{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T09:27:11Z","timestamp":1772184431245,"version":"3.50.1"},"reference-count":49,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2018,4,25]],"date-time":"2018-04-25T00:00:00Z","timestamp":1524614400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJGI"],"abstract":"<jats:p>Rapidly growing GPS (Global Positioning System) trajectories hide much valuable information, such as city road planning, urban travel demand, and population migration. In order to mine the hidden information and to capture better clustering results, a trajectory regression clustering method (an unsupervised trajectory clustering method) is proposed to reduce local information loss of the trajectory and to avoid getting stuck in the local optimum. Using this method, we first define our new concept of trajectory clustering and construct a novel partitioning (angle-based partitioning) method of line segments; second, the Lagrange-based method and Hausdorff-based K-means++ are integrated in fuzzy C-means (FCM) clustering, which are used to maintain the stability and the robustness of the clustering process; finally, least squares regression model is employed to achieve regression clustering of the trajectory. In our experiment, the performance and effectiveness of our method is validated against real-world taxi GPS data. When comparing our clustering algorithm with the partition-based clustering algorithms (K-means, K-median, and FCM), our experimental results demonstrate that the presented method is more effective and generates a more reasonable trajectory.<\/jats:p>","DOI":"10.3390\/ijgi7050164","type":"journal-article","created":{"date-parts":[[2018,4,25]],"date-time":"2018-04-25T11:15:39Z","timestamp":1524654939000},"page":"164","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["A Trajectory Regression Clustering Technique Combining a Novel Fuzzy C-Means Clustering Algorithm with the Least Squares Method"],"prefix":"10.3390","volume":"7","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9349-7487","authenticated-orcid":false,"given":"Xiangbing","family":"Zhou","sequence":"first","affiliation":[{"name":"School of Information and Engineering, Sichuan Tourism University, Chengdu 610100, China"},{"name":"Key Lab of Earth Exploration &amp; Information Techniques of Ministry Education, Chengdu University of Technology, Chengdu 610059, China"},{"name":"School of Mathematics and Computer Science, Aba Teachers University, Wenchuan 623002, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fang","family":"Miao","sequence":"additional","affiliation":[{"name":"Key Lab of Earth Exploration &amp; Information Techniques of Ministry Education, Chengdu University of Technology, Chengdu 610059, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hongjiang","family":"Ma","sequence":"additional","affiliation":[{"name":"School of Computer Science, Chengdu University of Information Technology, Chengdu 610225, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hua","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Information and Engineering, Sichuan Tourism University, Chengdu 610100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huaming","family":"Gong","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computer Science, Aba Teachers University, Wenchuan 623002, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,4,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Zheng, Y., Liu, Y., Yuan, J., and Xie, X. (2011, January 17\u201321). Urban computing with taxicabs. Proceedings of the 13th International Conference on Ubiquitous Computing, Beijing, China.","DOI":"10.1145\/2030112.2030126"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/j.eswa.2016.12.018","article-title":"Detection of traffic congestion and incidents from gps trace analysis","volume":"73","author":"Marcelloni","year":"2017","journal-title":"Expert Syst. Appl."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1016\/j.ins.2016.06.033","article-title":"Mining urban recurrent congestion evolution patterns from gps-equipped vehicle mobility data","volume":"373","author":"An","year":"2016","journal-title":"Inf. Sci."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"344","DOI":"10.1016\/j.neucom.2017.06.017","article-title":"Efficient traffic congestion estimation using multiple spatio-temporal properties","volume":"267","author":"Yang","year":"2017","journal-title":"Neurocomputing"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1016\/j.neucom.2015.08.100","article-title":"Identifying mismatch between urban travel demand and transport network services using gps data: A case study in the fast growing chinese city of harbin","volume":"181","author":"Cui","year":"2016","journal-title":"Neurocomputing"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Qu, M., Zhu, H., Liu, J., Liu, G., and Xiong, H. (2014, January 24\u201327). A cost-effective recommender system for taxi drivers. Proceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Las Vegas, NV, USA.","DOI":"10.1145\/2623330.2623668"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1016\/j.jtrangeo.2015.12.007","article-title":"Detecting urban road network accessibility problems using taxi gps data","volume":"51","author":"Cui","year":"2016","journal-title":"J. Transp. Geogr."