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Coarse-DTW for Sparse Time Series Alignment

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Advanced Analysis and Learning on Temporal Data (AALTD 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9785))

Abstract

Dynamic Time Warping (DTW) is considered as a robust measure to compare numerical time series when some time elasticity is required. However, speed is a known major drawback of DTW due to its quadratic complexity. Previous work has mainly considered designing speed optimization based on early-abandoning strategies applied to nearest-neighbor classification, although some of these optimizations are restricted to uni-dimensional time series. In this paper, we introduce Coarse-DTW, a reinterpretation of DTW for sparse time series, which exploits adaptive downsampling to achieve speed enhancement, even when faced with multidimensional time series. We show that Coarse-DTW achieves nontrivial speedups in nearest-neighbor classification and even admits a positive-definite kernelization suitable for SVM classification, hence offering a good tradeoff between speed and accuracy.

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References

  1. Al-Naymat, G., Chawla, S., Taheri, J.: Sparsedtw: a novel approach to speed up dynamic time warping. In: Proceedings of the Eighth Australasian Data Mining Conference, AusDM 2009, Darlinghurst, Australia, vol. 101, pp. 117–127. Australian Computer Society Inc., Australia (2009)

    Google Scholar 

  2. Apostolico, A., Landau, G.M., Skiena, S.: Matching for run-length encoded strings. In: 1997 Proceedings of the Compression and Complexity of Sequences, pp. 348–356, June 1997

    Google Scholar 

  3. Berg, C., Christensen, J.P.R., Ressel, P.: Harmonic Analysis on Semigroups: Theory of Positive Definite and Related Functions. Graduate Texts in Mathematics, vol. 100. Springer, New York (1984)

    MATH  Google Scholar 

  4. Chakrabarti, K., Keogh, E., Mehrotra, S., Pazzani, M.: Locally adaptive dimensionality reduction for indexing large time series databases. ACM Trans. Database Syst. 27(2), 188–228 (2002)

    Article  Google Scholar 

  5. Chen, L., Ng, R.: On the marriage of Lp-norm and edit distance. In: Proceedings of the 30th International Conference on Very Large Data Bases, pp. 792–801 (2004)

    Google Scholar 

  6. Chu, S., Keogh, E.J., Hart, D.M., Pazzani, M.J.: Iterative deepening dynamic time warping for time series. In: Grossman, R.L., Han, J., Kumar, V., Mannila, H., Motwani, R. (eds.) Proceedings of the Second SIAM International Conference on Data Mining, Arlington, VA, USA, 11–13 April 2002, pp. 195–212. SIAM (2002)

    Google Scholar 

  7. Cuturi, M., Vert, J.-P., Birkenes, O., Matsui, T.: A kernel for time series based on global alignments. In: IEEE ICASSP 2007, vol. 2, pp. II-413–II-416, April 2007

    Google Scholar 

  8. Fréchet, M.: Sur Quelques Points du Calcul Fonctionnel. Thèse, Faculté des Sciences de Paris (1906)

    Google Scholar 

  9. Gudmundsson, S., Runarsson, T.P., Sigurdsson, S.: Support vector machines and dynamic time warping for time series. In: 2008 IEEE International Joint Conference on Neural Networks, IJCNN 2008. IEEE World Congress on Computational Intelligence, pp. 2772–2776, June 2008

    Google Scholar 

  10. Itakura, F.: Minimum prediction residual principle applied to speech recognition. IEEE Trans. Acoust. Speech Sig. Process. 23(1), 67–72 (1975)

    Article  Google Scholar 

  11. Keogh, E.J., Xi, X., Wei, L., Ratanamahatana, C.A.: The UCR time series classification-clustering datasets (2006). http://wwwcs.ucr.edu/eamonn/time_series_data/

  12. Keogh, E., Chakrabarti, K., Pazzani, M., Mehrotra, S.: Dimensionality reduction for fast similarity search in large time series databases. J. Knowl. Inf. Syst. 3, 263–286 (2000)

