{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,13]],"date-time":"2026-06-13T00:05:09Z","timestamp":1781309109211,"version":"3.54.1"},"reference-count":50,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2021,11,10]],"date-time":"2021-11-10T00:00:00Z","timestamp":1636502400000},"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":["42171396"],"award-info":[{"award-number":["42171396"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJGI"],"abstract":"<jats:p>Automatic Identification System (AIS) data have been widely used in many fields, such as collision detection, navigation, and maritime traffic management. Similarity analysis is an important process for most AIS trajectory analysis topics. However, most traditional AIS trajectory similarity analysis methods calculate the distance between trajectory points, which requires complex and time-consuming calculations, often leading to substantial errors when processing AIS trajectory data characterized by substantial differences in length or uneven trajectory points. Therefore, we propose a cell-based similarity analysis method that combines the weight of the direction and k-neighborhood (WDN-SIM). This method quantifies the similarity between trajectories based on the degree of proximity and differences in motion direction. In terms of its effectiveness and efficiency, WDN-SIM outperformed seven traditional methods for trajectory similarity analysis. Particularly, WDN-SIM has a high robustness to noise and can distinguish the similarities between trajectories under complex situations, such as when there are opposing directions of motion, large differences in length, and uneven point distributions.<\/jats:p>","DOI":"10.3390\/ijgi10110757","type":"journal-article","created":{"date-parts":[[2021,11,10]],"date-time":"2021-11-10T09:19:21Z","timestamp":1636535961000},"page":"757","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Trajectory Similarity Analysis with the Weight of Direction and k-Neighborhood for AIS Data"],"prefix":"10.3390","volume":"10","author":[{"given":"Pin","family":"Nie","sequence":"first","affiliation":[{"name":"School of Geography and Ocean Science, Nanjing University, Nanjing 210023, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3033-8470","authenticated-orcid":false,"given":"Zhenjie","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Geography and Ocean Science, Nanjing University, Nanjing 210023, China"},{"name":"Jiangsu Provincial Key Laboratory of Geographic Information Science and Technology, Nanjing University, Nanjing 210023, China"},{"name":"Collaborative Innovation Center of South China Sea Studies, Nanjing University, Nanjing 210023, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nan","family":"Xia","sequence":"additional","affiliation":[{"name":"School of Geography and Ocean Science, Nanjing University, Nanjing 210023, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qiuhao","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Geography and Ocean Science, Nanjing University, Nanjing 210023, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Feixue","family":"Li","sequence":"additional","affiliation":[{"name":"School of Geography and Ocean Science, Nanjing University, Nanjing 210023, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1834","DOI":"10.1111\/1365-2664.13139","article-title":"Using satellite AIS to improve our understanding of shipping and fill gaps in ocean observation data to support marine spatial planning","volume":"55","author":"Metcalfe","year":"2018","journal-title":"J. Appl. Ecol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"102637","DOI":"10.1016\/j.jtrangeo.2020.102637","article-title":"Analysis of global marine oil trade based on automatic identification system (AIS) data","volume":"83","author":"Yan","year":"2020","journal-title":"J. Transp. Geogr."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"677","DOI":"10.1007\/s11431-018-9335-1","article-title":"Using big data to track marine oil transportation along the 21st-century maritime silk road","volume":"62","author":"Cheng","year":"2019","journal-title":"Sci. China Technol. Sci."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"102741","DOI":"10.1016\/j.jtrangeo.2020.102741","article-title":"Time efficiency assessment of ship movements in maritime ports: A case study of two ports based on AIS data","volume":"86","author":"Feng","year":"2020","journal-title":"J. Transp. Geogr."