{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T00:55:41Z","timestamp":1773017741473,"version":"3.50.1"},"reference-count":39,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2021,12,30]],"date-time":"2021-12-30T00:00:00Z","timestamp":1640822400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["72001023"],"award-info":[{"award-number":["72001023"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJGI"],"abstract":"<jats:p>The distribution of passengers reflects the characteristics of urban rail stations. The automatic fare collection system of rail transit collects a large amount of passenger trajectory data tracking the entry and exit continuously, which provides a basis for detailed passenger distributions. We first exploit the Automatic Fare Collection (AFC) data to construct the passenger visit pattern distribution for stations. Then we measure the similarity of all stations using Wasserstein distance. Different from other similarity metrics, Wasserstein distance takes the similarity between values of quantitative variables in the one-dimensional distribution into consideration and can reflect the correlation between different dimensions of high-dimensional data. Even though the computational complexity grows, it is applicable in the metro stations since the scale of urban rail transit stations is limited to tens to hundreds and detailed modeling of the stations can be performed offline. Therefore, this paper proposes an integrated method that can cluster multi-dimensional joint distribution considering similarity and correlation. Then this method is applied to cluster the rail transit stations by the passenger visit distribution, which provides some valuable insight into the flow management and the station replanning of urban rail transit in the future.<\/jats:p>","DOI":"10.3390\/ijgi11010018","type":"journal-article","created":{"date-parts":[[2021,12,30]],"date-time":"2021-12-30T21:41:21Z","timestamp":1640900481000},"page":"18","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Measuring the Similarity of Metro Stations Based on the Passenger Visit Distribution"],"prefix":"10.3390","volume":"11","author":[{"given":"Kangli","family":"Zhu","sequence":"first","affiliation":[{"name":"State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6653-6789","authenticated-orcid":false,"given":"Haodong","family":"Yin","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yunchao","family":"Qu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianjun","family":"Wu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing 100044, China"},{"name":"Key Laboratory of Transport Industry of Big Data Application Technologies for Comprehensive Transport, Ministry of Transport, School of Traffic and Transportation, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,12,30]]},"reference":[{"key":"ref_1","unstructured":"(2021, November 15). Beijing Statistical Yearbook, Available online: http:\/\/Nj.Tjj.Beijing.Gov.Cn\/Nj\/Main\/2020-Tjnj\/Zk\/Indexch.Htm."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1007\/s42524-021-0175-z","article-title":"Special Issue: Reliability Management of Complex System","volume":"8","author":"Wu","year":"2021","journal-title":"Front. Eng. Manag."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"568","DOI":"10.1016\/j.trb.2017.05.001","article-title":"Two-Phase Decomposition Method for the Last Train Departure Time Choice in Subway Networks","volume":"104","author":"Kang","year":"2017","journal-title":"Transp. Res. Part B-Methodol."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Liu, L., Hou, A., Biderman, A., Ratti, C., and Chen, J. (2009, January 4\u20137). Understanding Individual and Collective Mobility Patterns From Smart Card Records: A Case Study in Shenzhen. Proceedings of the 2009 12th International IEEE Conference on Intelligent Transportation Systems, St. Louis, MO, USA.","DOI":"10.1109\/ITSC.2009.5309662"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"557","DOI":"10.1016\/j.trc.2010.12.003","article-title":"Smart Card Data Use In Public Transit: A Literature Review","volume":"19","author":"Pelletier","year":"2011","journal-title":"Transp. Res. Part C-Emerg. Technol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.trc.2013.07.010","article-title":"Mining Smart Card Data For Transit Riders\u2019 Travel Patterns","volume":"36","author":"Ma","year":"2013","journal-title":"Transp. Res. Part C-Emerg. Technol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/j.compenvurbsys.2015.02.005","article-title":"Combining Smart Card Data and Household Travel Survey to Analyze Jobs-Housing Relationships in Beijing","volume":"53","author":"Long","year":"2015","journal-title":"Comput. Environ. Urban Syst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/j.jtrangeo.2016.12.001","article-title":"Understanding Commuting Patterns Using Transit Smart Card Data","volume":"58","author":"Ma","year":"2017","journal-title":"J. Transp. Geogr."