probabilistic graphical model based on adaptive expectation maximization attention (STPGM-AEMA) to achieve the reconstruction of individual trajectories. The approach consists of three steps: first, the potential train alternative set and the egress time alternative set of individuals are obtained through data mining and combinatorial enumeration. Then, global and local potential variables are introduced to construct a spatiotemporal probabilistic graphical model, provide the inference process for unknown events, and state information about individual trajectories. Further, considering the effect of missing data, an attention mechanism-enhanced expectation-maximization algorithm is proposed to achieve maximum likelihood estimation of individual trajectories. Finally, typical datasets of origin-destination pairs and actual individual trajectory tracking data are used to validate the effectiveness of the proposed method. The results show that the STPGM-AEMA method is more than 95% accurate in recovering missing information in the observed data, which is at least 15% more accurate than the traditional methods (i.e., PTAM-MLE and MPTAM-EM).<\/jats:p>","DOI":"10.3390\/e26050388","type":"journal-article","created":{"date-parts":[[2024,4,30]],"date-time":"2024-04-30T09:50:07Z","timestamp":1714470607000},"page":"388","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Spatiotemporal Probabilistic Graphical Model Based on Adaptive Expectation-Maximization Attention for Individual Trajectory Reconstruction Considering Incomplete Observations"],"prefix":"10.3390","volume":"26","author":[{"given":"Xuan","family":"Sun","sequence":"first","affiliation":[{"name":"School of Traffic and Transportation, Beijing Jiaotong University, No. 3 Shangyuancun, Haidian District, Beijing 100044, China"},{"name":"State Key Laboratory of Advanced Rail Autonomous Operation, Beijing Jiaotong University, No. 3 Shangyuancun, Haidian District, Beijing 100044, China"}]},{"given":"Jianyuan","family":"Guo","sequence":"additional","affiliation":[{"name":"School of Traffic and Transportation, Beijing Jiaotong University, No. 3 Shangyuancun, Haidian District, Beijing 100044, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6519-8316","authenticated-orcid":false,"given":"Yong","family":"Qin","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Advanced Rail Autonomous Operation, Beijing Jiaotong University, No. 3 Shangyuancun, Haidian District, Beijing 100044, China"}]},{"given":"Xuanchuan","family":"Zheng","sequence":"additional","affiliation":[{"name":"School of Traffic and Transportation, Beijing Jiaotong University, No. 3 Shangyuancun, Haidian District, Beijing 100044, China"},{"name":"Beijing Urban Construction Design & Development Group Co., Ltd., No. 5 Fuchengmen North Street, Xicheng District, Beijing 100032, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9636-038X","authenticated-orcid":false,"given":"Shifeng","family":"Xiong","sequence":"additional","affiliation":[{"name":"NCMIS, KLSC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-4142-0891","authenticated-orcid":false,"given":"Jie","family":"He","sequence":"additional","affiliation":[{"name":"School of Traffic and Transportation, Beijing Jiaotong University, No. 3 Shangyuancun, Haidian District, Beijing 100044, China"},{"name":"State Key Laboratory of Advanced Rail Autonomous Operation, Beijing Jiaotong University, No. 3 Shangyuancun, Haidian District, Beijing 100044, China"}]},{"given":"Qi","family":"Sun","sequence":"additional","affiliation":[{"name":"Beijing Metro Network Administration Co., Ltd., No. 6 Xiaoying North Road, Chaoyang District, Beijing 100020, China"}]},{"given":"Limin","family":"Jia","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Advanced Rail Autonomous Operation, Beijing Jiaotong University, No. 3 Shangyuancun, Haidian District, Beijing 100044, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,4,30]]},"reference":[{"key":"ref_1","unstructured":"Beijing Transport Institute (2023). Beijing Transport Development Annual Report, Beijing Transport Institute."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"102896","DOI":"10.1016\/j.trc.2020.102896","article-title":"Passenger itinerary inference model for congested urban rail networks","volume":"123","author":"Zhu","year":"2021","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"8878011","DOI":"10.1155\/2021\/8878011","article-title":"A Review of Traffic Congestion Prediction Using Artificial Intelligence","volume":"2021","author":"Akhtar","year":"2021","journal-title":"J. Adv. Transp."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"354","DOI":"10.1016\/j.tra.2022.10.011","article-title":"Modeling the effect of real-time crowding information (RTCI) on passenger distribution in trains","volume":"166","author":"Peftitsi","year":"2022","journal-title":"Transp. Res. Part A Policy Pract."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"12014","DOI":"10.1109\/TITS.2021.3109428","article-title":"Individual Mobility Prediction in Mass Transit Systems Using Smart Card Data: An Interpretable Activity-Based Hidden Markov Approach","volume":"23","author":"Mo","year":"2022","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_6","first-page":"440","article-title":"A review of passenger flow assignment model and algorithm for urban rail transit network","volume":"37","author":"Zhou","year":"2017","journal-title":"Syst. Eng. Theory Pract."