{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,16]],"date-time":"2025-10-16T06:57:42Z","timestamp":1760597862449,"version":"build-2065373602"},"reference-count":43,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2018,12,27]],"date-time":"2018-12-27T00:00:00Z","timestamp":1545868800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Spanish ministry MINECO","award":["TIN2016-75866-C3-3-R"],"award-info":[{"award-number":["TIN2016-75866-C3-3-R"]}]},{"name":"Catalan Government","award":["2017-SGR-1101"],"award-info":[{"award-number":["2017-SGR-1101"]}]},{"name":"Secretaria d'Universitats i Recerca del Departament d'Empresa i Coneixement de la Generalitat de Catalunya","award":["FI"],"award-info":[{"award-number":["FI"]}]},{"DOI":"10.13039\/501100004895","name":"European Social Fund","doi-asserted-by":"publisher","award":["FI"],"award-info":[{"award-number":["FI"]}],"id":[{"id":"10.13039\/501100004895","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>To perform anomaly detection for trajectory data, we study the Sequential Hausdorff Nearest-Neighbor Conformal Anomaly Detector (SHNN-CAD) approach, and propose an enhanced version called SHNN-CAD     +. SHNN-CAD was introduced based on the theory of conformal prediction dealing with the problem of online detection. Unlike most related approaches requiring several not intuitive parameters, SHNN-CAD has the advantage of being parameter-light which enables the easy reproduction of experiments. We propose to adaptively determine the anomaly threshold during the online detection procedure instead of predefining it without any prior knowledge, which makes the algorithm more usable in practical applications. We present a modified Hausdorff distance measure that takes into account the direction difference and also reduces the computational complexity. In addition, the anomaly detection is more flexible and accurate via a re-do strategy. Extensive experiments on both real-world and synthetic data show that SHNN-CAD     +     outperforms SHNN-CAD with regard to accuracy and running time.<\/jats:p>","DOI":"10.3390\/s19010084","type":"journal-article","created":{"date-parts":[[2018,12,27]],"date-time":"2018-12-27T11:29:43Z","timestamp":1545910183000},"page":"84","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["SHNN-CAD+: An Improvement on SHNN-CAD for Adaptive Online Trajectory Anomaly Detection"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5535-2420","authenticated-orcid":false,"given":"Yuejun","family":"Guo","sequence":"first","affiliation":[{"name":"Graphics and Imaging Lab, Universitat de Girona, Campus Montilivi, 17071 Girona, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9648-0624","authenticated-orcid":false,"given":"Anton","family":"Bardera","sequence":"additional","affiliation":[{"name":"Graphics and Imaging Lab, Universitat de Girona, Campus Montilivi, 17071 Girona, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,12,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"809","DOI":"10.1109\/34.868683","article-title":"W4: Real-Time Surveillance of People and Their Activities","volume":"22","author":"Haritaoglu","year":"2000","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_2","unstructured":"Majecka, B. (2009). Statistical Models of Pedestrian Behaviour in the Forum. [Master\u2019s Thesis, School of Informatics, University of Edinburgh]."},{"key":"ref_3","unstructured":"Wang, Q., Chen, M., Nie, F., and Li, X. (2018). Detecting Coherent Groups in Crowd Scenes by Multiview Clustering. IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1511","DOI":"10.1109\/TITS.2011.2160628","article-title":"Trajectory Clustering and an Application to Airspace Monitoring","volume":"12","author":"Gariel","year":"2011","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2749","DOI":"10.1175\/1520-0477(2001)082<2749:AOUSTC>2.3.CO;2","article-title":"Accuracy of United States Tropical Cyclone Landfall Forecasts in the Atlantic Basin (1976\u20132000)","volume":"82","author":"Powell","year":"2001","journal-title":"Bull. Am. Meteorol. Soc."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Meng, F., Yuan, G., Lv, S., Wang, Z., and Xia, S. (2018). An Overview on Trajectory Outlier Detection. Artif. Intell. Rev.","DOI":"10.1007\/s10462-018-9619-1"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Keogh, E., Lonardi, S., and Ratanamahatana, C.A. (2004, January 22\u201325). Towards Parameter-free Data Mining. Proceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Seattle, WA, USA.","DOI":"10.1145\/1014052.1014077"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Laxhammar, R., and Falkman, G. (2010, January 25). Conformal Prediction for Distribution-independent Anomaly Detection in Streaming Vessel Data. Proceedings of the International Workshop on Novel Data Stream Pattern Mining Techniques, Washington, DC, USA.","DOI":"10.1145\/1833280.1833287"},{"key":"ref_9","unstructured":"Laxhammar, R., and Falkman, G. (2011, January 5\u20138). Sequential Conformal Anomaly Detection in Trajectories Based on Hausdorff Distance. Proceedings of the International Conference on Information Fusion, Chicago, IL, USA."