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Liu, J., Shi, W., and Chen, P. (2020). Exploring Travel Patterns During The Holiday Season-A Case Study of Shenzhen Metro System During the Chinese Spring Festival. ISPRS Int. J. Geo-Inf., 9.","DOI":"10.3390\/ijgi9110651"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"304","DOI":"10.1007\/s10955-012-0645-0","article-title":"Spatiotemporal Patterns Of Urban Human Mobility","volume":"151","author":"Hasan","year":"2013","journal-title":"J. Stat. Phys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"102810","DOI":"10.1016\/j.trc.2020.102810","article-title":"Inferring Temporal Motifs for Travel Pattern Analysis Using Large Scale Smart Card Data","volume":"120","author":"Lei","year":"2020","journal-title":"Transp. Res. Part C-Emerg. Technol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"712","DOI":"10.1109\/TITS.2016.2600515","article-title":"Clustering Smart Card Data For Urban Mobility Analysis","volume":"18","author":"Come","year":"2017","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"126058","DOI":"10.1016\/j.physa.2021.126058","article-title":"Assessing Temporal-Spatial Characteristics of Urban Travel Behaviors from Multiday Smart-Card Data","volume":"576","author":"Deng","year":"2021","journal-title":"Phys. A-Stat. Mech. Its Appl."},{"key":"ref_14","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_15","first-page":"56","article-title":"A Classification of Public Transit Users with Smart Card Data Based on Time Series Distance Metrics and A Hierarchical Clustering Method","volume":"16","author":"He","year":"2020","journal-title":"Transp. A-Transp. Sci."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Yang, Y., Heppenstall, A., Turner, A., and Comber, A. (2019). Who, Where, Why and When? Using Smart Card and Social Media Data to Understand Urban Mobility. ISPRS Int. J. Geo-Inf., 8.","DOI":"10.3390\/ijgi8060271"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Du, B., Yang, Y., and Lv, W. (2013, January 18\u201321). Understand Group Travel Behaviors in an Urban Area Using Mobility Pattern Mining. Proceedings of the IEEE 10th International Conference on Ubiquitous Intelligence and Computing, UIC 2013 and IEEE 10th International Conference on Autonomic and Trusted Computing, ATC 2013, Vietri sul Mare, Italy.","DOI":"10.1109\/UIC-ATC.2013.64"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1016\/j.trb.2016.06.011","article-title":"Understanding Urban Mobility Patterns With A Probabilistic Tensor Factorization Framework","volume":"91","author":"Sun","year":"2016","journal-title":"Transp. Res. Part B Methodol."},{"key":"ref_19","unstructured":"(2021, December 22). Beijing Municipal Bureau Statistics Beijing Statistical Yearbook, Available online: http:\/\/Nj.Tjj.Beijing.Gov.Cn\/Nj\/Main\/2021-Tjnj\/Zk\/Indexch.Htm."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"278","DOI":"10.1016\/j.trc.2015.06.007","article-title":"Traffic Zone Division Based on Big Data from Mobile Phone Base Stations","volume":"58","author":"Dong","year":"2015","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"352","DOI":"10.1080\/10095020.2020.1846463","article-title":"Cluster and Characteristic Analysis of Shanghai Metro Stations Based on Metro Card and Land-Use Data","volume":"23","author":"Shen","year":"2020","journal-title":"Geo-Spat. Inf. Sci."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Xiong, L., Chen, X., Huang, T.K., Schneider, J., and Carbonell, J.G. (May, January 29). Temporal Collaborative Filtering with Bayesian Probabilistic Tensor Factorization. Proceedings of the 10th Siam International Conference on Data Mining, SDM 2010, Columbus, OH, USA.","DOI":"10.1137\/1.9781611972801.19"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"6160","DOI":"10.1109\/TSP.2016.2602809","article-title":"Learning Laplacian Matrix in Smooth Graph Signal Representations","volume":"64","author":"Dong","year":"2016","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_24","unstructured":"Lee, D.D., Sugiyama, M., Luxburg, U.V., Guyon, I., and Garnett, R. (2016, January 5\u201310). Temporal Regularized Matrix Factorization for High-Dimensional Time Series Prediction. Proceedings of the Advances in Neural Information Processing Systems 29 (NIPS 2016), Barcelona, Spain."