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"5451017","DOI":"10.1155\/2022\/5451017","article-title":"Data-Driven Method for Passenger Path Choice Inference in Congested Subway Network","volume":"2022","author":"Su","year":"2022","journal-title":"Complexity"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1016\/j.trb.2023.05.004","article-title":"Estimation of recursive route choice models with incomplete trip observations","volume":"173","author":"Mai","year":"2023","journal-title":"Transp. Res. Part B Methodol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"101368","DOI":"10.1016\/j.compenvurbsys.2019.101368","article-title":"Inferring demographics from human trajectories and geographical context","volume":"77","author":"Wu","year":"2019","journal-title":"Comput. Environ. Urban Syst."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"18337","DOI":"10.1109\/TITS.2022.3171332","article-title":"GLTC: A Metro Passenger Identification Method across AFC Data and Sparse WiFi Data","volume":"23","author":"Zhao","year":"2022","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"472","DOI":"10.1016\/j.apm.2024.03.013","article-title":"Logistic model for pattern inference of subway passenger flows based on fare collection and vehicle location data","volume":"130","author":"Li","year":"2024","journal-title":"Appl. Math. Model."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1002\/asmb.2660","article-title":"Statistical estimation in passenger-to-train assignment models based on automated data","volume":"38","author":"Xiong","year":"2021","journal-title":"Appl. Stoch. Models Bus. Ind."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1311","DOI":"10.1016\/j.ins.2022.06.034","article-title":"An unsupervised approach for semantic place annotation of trajectories based on the prior probability","volume":"607","author":"Cheng","year":"2022","journal-title":"Inf. Sci."},{"key":"ref_14","first-page":"921","article-title":"Deep Trajectory Recovery with Fine-Grained Calibration using Kalman Filter","volume":"33","author":"Wang","year":"2021","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1137","DOI":"10.1109\/TVT.2015.2409815","article-title":"Spatiotemporal Segmentation of Metro Trips Using Smart Card Data","volume":"65","author":"Zhang","year":"2016","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1066","DOI":"10.1109\/TIV.2023.3336048","article-title":"A Novel Fault-Tolerant Scheme for Multi-Model Ensemble Estimation of Tire Road Friction Coefficient with Missing Measurements","volume":"9","author":"Wang","year":"2024","journal-title":"IEEE Trans. Intell. Veh."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3135","DOI":"10.1109\/TITS.2017.2679179","article-title":"Spatio-Temporal Analysis of Passenger Travel Patterns in Massive Smart Card Data","volume":"18","author":"Zhao","year":"2017","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2035","DOI":"10.1007\/s11116-020-10120-0","article-title":"Probabilistic model for destination inference and travel pattern mining from smart card data","volume":"48","author":"Cheng","year":"2020","journal-title":"Transportation"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/j.trb.2018.12.015","article-title":"Integrating Lagrangian and Eulerian observations for passenger flow state estimation in an urban rail transit network: A space-time-state hyper network-based assignment approach","volume":"121","author":"Shang","year":"2019","journal-title":"Transp. Res. Part B Methodol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"522","DOI":"10.1016\/j.trb.2017.04.012","article-title":"A probabilistic Passenger-to-Train Assignment Model based on automated data","volume":"104","author":"Zhu","year":"2017","journal-title":"Transp. Res. Part B Methodol."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1016\/j.trc.2015.01.001","article-title":"An integrated Bayesian approach for passenger flow assignment in metro networks","volume":"52","author":"Sun","year":"2015","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"57","DOI":"10.3141\/2284-07","article-title":"Model of Passenger Flow Assignment for Urban Rail Transit Based on Entry and Exit Time Constraints","volume":"2284","author":"Zhou","year":"2012","journal-title":"Transp. Res. Rec."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1574","DOI":"10.1109\/TITS.2018.2852726","article-title":"Calibrating a Bayesian Transit Assignment Model Using Smart Card Data","volume":"20","author":"Rahbar","year":"2019","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"129175","DOI":"10.1016\/j.physa.2023.129175","article-title":"A new approach on passenger flow assignment with multi-connected agents","volume":"628","author":"Yu","year":"2023","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"731","DOI":"10.1007\/s11116-010-9290-0","article-title":"Estimation method for railway passengers\u2019 train choice behavior with smart card transaction data","volume":"37","author":"Kusakabe","year":"2010","journal-title":"Transportation"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Sun, L., Lee, D.-H., Erath, A., and Huang, X. (2012, January 12). Using smart card data to extract passenger\u2019s spatio-temporal density and train\u2019s trajectory of MRT system. Proceedings of the ACM SIGKDD International Workshop on Urban Computing, Beijing, China.","DOI":"10.1145\/2346496.2346519"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"539756","DOI":"10.1155\/2015\/539756","article-title":"Splitting Travel Time Based on AFC Data: Estimating Walking, Waiting, Transfer, and In-Vehicle Travel Times in Metro System","volume":"2015","author":"Zhang","year":"2015","journal-title":"Discret. Dyn. Nat. Soc."