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1158","DOI":"10.1109\/TPAMI.2013.172","article-title":"Online Learning and Sequential Anomaly Detection in Trajectories","volume":"36","author":"Laxhammar","year":"2014","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2250","DOI":"10.1109\/TKDE.2013.184","article-title":"Outlier Detection for Temporal Data: A Survey","volume":"26","author":"Gupta","year":"2014","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"32","DOI":"10.23956\/ijarcsse\/V7I4\/0142","article-title":"Anomaly Detection in Data Mining: A Review","volume":"7","author":"Parmar","year":"2017","journal-title":"Int. J. Adv. Res. Comput. Sci. Softw. Eng."},{"key":"ref_13","unstructured":"Ester, M., Kriegel, H.P., Sander, J., and Xu, X. (1996, January 2\u20134). A Density-Based Algorithm for Discovering Clusters in Large Spatial Databases with Noise. Proceedings of the International Conference on Knowledge Discovery and Data Mining, Portland, OR, USA."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1016\/j.datak.2006.01.013","article-title":"ST-DBSCAN: An Algorithm for Clustering Spatial-Temporal Data","volume":"60","author":"Birant","year":"2007","journal-title":"Data Knowl. Eng."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Phung, D., Tseng, V.S., Webb, G.I., Ho, B., Ganji, M., and Rashidi, L. (2018). Angelova, M. A Distance Scaling Method to Improve Density-Based Clustering. Advances in Knowledge Discovery and Data Mining, Springer.","DOI":"10.1007\/978-3-319-93040-4"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1007\/s00371-015-1192-x","article-title":"A Visual-Numeric Approach to Clustering and Anomaly Detection for Trajectory Data","volume":"33","author":"Kumar","year":"2017","journal-title":"Vis. Comput."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Annoni, R., and Forster, C.H.Q. (2012, January 16\u201319). Analysis of Aircraft Trajectories Using Fourier Descriptors and Kernel Density Estimation. Proceedings of the International IEEE Conference on Intelligent Transportation Systems, Anchorage, AK, USA.","DOI":"10.1109\/ITSC.2012.6338863"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Guo, Y., Xu, Q., Li, P., Sbert, M., and Yang, Y. (2017). Trajectory Shape Analysis and Anomaly Detection Utilizing Information Theory Tools. Entropy, 19.","DOI":"10.3390\/e19070323"},{"key":"ref_19","unstructured":"Keogh, E., Lin, J., and Fu, A. (2005, January 27\u201330). HOT SAX: Efficiently Finding the Most Unusual Time Series Subsequence. Proceedings of the IEEE International Conference on Data Mining, Houston, TX, USA."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1007\/s10115-008-0131-9","article-title":"Disk Aware Discord Discovery: Finding Unusual Time Series in Terabyte Sized Datasets","volume":"17","author":"Yankov","year":"2008","journal-title":"Knowl. Inf. Syst."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Lee, J.G., Han, J., and Li, X. (2008, January 7\u201312). Trajectory Outlier Detection: A Partition-and-Detect Framework. Proceedings of the International Conference on Data Engineering, Cancun, Mexico.","DOI":"10.1109\/ICDE.2008.4497422"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1007\/s00521-017-3148-8","article-title":"A Group-Based Signal Filtering Approach for Trajectory Abstraction and Restoration","volume":"29","author":"Guo","year":"2018","journal-title":"Neural Comput. Appl."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Banerjee, P., Yawalkar, P., and Ranu, S. (2016, January 13\u201317). MANTRA: A Scalable Approach to Mining Temporally Anomalous Sub-trajectories. Proceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Francisco, CA, USA.","DOI":"10.1145\/2939672.2939846"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1198","DOI":"10.1109\/TITS.2016.2601655","article-title":"Anomaly Detection in Traffic Scenes via Spatial-Aware Motion Reconstruction","volume":"18","author":"Yuan","year":"2017","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1016\/j.eswa.2017.04.028","article-title":"Detecting anomalies in time series data via a deep learning algorithm combining wavelets, neural networks and Hilbert transform","volume":"85","author":"Kanarachos","year":"2017","journal-title":"Expert Syst. Appl."