A. Andoni and P. Indyk, Near-optimal hashing algorithms for approximate nearest neighbor in high dimensions, Commun. ACM, vol.51, p.117122, 2008.

L. Arge, K. G. Larsen, T. Mølhave, and F. Van-walderveen, Cleaning massive sonar point clouds, Proceedings of the 18th SIGSPATIAL International Conference on Advances in Geographic Information Systems, GIS '10, p.152161
DOI : 10.1145/1869790.1869815

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.297.584

A. Beygelzimer, S. Kakade, and J. Langford, Cover trees for nearest neighbor, Proceedings of the 23rd international conference on Machine learning , ICML '06, 2006.
DOI : 10.1145/1143844.1143857

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.295.7306

R. Bruntrup, S. Edelkamp, S. Jabbar, and B. Scholz, Incremental map generation with GPS traces, Proceedings. 2005 IEEE Intelligent Transportation Systems, 2005., p.574579, 2005.
DOI : 10.1109/ITSC.2005.1520084

L. Cao and J. Krumm, From GPS traces to a routable road map, Proceedings of the 17th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems, GIS '09, p.312, 2009.
DOI : 10.1145/1653771.1653776

F. Chazal, D. Cohen-steiner, and Q. Mérigot, Geometric Inference for Probability Measures, Foundations of Computational Mathematics, vol.40, issue.2, 2011.
DOI : 10.1007/s10208-011-9098-0

URL : https://hal.archives-ouvertes.fr/hal-00772444

D. Chen, A. Driemel, L. J. Guibas, A. Nguyen, and C. Wenk, Approximate Map Matching with respect to the Fr??chet Distance, ALENEX, 2011.
DOI : 10.1137/1.9781611972917.8

D. Chen, C. Lu, Y. Kou, and F. Chen, On Detecting Spatial Outliers, GeoInformatica, vol.75, issue.3, pp.455475-10707, 1007.
DOI : 10.1007/s10707-007-0038-8

F. Chen, C. Lu, and A. P. Boedihardjo, GLS-SOD, Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining, KDD '10, p.10691078, 2010.
DOI : 10.1145/1835804.1835939

H. Chen, W. Ku, H. Wang, and M. Sun, Leveraging spatio-temporal redundancy for rd data cleansing, International Conference on Management of Data, p.5162, 2010.

Z. Chen, H. T. Shen, and X. Zhou, Discovering popular routes from trajectories, 2011 IEEE 27th International Conference on Data Engineering, p.900911, 2011.
DOI : 10.1109/ICDE.2011.5767890

R. Cheng, J. Chen, and X. Xie, Cleaning uncertain data with quality guarantees, Proceedings of The Vldb Endowment, p.722735, 2008.
DOI : 10.14778/1453856.1453935

H. Cherno, A measure of asymptotic eciency of tests of a hypothesis based on the sum of observations, Annals of Mathematical Statistics, 1952.

K. L. Clarkson, A Randomized Algorithm for Closest-Point Queries, SIAM Journal on Computing, vol.17, issue.4, p.830847, 1988.
DOI : 10.1137/0217052

E. Guilbert and H. Lin, B-Spline curve smoothing under position constraints for line generalisation, Proceedings of the 14th annual ACM international symposium on Advances in geographic information systems , GIS '06, p.310, 2006.
DOI : 10.1145/1183471.1183474

M. M. Hall, A. N. Alazzawi, A. A. Abdelmoty, and C. B. Jones, Improving the quality of gps-based personal gazetteers

S. Har-peled, A replacement for Voronoi diagrams of near linear size, Proceedings 2001 IEEE International Conference on Cluster Computing, p.94, 2001.
DOI : 10.1109/SFCS.2001.959884

T. Hastie and W. Stuetzle, Principal Curves, Journal of the American Statistical Association, vol.26, issue.406, p.502516, 1989.
DOI : 10.1080/03610927508827223

T. Hastie, R. Tibshirani, and J. Friedman, The Elements of Statistical Learning, 2001.

T. J. Hastie and R. J. Tibshirani, Generalized additive models, 1990.

N. Hönle, M. Grossmann, S. Reimann, and B. Mitschang, Usability analysis of compression algorithms for position data streams, Proceedings of the 18th SIGSPATIAL International Conference on Advances in Geographic Information Systems, GIS '10, p.240249, 2010.

