{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,13]],"date-time":"2026-10-13T18:36:29Z","timestamp":1791916589252,"version":"4.3.4"},"reference-count":39,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,1,4]],"date-time":"2023-01-04T00:00:00Z","timestamp":1672790400000},"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":["61663047"],"award-info":[{"award-number":["61663047"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2020SE314"],"award-info":[{"award-number":["2020SE314"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2022Y032"],"award-info":[{"award-number":["2022Y032"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Open Foundation of Key Laboratory in Software Engineering of Yunnan Province","award":["61663047"],"award-info":[{"award-number":["61663047"]}]},{"name":"Open Foundation of Key Laboratory in Software Engineering of Yunnan Province","award":["2020SE314"],"award-info":[{"award-number":["2020SE314"]}]},{"name":"Open Foundation of Key Laboratory in Software Engineering of Yunnan Province","award":["2022Y032"],"award-info":[{"award-number":["2022Y032"]}]},{"name":"Scientific Research Fund project of Yunnan Provincial Department of Education","award":["61663047"],"award-info":[{"award-number":["61663047"]}]},{"name":"Scientific Research Fund project of Yunnan Provincial Department of Education","award":["2020SE314"],"award-info":[{"award-number":["2020SE314"]}]},{"name":"Scientific Research Fund project of Yunnan Provincial Department of Education","award":["2022Y032"],"award-info":[{"award-number":["2022Y032"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJGI"],"abstract":"<jats:p>Traffic flows (e.g., the traffic of vehicles, passengers, and bikes) aim to reveal traffic flow phenomena generated by traffic participants in traffic activities. Various studies of traffic flows rely heavily on high-quality traffic data. The taxi GPS trajectory data are location data that include latitude, longitude, and time. These data are critical for traffic flow analysis, planning, infrastructure layout, and recommendations for urban residents. A city map can be divided into multiple grids according to the latitude and longitude coordinates, and traffic passenger flows data derived from taxi trajectory data can be extracted. However, random missing data occur due to weather and equipment failure. Therefore, the effective imputation of missing traffic flow data is a hot topic. This study proposes the spatio-temporal generative adversarial imputation net (ST-GAIN) model to solve the traffic passenger flows imputation. An adversarial game with multiple generators and one discriminator is established. The generator observes some components of the time-domain and regional traffic data vector extracted from the grid. It effectively imputes the missing values of the spatio-temporal traffic passenger flow data. The experimental data are accurate Kunming taxi trajectory data, and experimental results show that the proposed method outperforms five baseline methods regarding the imputation accuracy. It is significant and suggests the possibility of effectively applying the model to predict the passenger flows in some areas where traffic data cannot be collected for some reason or traffic data are randomly missing.<\/jats:p>","DOI":"10.3390\/ijgi12010013","type":"journal-article","created":{"date-parts":[[2023,1,4]],"date-time":"2023-01-04T04:08:07Z","timestamp":1672805287000},"page":"13","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Spatial\u2013Temporal Data Imputation Model of Traffic Passenger Flow Based on Grid Division"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8298-0449","authenticated-orcid":false,"given":"Li","family":"Cai","sequence":"first","affiliation":[{"name":"The School of Software, Yunnan University, Kunming 650091, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8080-2657","authenticated-orcid":false,"given":"Cong","family":"Sha","sequence":"additional","affiliation":[{"name":"The School of Software, Yunnan University, Kunming 650091, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jing","family":"He","sequence":"additional","affiliation":[{"name":"The School of Software, Yunnan University, Kunming 650091, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shaowen","family":"Yao","sequence":"additional","affiliation":[{"name":"The School of Software, Yunnan University, Kunming 650091, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Zhang, N., Chen, H., Chen, X., and Chen, J. (2016). Forecasting public transit use by crowdsensing and semantic trajectory mining: Case studies. ISPRS Int. J. Geo-Inf., 5.","DOI":"10.3390\/ijgi5100180"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"614","DOI":"10.1016\/j.eswa.2018.08.053","article-title":"An indoor trajectory frequent pattern mining algorithm based on vague grid sequence","volume":"118","author":"Chen","year":"2019","journal-title":"Expert Syst. Appl."