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1542","DOI":"10.14778\/1454159.1454226","article-title":"Querying and Mining of Time Series Data: Experimental Comparison of Representations and Distance Measures","volume":"1","author":"Ding","year":"2008","journal-title":"VLDB Endow."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1093\/comjnl\/bxl065","article-title":"Hedging Predictions in Machine Learning","volume":"50","author":"Gammerman","year":"2007","journal-title":"Comput. J."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"15:1","DOI":"10.1145\/1541880.1541882","article-title":"Anomaly Detection: A Survey","volume":"41","author":"Chandola","year":"2009","journal-title":"ACM Comput. Surv."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1145\/191843.191925","article-title":"Fast Subsequence Matching in Time-Series Databases","volume":"23","author":"Faloutsos","year":"1994","journal-title":"SIGMOD Rec."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Albers, S., Alt, H., and N\u00e4her, S. (2009). The Computational Geometry of Comparing Shapes. Efficient Algorithms: Essays Dedicated to Kurt Mehlhorn on the Occasion of His 60th Birthday, Springer.","DOI":"10.1007\/978-3-642-03456-5"},{"key":"ref_31","unstructured":"Guo, Y. (2018, December 13). Matlab Code of Experiments. Available online: http:\/\/gilabparc.udg.edu\/trajectory\/experiments\/Experiments.zip."},{"key":"ref_32","unstructured":"Tan, P.N., Steinbach, M., and Kumar, V. (2007). Introduction to Data Mining, Pearson Education."},{"key":"ref_33","unstructured":"Piciarelli, C., Micheloni, C., and Foresti, G.L. (2018, December 14). Synthetic Trajectories by Piciarelli et al. Available online: https:\/\/avires.dimi.uniud.it\/papers\/trclust\/."},{"key":"ref_34","unstructured":"Morris, B., and Trivedi, M. (2018, December 14). Trajectory Clustering Datasets. Available online: http:\/\/cvrr.ucsd.edu\/bmorris\/datasets\/dataset_trajectory_clustering.html."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Morris, B., and Trivedi, M. (2009, January 20\u201325). Learning Trajectory Patterns by Clustering: Experimental Studies and Comparative Evaluation. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Miami, FL, USA.","DOI":"10.1109\/CVPR.2009.5206559"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1080\/01621459.1952.10483441","article-title":"Use of Ranks in One-Criterion Variance Analysis","volume":"47","author":"Kruskal","year":"1952","journal-title":"Am. Stat. Assoc."},{"key":"ref_37","unstructured":"Antunes, C.M., and Oliveira, A.L. (2001, January 26\u201329). Temporal Data Mining: An Overview. Proceedings of the KDD Workshop on Temporal Data Mining, San Francisco, CA, USA."},{"key":"ref_38","unstructured":"Lazarevi\u0107, A. (2018, December 14). First Set of Recorded Video Trajectories. Available online: https:\/\/www-users.cs.umn.edu\/~lazar027\/inclof\/."},{"key":"ref_39","unstructured":"Laxhammar, R. (2018, December 14). Synthetic Trajectories by Laxhammar. Available online: https:\/\/www.researchgate.net\/publication\/236838887_Synthetic_trajectories."},{"key":"ref_40","unstructured":"Piciarelli, C., Micheloni, C., and Foresti, G.L. (2018, December 14). Synthetic Trajectory Generator. Available online: https:\/\/avires.dimi.uniud.it\/papers\/trclust\/create_ts2.m."},{"key":"ref_41","unstructured":"Guo, Y. (2018, December 14). Synthetic Trajectories by Guo. Available online: http:\/\/gilabparc.udg.edu\/trajectory\/data\/SyntheticTrajectories.zip."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"14984","DOI":"10.1016\/j.eswa.2011.05.048","article-title":"Learning patterns of university student retention","volume":"38","author":"Nandeshwar","year":"2011","journal-title":"Expert Syst. Appl."},{"key":"ref_43","unstructured":"Chen, Y., Keogh, E., Hu, B., Begum, N., Bagnall, A., Mueen, A., and Batista, G. (2018, December 14). The UCR Time Series Classification Archive. Available online: www.cs.ucr.edu\/~eamonn\/time_series_data\/."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/1\/84\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:36:20Z","timestamp":1760196980000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/1\/84"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,12,27]]},"references-count":43,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2019,1]]}},"alternative-id":["s19010084"],"URL":"https:\/\/doi.org\/10.3390\/s19010084","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2018,12,27]]}}}