Finding long and similar parts of trajectories

A natural time-dependent similarity measure for two trajectories is their average distance at corresponding times. We give algorithms for computing the most similar subtrajectories under this measure, assuming the two trajectories are given as two polygonal, possibly self-intersecting lines with time stamps. For the case when a minimum duration of the subtrajectories is specified and the subtrajectories must start at corresponding times, we give a linear-time algorithm. The algorithm is based on a result of independent interest: We present a linear-time algorithm to find, for a piece-wise monotone function, an interval of at least a given length that has minimum average value. In the case that the subtrajectories may start at non-corresponding times, it appears difficult to give exact algorithms, even if the duration of the subtrajectories is fixed. For this case, we give (1+@e)-approximation algorithms, for both fixed duration and when only a minimum duration is specified.

[1]  Friedrich Eisenbrand,et al.  A geometric framework for solving subsequence problems in computational biology efficiently , 2007, SCG '07.

[2]  Joachim Gudmundsson,et al.  Compressing Spatio-temporal Trajectories , 2007, ISAAC.

[3]  Ming-Yang Kao,et al.  Linear-time algorithms for computing maximum-density sequence segments with bioinformatics applications , 2002, J. Comput. Syst. Sci..

[4]  Yaw-Ling Lin,et al.  Efficient algorithms for locating the length-constrained heaviest segments with applications to biomolecular sequence analysis , 2002, J. Comput. Syst. Sci..

[5]  Jae-Gil Lee,et al.  TraClass: trajectory classification using hierarchical region-based and trajectory-based clustering , 2008, Proc. VLDB Endow..

[6]  Eamonn J. Keogh,et al.  Scaling up dynamic time warping for datamining applications , 2000, KDD '00.

[7]  Marc van Kreveld,et al.  The definition and computation of trajectory and subtrajectory similarity , 2007, GIS.

[8]  Joseph O'Rourke,et al.  Handbook of Discrete and Computational Geometry, Second Edition , 1997 .

[9]  Dimitrios Gunopulos,et al.  Discovering similar multidimensional trajectories , 2002, Proceedings 18th International Conference on Data Engineering.

[10]  Roberto Tamassia,et al.  Dynamics-aware similarity of moving objects trajectories , 2007, GIS.

[11]  Michael T. Goodrich,et al.  Efficiently Approximating Polygonal Paths in Three and Higher Dimensions , 1998, SCG '98.

[12]  Kevin Buchin,et al.  Exact algorithms for partial curve matching via the Fréchet distance , 2009, SODA.

[13]  Hsueh-I Lu,et al.  An Optimal Algorithm for the Maximum-Density Segment Problem , 2003, SIAM J. Comput..

[14]  Jae-Gil Lee,et al.  Trajectory clustering: a partition-and-group framework , 2007, SIGMOD '07.

[15]  Dino Pedreschi,et al.  Time-focused clustering of trajectories of moving objects , 2006, Journal of Intelligent Information Systems.

[16]  Yannis Theodoridis,et al.  Index-based Most Similar Trajectory Search , 2007, 2007 IEEE 23rd International Conference on Data Engineering.

[17]  David M. Mark,et al.  Measuring similarity between geospatial lifelines in studies of environmental health , 2005, J. Geogr. Syst..

[18]  Tetsuji Satoh,et al.  Shape-Based Similarity Query for Trajectory of Mobile Objects , 2003, Mobile Data Management.

[19]  Ouri Wolfson,et al.  Spatio-temporal data reduction with deterministic error bounds , 2003, DIALM-POMC '03.

[20]  Lei Chen,et al.  Robust and fast similarity search for moving object trajectories , 2005, SIGMOD '05.

[21]  Dimitrios Gunopulos,et al.  Rotation invariant distance measures for trajectories , 2004, KDD.

[22]  Joachim Gudmundsson,et al.  Detecting Commuting Patterns by Clustering Subtrajectories , 2008, Int. J. Comput. Geom. Appl..

[23]  Joachim Gudmundsson,et al.  Constrained free space diagrams: a tool for trajectory analysis , 2010, Int. J. Geogr. Inf. Sci..