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Little, R.J.A., and Rubin, D.B. (2019). Statistical Analysis with Missing Data, John Wiley Sons.","DOI":"10.1002\/9781119482260"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"913","DOI":"10.1080\/08839514.2019.1637138","article-title":"Comparison of performance of data imputation methods for numeric dataset","volume":"33","author":"Jadhav","year":"2019","journal-title":"Appl. Artif. Intell."},{"key":"ref_5","first-page":"2287","article-title":"Spectral regularization algorithms for learning large incomplete matrices","volume":"11","author":"Mazumder","year":"2010","journal-title":"J. Mach. Learn. Res."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.18637\/jss.v045.i04","article-title":"Multiple imputation by chained equations (MICE): Implementation in Stata","volume":"45","author":"Royston","year":"2011","journal-title":"J. Stat. Softw."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1093\/bioinformatics\/btr597","article-title":"MissForest\u2014Non-parametric missing value imputation for mixed-type data","volume":"28","author":"Stekhoven","year":"2012","journal-title":"Bioinformatics"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"162938","DOI":"10.1155\/2013\/162938","article-title":"Missing value estimation for microarray data by Bayesian principal component analysis and iterative local least squares","volume":"2013","author":"Shi","year":"2013","journal-title":"Math. Probl. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2935248","DOI":"10.1155\/2018\/2935248","article-title":"An imputation method for missing traffic data based on FCM optimized by PSO-SVR","volume":"2018","author":"Shang","year":"2018","journal-title":"J. Adv. Transp."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/j.trc.2014.11.003","article-title":"A hybrid approach to integrate fuzzy C-means based imputation method with genetic algorithm for missing traffic volume data estimation","volume":"51","author":"Tang","year":"2015","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_11","first-page":"61","article-title":"A comparative analysis of data imputation methods for missing traffic flow data","volume":"36","author":"Meng","year":"2018","journal-title":"J. Transp. Inf. Saf."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Zhang, A., Song, S., Sun, Y., and Wang, J. (2019, January 8\u201311). Learning individual models for imputation. Proceedings of the 2019 IEEE 35th International Conference on Data Engineering (ICDE), Macao, China.","DOI":"10.1109\/ICDE.2019.00023"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"125776","DOI":"10.1016\/j.physa.2021.125776","article-title":"Missing traffic data imputation considering approximate intervals: A hybrid structure integrating adaptive network-based inference and fuzzy rough set","volume":"573","author":"Tang","year":"2021","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2933","DOI":"10.1109\/TITS.2018.2869768","article-title":"Missing value imputation for traffic-related time series data based on a multi-view learning method","volume":"20","author":"Li","year":"2018","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_15","first-page":"1603","article-title":"Multivariate time series imputation with generative adversarial networks","volume":"31","author":"Luo","year":"2018","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_16","first-page":"63","article-title":"Urban traffic flow data recovery method based on generative adversarial network","volume":"18","author":"Wang","year":"2018","journal-title":"J. Sci. J. Transp. Syst. Eng. Inf. Technol."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Luo, Y., Zhang, Y., Cai, X., and Yuan, X. (2019, January 10\u201316). E2gan: End-to-end generative adversarial network for multivariate time series imputation. Proceedings of the 28th International Joint Conference on Artificial Intelligence, Macao, China.","DOI":"10.24963\/ijcai.2019\/429"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"106705","DOI":"10.1016\/j.knosys.2020.106705","article-title":"ST-LBAGAN: Spatio-temporal learnable bidirectional attention generative adversarial networks for missing traffic data imputation","volume":"215","author":"Yang","year":"2021","journal-title":"Knowl.-Based Syst."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2611","DOI":"10.1016\/j.sbspro.2013.08.292","article-title":"Correlation analysis for tensor-based traffic data imputation method","volume":"96","author":"Tan","year":"2013","journal-title":"Procedia-Soc. Behav. Sci."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Yan, J., Li, H., Bai, Y., and Lin, Y. (2021). Spatial\u2014Temporal Traffic Flow Data Restoration and Prediction Method Based on the Tensor Decomposition. Appl. Sci., 11.","DOI":"10.3390\/app11199220"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"12301","DOI":"10.1109\/TITS.2021.3113608","article-title":"Low-rank autoregressive tensor completion for spatiotemporal traffic data imputation","volume":"23","author":"Chen","year":"2022","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"6618","DOI":"10.1109\/JIOT.2019.2909038","article-title":"SSIM\u2014A deep learning approach for recovering missing time series sensor data","volume":"6","author":"Zhang","year":"2019","journal-title":"IEEE Internet Things J."