H. Huang, Y. Zhu, X. Li, M. Li, and M. Wu, META: A Mobility Model of MEtropolitan TAxis Extracted from GPS Traces, 2010 IEEE Wireless Communication and Networking Conference, p.16, 2010.
DOI : 10.1109/WCNC.2010.5506591

L. Huang, Q. Li, and Y. Yue, Activity identication from gps trajectories using spatial temporal pois' attractiveness, Proceedings of the ACM SIGSPATIAL International Workshop on Location Based Social Networks, 2010.

P. Indyk and R. Motwani, Approximate nearest neighbors, Proceedings of the thirtieth annual ACM symposium on Theory of computing , STOC '98, p.604613, 1998.
DOI : 10.1145/276698.276876

H. Jeung, M. L. Yiu, X. Zhou, C. S. Jensen, and H. T. Shen, Discovery of convoys in trajectory databases, Proceedings of the VLDB Endowment, vol.1, issue.1, 2010.
DOI : 10.14778/1453856.1453971

S. Johansson and M. Jern, Geoanalytics visual inquiry and ltering tools in parallel coordinates plots, Proceedings of the 15th annual ACM international symposium on Advances in geographic information systems, GIS '07, 2007.

D. G. Kendall, Shape Manifolds, Procrustean Metrics, and Complex Projective Spaces. Bulletin of the, p.81121, 1984.

X. Liu, C. Lu, and F. Chen, Spatial outlier detection, Proceedings of the 18th SIGSPATIAL International Conference on Advances in Geographic Information Systems, GIS '10, p.370379, 2010.
DOI : 10.1145/1869790.1869841

D. Mount and S. Arya, Ann: A library for approximate nearest neighbor searching

M. Okamoto, Some inequalities relating to the partial sum of binomial probabilities, Annals of the Institute of Statistical Mathematics, vol.7, issue.1, 1958.
DOI : 10.1007/BF02883985

B. Oksendal, Stochastic dierential equations): an introduction with applications, 1992.

A. Panangadan and A. Talukder, A variant of particle ltering using historic datasets for tracking complex geospatial phenomena, Proceedings of the 18th SIGSPATIAL International Conference on Advances in Geographic Information Systems, GIS '10, p.232239, 2010.

D. Ruppert and M. P. Wand, Multivariate locally weighted least squares regression. The Annals of Statistics, p.13461370, 1994.

Y. Sabharwal, N. Sharma, and S. Sen, Nearest neighbors search using point location in balls with applications to approximate voronoi decompositions

G. Sánchez, J. Lladós, and K. Tombre, A mean string algorithm to compute the average among a set of 2D shapes, Pattern Recognition Letters, vol.23, issue.1-3, p.203213, 2002.
DOI : 10.1016/S0167-8655(01)00122-2

M. I. Shamos and D. Hoey, Closest-point problems, 16th Annual Symposium on Foundations of Computer Science (sfcs 1975), p.151162, 1975.
DOI : 10.1109/SFCS.1975.8

S. Shekhar, C. Lu, and P. Zhang, Detecting graph-based spatial outliers, Proceedings of the seventh ACM SIGKDD international conference on Knowledge discovery and data mining , KDD '01
DOI : 10.1145/502512.502567

S. Shekhar, C. Tien-lu, and P. Zhang, A unied approach to detecting spatial outliers, Geoinformatica, vol.7, p.139166, 2003.

F. Takens, Detecting strange attractors in turbulence
DOI : 10.1007/BF01646553

C. Tien-lu, D. Chen, and Y. Kou, Multivariate spatial outlier detection, International Journal on Articial Intelligence Tools, vol.13, p.801812, 2004.

G. Welch and G. Bishop, An introduction to the kalman lter, 1995.

H. Yoon, Y. Zheng, X. Xie, and W. Woo, Smart Itinerary Recommendation Based on User-Generated GPS Trajectories, Ubiquitous Intelligence and Computing -7th International Conference. Proceedings, p.1934, 2010.
DOI : 10.1007/978-3-642-16355-5_5

L. Zhang, F. Thiemann, and M. Sester, Integration of GPS traces with road map, Proceedings of the Second International Workshop on Computational Transportation Science, IWCTS '10, 2010.
DOI : 10.1145/1899441.1899447

Y. Zheng and X. Xie, Learning travel recommendations from user-generated GPS traces, ACM Transactions on Intelligent Systems and Technology, vol.2, issue.1, 2011.
DOI : 10.1145/1889681.1889683

·. ·. Proof, When the sampled time points on f (i) are not synchronized with that on g. Let k be the time points on f (i) which is closest to 0. We consider two cases: either |x| < 1/4 or |x| ? 1/4. We will show that in any of the two cases, the lifted image on?fon? on?f (i) whose delay coordinates centered at k will be one of the two nearest neighbors of g ?n