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[Page no. 2] "A survey on trajectory clustering analysis Jiang Biana, Dayong Tianb,∗, Yuanyan Tangc, Dacheng Taod aCentre for Artiﬁcial Intelligence, FEIT, University of Technology Sydney, Australia bSchool of Electronics and Information, Northwestern Polytechnical University, China cFaculty of Science and Technology, University of Macau, China dUBTECH Sydney AI Centre, FEIT, University of Sydney, Australia Abstract This paper comprehensively surveys the development of trajectory clustering. Considering the critical role of trajectory data mining in modern intelligent systems for surveillance security, abnormal behavior detection, crowd behav- ior analysis, and traﬃc control, trajectory clustering has attracted growing attention. Existing trajectory clustering methods can be grouped into three categories: unsupervised, supervised and semi-supervised algorithms. In spite of achieving a certain level of development, trajectory clustering is limited in its success by complex conditions such as application scenarios and data di- mensions. This paper provides a holistic understanding and deep insight into trajectory clustering, and presents a comprehensive analysis of representative methods and promising future directions. Keywords: trajectory clustering, object movement, pattern recognition, survey, review 1. Introduction With the development of tracking and surveillance devices, tremendous num- bers of object trajectory data were collected, which makes extracting useful information imperative and challenging. Trajectory clustering is an eﬃcient ∗Corresponding author Email addresses: <PRESIDIO_ANONYMIZED_EMAIL_ADDRESS> (Jiang Bian), <PRESIDIO_ANONYMIZED_EMAIL_ADDRESS> (Dayong Tian), <PRESIDIO_ANONYMIZED_EMAIL_ADDRESS> (Yuanyan Tang), <PRESIDIO_ANONYMIZED_EMAIL_ADDRESS> (Dacheng Tao) Preprint submitted to Journal of LATEX Templates July 18, 2024 arXiv:1802.06971v1 [cs.CV] 20 Feb 2018  method to analyze trajectory data and it has been applied in pattern recogni- tion, data analysis and machine learning, etc. Furthermore, trajectory clustering aims to gain space, time or even potential information inside trajectory data, so it is ubiquitous in some application ﬁelds such as object motion prediction [1], traﬃc monitoring [2][3][4], activity understanding [5][6][7], abnormal detection [8][9][10][11], 3 dimensional reconstruction[12], weather forecasting [13] and ge- ography [14]. Trajectory"

[Page no. 26] "in CNN. In addition, it should be noticed that a meaningful distance metric is essential for Nearest Neighbor algorithms. 7. Conclusion In this paper, we reviewed the methods of trajectory clustering. They are classiﬁed into three categories: unsupervised, supervised and semi-supervised algorithms. Unsupervised algorithms can be grouped into three sub-categories: 24  Densely Clustering models, Hierarchical Clustering models and Spectral Clus- tering models. Supervised algorithms are divided into Nearest Neighbor algo- rithms, statistical models and Neural Network. By means of a comprehensive analysis, we found that unsupervised algorithms have the disadvantages of high computation cost and heavy memory load, although there is no training data requirement and human experts supervising. Semi-supervised algorithms com- bine the advantages of both previous algorithms, and may result in more eﬃcient methods. Finally, we proposed several promising future directions and tasks, and this paper could help readers to gain a thorough understanding of trajec- tory clustering. References References [1] Z. Chen, H. T. Shen, X. Zhou, Y. Zheng, X. Xie, Searching trajectories by locations: an eﬃciency study, in: Proceedings of the 2010 ACM SIGMOD International Conference on Management of data, ACM, 2010, pp. 255– 266. [2] S. Atev, O. Masoud, N. Papanikolopoulos, Learning traﬃc patterns at intersections by spectral clustering of motion trajectories, in: IROS, 2006, pp. 4851–4856. [3] X. Li, J. Han, J.-G. Lee, H. Gonzalez, Traﬃc density-based discovery of hot routes in road networks, in: International Symposium on Spatial and Temporal Databases, Springer, 2007, pp. 441–459. [4] S. Gurung, D. Lin, W. Jiang, A. Hurson, R. Zhang, Traﬃc information publication with privacy preservation, ACM Transactions on Intelligent Systems and Technology (TIST) 5 (3) (2014) 44. 25  [5] F. I. Bashir, A. A. Khokhar, D. Schonfeld, Object trajectory-based ac- tivity classiﬁcation and recognition using hidden markov models, IEEE transactions on Image Processing 16"