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Mou, N., Ren, H., Zheng, Y., Chen, J., Niu, J., Yang, T., Zhang, L., and Liu, F. (2021). Traffic Inequality and Relations in Maritime Silk Road: A Network Flow Analysis. ISPRS Int. J. Geo-Inf., 10.","DOI":"10.3390\/ijgi10010040"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"e1266","DOI":"10.1002\/widm.1266","article-title":"Maritime anomaly detection: A review","volume":"8","author":"Riveiro","year":"2018","journal-title":"Wiley Interdiscip. Rev. Data Min. Knowl. Discov."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"456","DOI":"10.1016\/j.oceaneng.2018.12.019","article-title":"A trajectory clustering method based on Douglas-Peucker compression and density for marine traffic pattern recognition","volume":"172","author":"Zhao","year":"2019","journal-title":"Ocean Eng."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"894","DOI":"10.1017\/S0373463319000031","article-title":"Maritime Anomaly Detection using Density-based Clustering and Recurrent Neural Network","volume":"72","author":"Zhao","year":"2019","journal-title":"J. Navig."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Chen, R., Chen, M., Li, W., Wang, J., and Yao, X. (2019). Mobility Modes Awareness from Trajectories Based on Clustering and a Convolutional Neural Network. ISPRS Int. J. Geo-Inf., 8.","DOI":"10.3390\/ijgi8050208"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1016\/j.ijar.2013.03.012","article-title":"Anomaly detection in vessel tracks using Bayesian networks","volume":"55","author":"Mascaro","year":"2014","journal-title":"Int. J. Approx. Reason."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1007\/s13131-014-0498-2","article-title":"Point association analysis of vessel target detection with SAR, HFSWR and AIS","volume":"33","author":"Ji","year":"2014","journal-title":"Acta Oceanol. Sin."},{"key":"ref_12","first-page":"1","article-title":"A GIS-based spatial-temporal autoregressive model for forecasting marine traffic volume of a shipping network","volume":"2019","author":"Zhang","year":"2019","journal-title":"Sci. Program."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1017\/S0373463320000442","article-title":"Vessel Trajectory Prediction Using Historical Automatic Identification System Data","volume":"74","author":"Alizadeh","year":"2021","journal-title":"J. Navig."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1559","DOI":"10.1109\/TITS.2017.2724551","article-title":"Exploiting AIS data for intelligent maritime navigation: A comprehensive survey from data to methodology","volume":"19","author":"Tu","year":"2018","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"102729","DOI":"10.1016\/j.trc.2020.102729","article-title":"AIS data driven general vessel destination prediction: A random forest based approach","volume":"118","author":"Zhang","year":"2020","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2218","DOI":"10.3390\/e15062218","article-title":"Vessel Pattern Knowledge Discovery from AIS Data: A Framework for Anomaly Detection and Route Prediction","volume":"15","author":"Pallotta","year":"2013","journal-title":"Entropy"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"879","DOI":"10.1017\/S0373463313000519","article-title":"Use of AIS data to characterise marine traffic patterns and ship collision risk off the coast of Portugal","volume":"66","author":"Silveira","year":"2013","journal-title":"J. Navig."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1016\/j.oceaneng.2015.07.046","article-title":"A method for detecting possible near miss ship collisions from AIS data","volume":"107","author":"Zhang","year":"2015","journal-title":"Ocean Eng."