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Xu, J. (2017). Map Sensitivity vs. Map Dependency: A Case Study of Subway Maps\u2019 Impact on Passenger Route Choices in Washington DC. Behav. Sci., 7.","DOI":"10.3390\/bs7040072"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Lei, B., Xu, J., Li, M., Li, H., Li, J., Cao, Z., Hao, Y., and Zhang, Y. (2019). Enhancing Role of Guiding Signs Setting in Metro Stations with Incorporation of Microscopic Behavior of Pedestrians. Sustainability, 11.","DOI":"10.3390\/su11216109"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1016\/j.ssci.2016.04.004","article-title":"Passengers\u2019 Awareness and Perceptions of Way Finding Tools in a Train Station","volume":"87","author":"Shiwakoti","year":"2016","journal-title":"Saf. Sci."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1179\/1942787515Y.0000000016","article-title":"Simulating Emergency Evacuation at Metro Stations: An Approach Based on Thorough Psychological Analysis","volume":"8","author":"Hong","year":"2016","journal-title":"Transp. Lett.-Int. J. Transp. Res."},{"key":"ref_29","first-page":"100421","article-title":"Behavioural Advertising In The Public Transit Network","volume":"32","author":"Faroqi","year":"2019","journal-title":"Res. Transp. Bus. Manag."},{"key":"ref_30","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_31","doi-asserted-by":"crossref","first-page":"776","DOI":"10.1016\/j.sbspro.2014.07.258","article-title":"Research on Optimization for Passenger Streamline of Hubs","volume":"138","author":"Zhu","year":"2014","journal-title":"Procedia-Soc. Behav. Sci."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1016\/S0968-090X(96)00028-9","article-title":"Effects of Familiarity on Route Choice Behavior in the Presence of Information","volume":"5","author":"Lotan","year":"1997","journal-title":"Transp. Res. Part C-Emerg. Technol."},{"key":"ref_33","unstructured":"(2021, December 22). Openstreetmap. Available online: https:\/\/www.openstreetmap.org\/."},{"key":"ref_34","first-page":"120","article-title":"The Opencv Library","volume":"25","author":"Bradski","year":"2000","journal-title":"Dobb\u2019s J. Softw. Tools"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1109\/TETC.2014.2330519","article-title":"A Survey of Clustering Algorithms for Big Data: Taxonomy and Empirical Analysis","volume":"2","author":"Fahad","year":"2014","journal-title":"IEEE Trans. Emerg. Top. Comput."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"E1219","DOI":"10.1002\/widm.1219","article-title":"Algorithms For Hierarchical Clustering: An Overview, II","volume":"7","author":"Murtagh","year":"2017","journal-title":"Wiley Interdiscip. Rev.-Data Min. Knowl. Discov."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"664","DOI":"10.1016\/j.neucom.2017.06.053","article-title":"A Review of Clustering Techniques and Developments","volume":"267","author":"Saxena","year":"2017","journal-title":"Neurocomputing"},{"key":"ref_38","first-page":"2825","article-title":"Scikit-Learn: Machine Learning in Python","volume":"12","author":"Pedregosa","year":"2011","journal-title":"J. Mach. Learn. Res."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/0377-0427(87)90125-7","article-title":"Silhouettes: A Graphical Aid to The Interpretation and Validation of Cluster Analysis","volume":"20","author":"Rousseeuw","year":"1984","journal-title":"J. Comput. Appl. Math."}],"container-title":["ISPRS International Journal of Geo-Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2220-9964\/11\/1\/18\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:56:08Z","timestamp":1760169368000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2220-9964\/11\/1\/18"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,12,30]]},"references-count":39,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2022,1]]}},"alternative-id":["ijgi11010018"],"URL":"https:\/\/doi.org\/10.3390\/ijgi11010018","relation":{},"ISSN":["2220-9964"],"issn-type":[{"value":"2220-9964","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,12,30]]}}}