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2149","DOI":"10.1109\/TVCG.2013.226","article-title":"Visual exploration of big spatio-temporal urban data: A study of new york city taxi trips","volume":"19","author":"Ferreira","year":"2013","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Kharrat, A., Popa, I.S., Zeitouni, K., and Faiz, S. (2008). Clustering algorithm for network constraint trajectories. Headway in Spatial Data Handling, Springer.","DOI":"10.1007\/978-3-540-68566-1_36"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Lee, J.-G., Han, J., and Whang, K.-Y. (2007, January 12\u201314). Trajectory clustering: A partition-and-group framework. Proceedings of the 2007 ACM SIGMOD International Conference on Management of Data, Beijing, China.","DOI":"10.1145\/1247480.1247546"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1007\/s10586-014-0413-9","article-title":"A scalable and fast optics for clustering trajectory big data","volume":"18","author":"Deng","year":"2015","journal-title":"Clust. Comput."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"416","DOI":"10.1109\/TMC.2013.119","article-title":"Road-network aware trajectory clustering: Integrating locality, flow, and density","volume":"14","author":"Han","year":"2015","journal-title":"IEEE Trans. Mob. Comput."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Lou, Y., Zhang, C., Zheng, Y., Xie, X., Wang, W., and Huang, Y. (2009, January 4\u20136). Map-matching for low-sampling-rate gps trajectories. Proceedings of the 17th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems, Seattle, WA, USA.","DOI":"10.1145\/1653771.1653820"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Yuan, J., Zheng, Y., Zhang, C., Xie, X., and Sun, G.-Z. (2010, January 23\u201326). An interactive-voting based map matching algorithm. Proceedings of the 2010 Eleventh International Conference on Mobile Data Management (MDM), Kansas City, MO, USA.","DOI":"10.1109\/MDM.2010.14"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1016\/j.jtrangeo.2015.12.003","article-title":"An analysis of drivers route choice behaviour using gps data and optimal alternatives","volume":"51","author":"Hadjidimitriou","year":"2016","journal-title":"J. Transp. Geogr."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Luo, T., Zheng, X., Xu, G., Fu, K., and Ren, W. (2017). An improved dbscan algorithm to detect stops in individual trajectories. ISPRS Int. J. Geo-Inf., 6.","DOI":"10.3390\/ijgi6030063"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"348","DOI":"10.1111\/tgis.12313","article-title":"Adcn: An anisotropic density-based clustering algorithm for discovering spatial point patterns with noise","volume":"22","author":"Mai","year":"2018","journal-title":"Trans. GIS"},{"key":"ref_18","unstructured":"Han, J., Pei, J., and Kamber, M. (2011). Data Mining: Concepts and Techniques, Elsevier."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"651","DOI":"10.1016\/j.patrec.2009.09.011","article-title":"Data clustering: 50 years beyond k-means","volume":"31","author":"Jain","year":"2010","journal-title":"Pattern Recognit. Lett."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1142","DOI":"10.1016\/j.neucom.2015.08.071","article-title":"The discovery of personally semantic places based on trajectory data mining","volume":"173","author":"Lv","year":"2016","journal-title":"Neurocomputing"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"942","DOI":"10.1109\/TKDE.2010.237","article-title":"Seeking quality of web service composition in a semantic dimension","volume":"23","author":"Lecue","year":"2011","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"ref_22","unstructured":"Arthur, D., and Vassilvitskii, S. (2007, January 7\u20139). K-means++: The advantages of careful seeding. Proceedings of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms, New Orleans, LA, USA."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"622","DOI":"10.14778\/2180912.2180915","article-title":"Scalable k-means++","volume":"5","author":"Bahmani","year":"2012","journal-title":"Proc. VLDB Endow."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"370","DOI":"10.1109\/91.413225","article-title":"On cluster validity for the fuzzy c-means model","volume":"3","author":"Pal","year":"1995","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_25","first-page":"69","article-title":"Completeness and total boundedness of the hausdorff metric","volume":"1","author":"Henrikson","year":"1999","journal-title":"MIT Undergrad. J. Math."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1016\/S0020-0255(02)00208-6","article-title":"An evolutionary technique based on k-means algorithm for optimal clustering in rn","volume":"146","author":"Bandyopadhyay","year":"2002","journal-title":"Inf. Sci."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1016\/j.patcog.2003.06.005","article-title":"Validity index for crisp and fuzzy clusters","volume":"37","author":"Pakhira","year":"2004","journal-title":"Pattern Recognit."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1650","DOI":"10.1109\/TPAMI.2002.1114856","article-title":"Performance evaluation of some clustering algorithms and validity indices","volume":"24","author":"Maulik","year":"2002","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_29","unstructured":"(2017, October 10). Real-World Taxi-Gps Data Sets. Available online: https:\/\/github.com\/bigdata002\/Location-data-sets."