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Lin, C., Dong, F., Le, J., and Wang, G. (2008, January 12\u201314). AIS system and the applications at the harbor traffic management. Proceedings of the 4th International Conference on Wireless Communications, Networking and Mobile Computing, Dalian, China.","DOI":"10.1109\/WiCom.2008.2859"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"LU, N., Liang, M., Yang, L., Wang, Y., Xiong, N., and Liu, R.W. (2020, January 8\u201311). Shape-Based Vessel Trajectory Similarity Computing and Clustering: A Brief Review. Proceedings of the 2020 5th IEEE International Conference on Big Data Analytics (ICBDA), Xiamen, China.","DOI":"10.1109\/ICBDA49040.2020.9101322"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Zhang, Y., and Shi, G. (2021, January 5\u20138). Trajectory Similarity Measure Design for Ship Trajectory Clustering. Proceedings of the 2021 6th IEEE International Conference on Big Data Analytics (ICBDA), Xiamen, China.","DOI":"10.1109\/ICBDA51983.2021.9403137"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"648","DOI":"10.1017\/S0373463316000850","article-title":"Maritime Anomaly Detection within Coastal Waters Based on Vessel Trajectory Clustering and Na\u00efve Bayes Classifier","volume":"70","author":"Zhen","year":"2017","journal-title":"J. Navig."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Mao, Y.Z., Zhong, H.S., Xiao, X.J., and Li, X.F. (2017). A segment-based trajectory similarity measure in the urban transportation systems. Sensors, 17.","DOI":"10.20944\/preprints201703.0028.v1"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"3306","DOI":"10.1109\/TITS.2016.2547641","article-title":"Review and Perspective for Distance-Based Clustering of Vehicle Trajectories","volume":"17","author":"Besse","year":"2016","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_25","first-page":"105","article-title":"Extraction method of marine lane boundary from exploiting trajectory big data","volume":"39","author":"Xu","year":"2019","journal-title":"J. Comput. Appl."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/3125634","article-title":"Grid-based method for GPS route analysis for retrieval","volume":"3","year":"2017","journal-title":"ACM Trans. Spat. Algorithms Syst. (TSAS)"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"107730","DOI":"10.1016\/j.patcog.2020.107730","article-title":"Averaging GPS segments competition 2019","volume":"112","year":"2021","journal-title":"Pattern Recognit."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Keogh, E.J., and Pazzani, M.J. (2000, January 20\u201323). Scaling up dynamic time warping for datamining applications. Proceedings of the 6th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Boston, MA, USA.","DOI":"10.1145\/347090.347153"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Li, H., Liu, J., Liu, R.W., Xiong, N., Wu, K., and Kim, T.H. (2017). A dimensionality reduction-based multi-step clustering method for robust vessel trajectory analysis. Sensors, 17.","DOI":"10.3390\/s17081792"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"290","DOI":"10.1017\/S0373463318000723","article-title":"A Novel Similarity Measure for Clustering Vessel Trajectories Based on Dynamic Time Warping","volume":"72","author":"Zhao","year":"2019","journal-title":"J. Navig."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"150677","DOI":"10.1109\/ACCESS.2019.2947111","article-title":"Adaptive Douglas-Peucker Algorithm With Automatic Thresholding for AIS-Based Vessel Trajectory Compression","volume":"7","author":"Liu","year":"2019","journal-title":"IEEE Access"},{"key":"ref_32","unstructured":"Lachos, M., Kollios, G., and Gunopulos, D. (March, January 26). Discovering similar multidimensional trajectories. Proceedings of the l8th International Conference on Data Engineering, San Jose, CA, USA."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/j.dam.2015.07.005","article-title":"Repetition-free longest common subsequence of random sequences","volume":"210","author":"Fernandes","year":"2016","journal-title":"Discret. Appl. Math."},{"key":"ref_34","unstructured":"Chen, L., and Ng, R. (2004\u20133, January 31). On The Marriage of Lp-norms and Edit Distance. Proceedings of the 30th International Conference on Very Large Data Bases, VLDB, Toronto, ON, Canada."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Chen, L., \u00d6zsu, M.T., and Oria, V. (2005, January 14\u201316). Robust and fast similarity search for moving object trajectories. Proceedings of the 24th ACM International Conference on Management of Data, Baltimore, MD, USA.","DOI":"10.1145\/1066157.1066213"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/j.jtrangeo.2019.05.003","article-title":"From edit distance to augmented space-time-weighted edit distance: Detecting and clustering patterns of human activities in Puget Sound region","volume":"78","author":"Zhai","year":"2019","journal-title":"J. Transp. Geogr."