},{"key":"ref_23","first-page":"4840021","article-title":"Data Imputation for Detected Traffic Volume of Freeway Using Regression of Multilayer Perceptron","volume":"2022","author":"Wang","year":"2022","journal-title":"J. Adv. Transp."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"6085","DOI":"10.1038\/s41598-018-24271-9","article-title":"Recurrent neural networks for multivariate time series with missing values","volume":"8","author":"Che","year":"2018","journal-title":"Sci. Rep."},{"key":"ref_25","unstructured":"Cao, W., Wang, D., Li, J., Zhou, H., Li, L., and Li, Y.B. (2018). Bidirectional recurrent imputation for time series. arXiv."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1751","DOI":"10.1109\/TPAMI.2015.2392756","article-title":"Bayesian CP factorization of incomplete tensors with automatic rank determination","volume":"37","author":"Zhao","year":"2015","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Zhou, W., Zheng, H., Feng, X., and Lin, D. (2019, January 23\u201325). A multi-source based coupled tensors completion algorithm for incomplete traffic data imputation. Proceedings of the 2019 11th International Conference on Wireless Communications and Signal Processing (WCSP), Xi\u2019an, China.","DOI":"10.1109\/WCSP.2019.8927918"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"63188","DOI":"10.1109\/ACCESS.2020.2984588","article-title":"Traffic flow prediction with missing data imputed by tensor completion methods","volume":"8","author":"Li","year":"2020","journal-title":"IEEE Access"},{"key":"ref_29","first-page":"2061","article-title":"The mining of urban hotspots based on multi-source location data fusion","volume":"35","author":"Cai","year":"2023","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"ref_30","unstructured":"Duan, Y., Lv, Y., and Kang, W. (2014, January 8\u201311). A deep learning based approach for traffic data imputation. Proceedings of the 17th International IEEE Conference on Intelligent Transportation Systems (ITSC), Qingdao, China."},{"key":"ref_31","unstructured":"Yoon, J., Jordon, J., and Schaar, M. (2018, January 10\u201315). Gain: Missing data imputation using generative adversarial nets. Proceedings of the International Conference on Machine Learning, Stockholm, Sweden."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1145\/3422622","article-title":"Generative adversarial nets","volume":"63","author":"Goodfellow","year":"2020","journal-title":"Commun. ACM"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"751","DOI":"10.1109\/TNNLS.2018.2851612","article-title":"A fused CP factorization method for incomplete tensors","volume":"30","author":"Wu","year":"2018","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Cho, K., Van Merri\u00ebnboer, B., Gulcehre, C., Bahdanau, 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":"1624","DOI":"10.1109\/TITS.2019.2910295","article-title":"Traffic flow imputation using parallel data and generative adversarial networks","volume":"21","author":"Chen","year":"2019","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1231","DOI":"10.1080\/13658816.2022.2032081","article-title":"A multi-view bidirectional spatiotemporal graph network for urban traffic flow imputation","volume":"36","author":"Wang","year":"2022","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"16343","DOI":"10.1109\/JIOT.2022.3151238","article-title":"A hybrid data-driven framework for spatiotemporal traffic flow data imputation","volume":"9","author":"Wang","year":"2022","journal-title":"IEEE Internet Things J."},{"key":"ref_38","first-page":"3","article-title":"Analysis of Several Correlation Coefficients and Their Implementation in R Language","volume":"34","author":"Jin","year":"2019","journal-title":"Stat. Inf. Forum"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"2141","DOI":"10.1080\/00949655.2010.520163","article-title":"Comparisons of various types of normality tests","volume":"81","author":"Yap","year":"2011","journal-title":"J. Stat. Comput. Simul."}],"container-title":["ISPRS International Journal of Geo-Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2220-9964\/12\/1\/13\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T17:58:22Z","timestamp":1760119102000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2220-9964\/12\/1\/13"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,1,4]]},"references-count":39,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,1]]}},"alternative-id":["ijgi12010013"],"URL":"https:\/\/doi.org\/10.3390\/ijgi12010013","relation":{},"ISSN":["2220-9964"],"issn-type":[{"value":"2220-9964","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,1,4]]}}}