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"354","DOI":"10.1080\/15230406.2022.2039775","article-title":"Interactive visual analytics of moving passenger flocks using massive smart card data","volume":"49","author":"Zhang","year":"2022","journal-title":"Cartogr. Geogr. Inf. Sci."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Lin, M., Huang, Z., Zhao, T., Zhang, Y., and Wei, H. (2022). Spatiotemporal Evolution of Travel Pattern Using Smart Card Data. Sustainability, 14.","DOI":"10.3390\/su14159564"},{"key":"ref_30","first-page":"100816","article-title":"Unravelling individual mobility temporal patterns using longitudinal smart card data","volume":"43","author":"Cats","year":"2022","journal-title":"Res. Transp. Bus. Manag."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1583","DOI":"10.1109\/TITS.2017.2728704","article-title":"Measuring Regularity of Individual Travel Patterns","volume":"19","author":"Koutsopoulos","year":"2018","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"04022065","DOI":"10.1061\/JTEPBS.0000721","article-title":"Recognizing Real-Time Transfer Patterns between Metro and Bus Systems Based on Spatial\u2013Temporal Constraints","volume":"148","author":"Wu","year":"2022","journal-title":"J. Transp. Eng. Part A Syst."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Zhang, Y., Yao, E., Wei, H., and Zheng, K. (2017). A constrained multinomial Probit route choice model in the metro network: Formulation, estimation and application. PLoS ONE, 12.","DOI":"10.1371\/journal.pone.0178789"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"103044","DOI":"10.1016\/j.trc.2021.103044","article-title":"Transit OD matrix estimation using smartcard data: Recent developments and future research challenges","volume":"125","author":"Hussain","year":"2021","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"102037","DOI":"10.1016\/j.tre.2020.102037","article-title":"Data-driven approach for solving the route choice problem with traveling backward behavior in congested metro systems","volume":"142","author":"Yu","year":"2020","journal-title":"Transp. Res. Part E Logist. Transp. Rev."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"787","DOI":"10.1016\/j.physa.2019.04.231","article-title":"Data-driven model for passenger route choice in urban metro network","volume":"524","author":"Wu","year":"2019","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1016\/j.tra.2010.12.004","article-title":"A topological route choice model for metro","volume":"45","author":"Raveau","year":"2011","journal-title":"Transp. Res. Part A Policy Pract."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1016\/j.tra.2014.05.010","article-title":"A behavioural comparison of route choice on metro networks: Time, transfers, crowding, topology and socio-demographics","volume":"66","author":"Raveau","year":"2014","journal-title":"Transp. Res. Part A Policy Pract."},{"key":"ref_39","unstructured":"Fu, Q. (2014). Modelling Route Choice Behaviour with Incomplete Data: An Application to the London Underground. [Ph.D. Thesis, The University of Leeds]."},{"key":"ref_40","first-page":"1516","article-title":"Probabilistic Forecasting of Bus Travel Time with a Bayesian Gaussian Mixture Model","volume":"57","author":"Chen","year":"2023","journal-title":"Transp. Sci."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"4271871","DOI":"10.1155\/2020\/4271871","article-title":"Estimating Wait Time and Passenger Load in a Saturated Metro Network: A Data-Driven Approach","volume":"2020","author":"Qu","year":"2020","journal-title":"J. Adv. Transp."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1016\/j.trc.2017.10.002","article-title":"Inferring left behind passengers in congested metro systems from automated data","volume":"94","author":"Zhu","year":"2018","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1109\/MITS.2023.3289969","article-title":"An Unsupervised Learning Approach for Robust Denied Boarding Probability Estimation Using Smart Card and Operation Data in Urban Railways","volume":"15","author":"Tuncel","year":"2023","journal-title":"IEEE Intell. Transp. Syst. Mag."},{"key":"ref_44","unstructured":"Li, X., Zhong, Z., Wu, J., Yang, Y., Lin, Z., and Liu, H. (November, January 27). Expectation-Maximization Attention Networks for Semantic Segmentation. Proceedings of the IEEE\/CVF International Conference on Computer Vision, Seoul, Republic of Korea."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1395","DOI":"10.1049\/itr2.12332","article-title":"Spatiotemporal path inference model for urban rail transit passengers based on travel time data","volume":"17","author":"Luo","year":"2023","journal-title":"IET Intell. Transp. Syst."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/26\/5\/388\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:37:19Z","timestamp":1760107039000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/26\/5\/388"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4,30]]},"references-count":45,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2024,5]]}},"alternative-id":["e26050388"],"URL":"https:\/\/doi.org\/10.3390\/e26050388","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2024,4,30]]}}}