},{"key":"ref_37","first-page":"1703","article-title":"Trajectory similarity measure based on multiple movement features","volume":"42","author":"Zhu","year":"2017","journal-title":"Geomat. Inf. Sci. Wuhan Univ."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Wang, Y., Qin, K., Chen, Y., and Zhao, P. (2018). Detecting Anomalous Trajectories and Behavior Patterns Using Hierarchical Clustering from Taxi GPS Data. ISPRS Int. J. Geo-Inf., 7.","DOI":"10.3390\/ijgi7010025"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Wang, L., Chen, P., Chen, L., and Mou, J. (2021). Ship ais trajectory clustering: An hdbscan-based approach. J. Mar. Sci. Eng., 9.","DOI":"10.3390\/jmse9060566"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Ma, W., Wu, Z., Yang, J., and Li, W. (2014, January 24\u201327). Vessel Motion Pattern Recognition Based on One-Way Distance and Spectral Clustering Algorithm. Proceedings of the Algorithms and Architectures for Parallel Processing, ICA3PP 2014, Dalian, China.","DOI":"10.1007\/978-3-319-11194-0_38"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1007\/s10707-007-0027-y","article-title":"One way distance: For shape based similarity search of moving object trajectories","volume":"12","author":"Lin","year":"2008","journal-title":"GeoInformatica"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Chen, P., Xu, K., Li, G., and Wan, J. (2016, January 10\u201311). A Segmented Template Optimization Using the Fr\u00e9chet Distance. Proceedings of the 9th International Symposium on Computational Intelligence and Design, Hangzhou, China.","DOI":"10.1109\/ISCID.2016.1102"},{"key":"ref_43","unstructured":"Shahbaz, K. (2013). Applied Similarity Problems Using Fr\u00e9chet Distance. [Doctoral Dissertation, Carleton University]."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"13351","DOI":"10.1007\/s10586-018-1910-z","article-title":"Map matching algorithm: Curve simplification for Fr\u00e9chet distance computing and precise navigation on road network using RTKLIB","volume":"22","author":"Sharma","year":"2018","journal-title":"Clust. Comput"},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Cao, J., Liang, M.H., Li, Y., Chen, J.W., Li, H.H., Liu, R.W., and Liu, J.X. (2018, January 9\u201312). PCA-based hierarchical clustering of AIS trajectories with automatic extraction of clusters. Proceedings of the 2018 IEEE 3rd International Conference on Big Data Analysis (ICBDA), Shanghai, China.","DOI":"10.1109\/ICBDA.2018.8367725"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1111\/gean.12178","article-title":"A shape-based local spatial association measure (LISShA): A case study in maritime anomaly detection","volume":"51","author":"Roberts","year":"2019","journal-title":"Geogr. Anal."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.proeps.2015.07.082","article-title":"Risk of navigation for marine traffic in the Malacca Strait using AIS","volume":"14","author":"Zaman","year":"2015","journal-title":"Procedia Earth Planet. Sci."},{"key":"ref_48","unstructured":"Wang, H., Su, H., Zheng, K., Sadiq, S., and Zhou, X. (February, January 29). An effectiveness study on trajectory similarity measures. Proceedings of the Twenty-Fourth Australasian Database Conference, Adelaide, Australia."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/j.jss.2016.06.016","article-title":"Employing traditional machine learning algorithms for big data streams analysis: The case of object trajectory prediction","volume":"127","author":"Valsamis","year":"2017","journal-title":"J. Syst. Softw."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1016\/j.oceaneng.2018.02.060","article-title":"Data-driven based automatic maritime routing from massive AIS trajectories in the face of disparity","volume":"155","author":"Zhang","year":"2018","journal-title":"Ocean Eng."}],"container-title":["ISPRS International Journal of Geo-Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2220-9964\/10\/11\/757\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:28:09Z","timestamp":1760167689000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2220-9964\/10\/11\/757"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,10]]},"references-count":50,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2021,11]]}},"alternative-id":["ijgi10110757"],"URL":"https:\/\/doi.org\/10.3390\/ijgi10110757","relation":{},"ISSN":["2220-9964"],"issn-type":[{"value":"2220-9964","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,11,10]]}}}