[Page no. 17] "distance is utilized to measure the similarities and set as weights of edges in [113]. Since the great performance of PageRank, it is used to score the edges in [114], too. 3.4. Discussion Densely Clustering models classify trajectories by distance metrics mostly, which may result in classifying trajectory data by spatial information. Hierar- 16  chical Clustering models ﬁx this problem by considering more attributes in each level. However, this operation cost much more time in computation. Spectral Clustering models compute internal relationships by analyzing the aﬃnity ma- trix, and it saves much more computational resource by processing all trajectory data together. But [115] mentions that Spectral Clustering models have their own limitation that they are well deﬁned only for the non-negative aﬃnities between trajectories. Furthermore, that trajectory lengths are required to be uniﬁed is another issue of applying Spectral Clustering models. 4. Supervised Algorithms of Trajectory Clustering Supervised algorithms aims at learning a function which determines the la- bels of testing data after analyzing labeled training data. Therefore, supervised algorithms outperform on scene understanding and utilization of ground truth, and the algorithms could save much more computation resource. In some su- pervised algorithms, trajectory data are classiﬁed by unsupervised algorithms and the representations of clusters are obtained to classify new inquiry trajec- tories. For example, in Densely Clustering models, the representations can be computed from the grouped training trajectory data and new coming trajec- tories are clustered quickly in [5] and [87]. Trajectory data are classiﬁed and organized in a tree-construction and new coming trajectories are clustered by searching the tree in [4] and [116]. 4.1. Nearest Neighbor Algorithms Nearest Neighbor algorithms, such as k-Nearest Neighbor algorithm (k-NN), are ﬁnding a voting system to determine the category of a new coming entity and all data are kept in the"

[Page no. 22] "diﬀerences of trajectory data and requires a huge number of data to train it. Though the su- pervised methods obtain the classiﬁers by observing a number of training data, 21  overﬁtting problem may happen when the model overreacts training data. 5. Semi-supervised Algorithms of Trajectory Clustering Semi-supervised algorithms fall between unsupervised algorithms and super- vised algorithms. The algorithms make use of a small number of labeled data and continuous inquiry data to complete tasks. The model is trained by labeled data ﬁrstly, then inquiry data are kept sending to the trained model to make sure that it can be updated to outperform the previous model. Semi-supervised procedure needs only a small cost in terms of human classiﬁcation eﬀorts. This procedure not only avoids overﬁtting problem, but also is more accurate than the unsupervised ones. Therefore, some semi-supervised algorithms are invented from unsupervised or supervised algorithms. For example, trajectory data are classiﬁed ﬁrstly and the new inquiry ones are clustered to update the classiﬁer automatically [4][8][9][132]. Detected anomaly trajectory data are used to recalculate the rep- resentation of anomaly trajectory clusters in [132]. Trajectory data of video are modeled as the combination of normal and abnormal patterns, and probabilistic terms characterize the patterns in [9]. From this modeling, the terms can be updated by the detected inquiry trajectory. In order to detect abnormal trajec- tories faster in complex scene, low-rank approximation is employed to describe trajectory data and the new detected abnormal ones update the threshold in [8]. Inspired by Hierarchical Frameworks, trajectories and the clusters are rep- resented as a tree where children nodes indicate trajectories and roots de- note the representations of the clusters in [133], [134] and [135]. A new clus- ter is created if no clusters close to the inquiry trajectory. Trajectory T is constructed as"

[Page no. 30] "video analysis, IEEE transactions on pattern analysis and machine intel- ligence 36 (6) (2014) 1187–1200. [38] E. Elhamifar, R. Vidal, Sparse subspace clustering, in: Computer Vision and Pattern Recognition, 2009. CVPR 2009. IEEE Conference on, IEEE, 2009, pp. 2790–2797. [39] O. Capp´e, S. J. Godsill, E. Moulines, An overview of existing methods and recent advances in sequential monte carlo, Proceedings of the IEEE 95 (5) (2007) 899–924. 29  [40] J.-G. Lee, J. Han, K.-Y. Whang, Trajectory clustering: a partition-and- group framework, in: Proceedings of the 2007 ACM SIGMOD interna- tional conference on Management of data, ACM, 2007, pp. 593–604. [41] A. Anagnostopoulos, M. Vlachos, M. Hadjieleftheriou, E. Keogh, P. S. Yu, Global distance-based segmentation of trajectories, in: Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining, ACM, 2006, pp. 34–43. [42] Z. Yan, C. Parent, S. Spaccapietra, D. Chakraborty, A hybrid model and computing platform for spatio-semantic trajectories, in: Extended Seman- tic Web Conference, Springer, 2010, pp. 60–75. [43] D. R. Faria, J. Dias, 3d hand trajectory segmentation by curvatures and hand orientation for classiﬁcation through a probabilistic approach, in: 2009 IEEE/RSJ International Conference on Intelligent Robots and Sys- tems, IEEE, 2009, pp. 1284–1289. [44] Z. Zhang, K. Huang, T. Tan, L. Wang, Trajectory series analysis based event rule induction for visual surveillance, in: 2007 IEEE Conference on Computer Vision and Pattern Recognition, IEEE, 2007, pp. 1–8. [45] T. Tuytelaars, K. Mikolajczyk, Local invariant feature detectors: a survey, Foundations and trends R⃝ in computer graphics and vision 3 (3) (2008) 177–280. [46] B. T. Morris, M. M. Trivedi, A survey of vision-based trajectory learning and analysis for surveillance, IEEE transactions on circuits and systems for video technology 18 (8) (2008) 1114–1127. [47] N. Brandle, D. Bauer, S. Seer, Track-based ﬁnding of stopping pedestrians-a practical"

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