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Zhou, X., Gu, J., Shen, S., Ma, H., Miao, F., Zhang, H., and Gong, H. (2017). An automatic k-means clustering algorithm of gps data combining a novel niche genetic algorithm with noise and density. ISPRS Int. J. Geo-Inf., 6.","DOI":"10.3390\/ijgi6120392"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"811","DOI":"10.1007\/s12650-016-0357-7","article-title":"Exploring od patterns of interested region based on taxi trajectories","volume":"19","author":"Lu","year":"2016","journal-title":"J. Vis."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1016\/j.datak.2007.10.008","article-title":"A conceptual view on trajectories","volume":"65","author":"Spaccapietra","year":"2008","journal-title":"Data Knowl. Eng."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1016\/j.knosys.2015.11.009","article-title":"Efficient reverse spatial and textual k nearest neighbor queries on road networks","volume":"93","author":"Luo","year":"2016","journal-title":"Knowl.-Based Syst."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Chang, C., and Zhou, B. (2009, January 6\u20139). Multi-granularity visualization of trajectory clusters using sub-trajectory clustering. Proceedings of the IEEE International Conference on Data Mining Workshops, Miami, FL, USA.","DOI":"10.1109\/ICDMW.2009.24"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"871","DOI":"10.1109\/TKDE.2003.1209005","article-title":"An approach for measuring semantic similarity between words using multiple information sources","volume":"15","author":"Li","year":"2003","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"ref_36","first-page":"81","article-title":"Means-type algorithm: A generalized convergence theorem and characterization of local optimality","volume":"6","author":"Sclim","year":"1984","journal-title":"IEEE. Trans. Pattern Anal."},{"key":"ref_37","unstructured":"Cox, E. (2005). Fuzzy Modeling and Genetic Algorithms for Data Mining and Exploration, Elsevier."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1016\/j.ins.2017.03.024","article-title":"Axiomatic generalization of the membership degree weighting function for fuzzy c means clustering: Theoretical development and convergence analysis","volume":"408","author":"Saha","year":"2017","journal-title":"Inf. Sci."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Bezdek, J.C. (1981). Pattern Recognition with Fuzzy Objective Function Algorithms, Plenum Press.","DOI":"10.1007\/978-1-4757-0450-1"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1016\/j.neucom.2015.01.106","article-title":"Kernel-based fuzzy c-means clustering algorithm based on genetic algorithm","volume":"188","author":"Ding","year":"2016","journal-title":"Neurocomputing"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"2744","DOI":"10.1016\/j.patcog.2009.04.018","article-title":"Towards improving fuzzy clustering using support vector machine: Application to gene expression data","volume":"42","author":"Mukhopadhyay","year":"2009","journal-title":"Pattern Recognit."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/j.ins.2017.11.020","article-title":"A constrained least squares regression model","volume":"429","author":"Yuan","year":"2018","journal-title":"Inf. Sci."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1016\/j.tcs.2016.05.044","article-title":"Fast quantum algorithms for least squares regression and statistic leverage scores","volume":"657","author":"Liu","year":"2017","journal-title":"Theor. Comput. Sci."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1016\/j.neucom.2016.12.029","article-title":"Robust regularized extreme learning machine for regression using iteratively reweighted least squares","volume":"230","author":"Chen","year":"2017","journal-title":"Neurocomputing"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1490","DOI":"10.1109\/TNNLS.2016.2551724","article-title":"Feature selection based on structured sparsity: A comprehensive study","volume":"28","author":"Gui","year":"2017","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Davies, D.L., and Bouldin, D.W. (1979). A cluster separation measure. IEEE. Trans. Pattern Anal., 224\u2013227.","DOI":"10.1109\/TPAMI.1979.4766909"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1080\/01969727308546046","article-title":"A fuzzy relative of the isodata process and its use in detecting compact well-separated clusters","volume":"3","author":"Dunn","year":"1973","journal-title":"J. Cybern."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"1210","DOI":"10.1016\/j.patcog.2008.11.006","article-title":"A genetic algorithm with gene rearrangement for k-means clustering","volume":"42","author":"Chang","year":"2009","journal-title":"Pattern Recognit."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"1506","DOI":"10.1109\/TGRS.2007.892604","article-title":"Multiobjective genetic clustering for pixel classification in remote sensing imagery","volume":"45","author":"Bandyopadhyay","year":"2007","journal-title":"IEEE Trans. Geosci. Remote Sens."}],"container-title":["ISPRS International Journal of Geo-Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2220-9964\/7\/5\/164\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:02:10Z","timestamp":1760194930000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2220-9964\/7\/5\/164"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,4,25]]},"references-count":49,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2018,5]]}},"alternative-id":["ijgi7050164"],"URL":"https:\/\/doi.org\/10.3390\/ijgi7050164","relation":{},"ISSN":["2220-9964"],"issn-type":[{"value":"2220-9964","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,4,25]]}}}