{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:45:49Z","timestamp":1760060749496,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2025,9,21]],"date-time":"2025-09-21T00:00:00Z","timestamp":1758412800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key R&amp;D Program of China","award":["2022YFB2602103","U2469205","JKF-20240769","20230484353"],"award-info":[{"award-number":["2022YFB2602103","U2469205","JKF-20240769","20230484353"]}]},{"name":"National Natural Science Foundation of China","award":["2022YFB2602103","U2469205","JKF-20240769","20230484353"],"award-info":[{"award-number":["2022YFB2602103","U2469205","JKF-20240769","20230484353"]}]},{"name":"Fundamental Research Funds for the Central Universities of China","award":["2022YFB2602103","U2469205","JKF-20240769","20230484353"],"award-info":[{"award-number":["2022YFB2602103","U2469205","JKF-20240769","20230484353"]}]},{"name":"Beijing Nova Program","award":["2022YFB2602103","U2469205","JKF-20240769","20230484353"],"award-info":[{"award-number":["2022YFB2602103","U2469205","JKF-20240769","20230484353"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Traffic data sequence imputation plays a crucial role in maintaining the integrity and reliability of transportation analytics and decision-making systems. With the proliferation of sensor technologies and IoT devices, traffic data often contain missing values due to sensor failures, communication issues, or data processing errors. It is necessary to effectively interpolate these missing parts to ensure the correctness of downstream work. Compared with other data, the monitoring data of traffic flow shows significant temporal and spatial correlations. However, most methods have not fully integrated the correlations of these types. In this work, we introduce the Temporal\u2013Spatial Fusion Neural Network (TSFNN), a framework designed to address missing data recovery in transportation monitoring by jointly modeling spatial and temporal patterns. The architecture incorporates a temporal component, implemented with a Recurrent Neural Network (RNN), to learn sequential dependencies, alongside a spatial component, implemented with a Multilayer Perceptron (MLP), to learn spatial correlations. For performance validation, the model was benchmarked against several established methods. Using real-world datasets with varying missing-data ratios, TSFNN consistently delivered more accurate interpolations than all baseline approaches, highlighting the advantage of combining temporal and spatial learning within a single framework.<\/jats:p>","DOI":"10.3390\/sym17091577","type":"journal-article","created":{"date-parts":[[2025,9,22]],"date-time":"2025-09-22T08:37:39Z","timestamp":1758530259000},"page":"1577","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Spatio-Temporal Recursive Method for Traffic Flow Interpolation"],"prefix":"10.3390","volume":"17","author":[{"given":"Gang","family":"Wang","sequence":"first","affiliation":[{"name":"Highway Monitoring and Emergency Response Center, Ministry of Transport of the P.R.C., Beijing 100029, China"},{"name":"School of Vehicle and Mobility, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuhao","family":"Mao","sequence":"additional","affiliation":[{"name":"CCSE Lab, Beihang University, Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xu","family":"Liu","sequence":"additional","affiliation":[{"name":"Highway Monitoring and Emergency Response Center, Ministry of Transport of the P.R.C., Beijing 100029, China"},{"name":"School of Economics and Management, Beihang University, Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haohan","family":"Liang","sequence":"additional","affiliation":[{"name":"CCSE Lab, Beihang University, Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Keqiang","family":"Li","sequence":"additional","affiliation":[{"name":"School of Vehicle and Mobility, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,9,21]]},"reference":[{"key":"ref_1","first-page":"187","article-title":"The Effects of the Irregular Sample and Missing Data in Time Series Analysis","volume":"10","author":"Kreindler","year":"2006","journal-title":"Nonlinear Dyn. 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