    Article  MATH  Google Scholar 

  13. Keogh, E., Ratanamahatana, C.A.: Exact indexing of dynamic time warping. Knowl. Inf. Syst. 7(3), 358–386 (2005)

    Article  Google Scholar 

  14. Keogh, E.J., Pazzani, M.J.: Scaling up dynamic time warping for datamining applications. In: Proceedings of the Sixth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 2000, pp. 285–289. ACM, New York, NY, USA (2000)

    Google Scholar 

  15. Lemire, D.: Faster retrieval with a two-pass dynamic-time-warping lower bound. Pattern Recogn. 42(9), 2169–2180 (2009)

    Article  MATH  Google Scholar 

  16. Li, W., Zhang, Z., Liu, Z.: Action recognition based on a bag of 3D points. In: Proceedings of IEEE International Workshop on CVPR for Human Communicative Behavior Analysis, pp. 9–14. IEEE CS Press (2010)

    Google Scholar 

  17. Marteau, P.F.: Time warp edit distance with stiffness adjustment for time series matching. IEEE Trans. Pattern Anal. Mach. Intell. 31(2), 306–318 (2008)

    Article  Google Scholar 

  18. Marteau, P.-F., Gibet, S.: On recursive edit distance kernels with application to time series classification. IEEE Trans. Neural Netw. Learn. Syst., 1–14 (2014)

    Google Scholar 

  19. Marteau, P.-F., Gibet, S., Reverdy, C.: Down-Sampling coupled to elastic kernel machines for efficient recognition of isolated gestures. In: International Conference on Pattern Recognition, ICPR 2014, pp. 336–368. IEEE, Stockholm, Sweden, August 2014

    Google Scholar 

  20. Patel, P., Keogh, E., Lin, J., Lonardi, S.: Mining motifs in massive time series databases. In: Proceedings of IEEE International Conference on Data Mining, ICDM 2002, pp. 370–377 (2002)

    Google Scholar 

  21. Sakoe, H., Chiba, S.: A dynamic programming approach to continuous speech recognition. In: Proceedings of the 7th International Congress of Acoustic, pp. 65–68 (1971)

    Google Scholar 

  22. Sakurai, Y., Yoshikawa, M., Faloutsos, C.: FTW: Fast similarity search under the time warping distance. In: Proceedings of the Twenty-Fourth ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, PODS 2005, pp. 326–337. ACM, New York, NY, USA (2005)

    Google Scholar 

  23. Salvador, S., Chan, P.: Toward accurate dynamic time warping in linear time and space. Intell. Data Anal. 11(5), 561–580 (2007)

    Google Scholar 

  24. Shou, Y., Mamoulis, N., Cheung, D.W.: Fast and exact warping of time series using adaptive segmental approximations. Mach. Learn. 58(2–3), 231–267 (2005)

    Article  MATH  Google Scholar 

  25. Velichko, V.M., Zagoruyko, N.G.: Automatic recognition of 200 words. Int. J. Man-Mach. Stud. 2, 223–234 (1970)

    Article  Google Scholar 

  26. Kim, S.W., Park, S., Chu, W.W.: An index-based approach for similarity search supporting time warping in large sequence databases. In: ICDE, pp. 607–614 (2001)

    Google Scholar 

  27. Yi, B.-K., Faloutsos, C.: Fast time sequence indexing for arbitrary Lp norms. In: Proceedings of the 26th International Conference on Very Large Data Bases, VLDB 2000, pp. 385–394. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2000)

    Google Scholar 

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Acknowledgements

This study was co-funded by the ANRT agency and Thales Optronique SAS, under the PhD CIFRE convention 2013/0932.

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Authors and Affiliations

  1. IRISA, Université de Bretagne Sud, Campus de Tohannic, Vannes, France

    Marc Dupont & Pierre-François Marteau

  2. Thales Optronique, 2 Avenue Gay Lussac, Elancourt, France

    Marc Dupont

Authors
  1. Marc Dupont
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  2. Pierre-François Marteau
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Correspondence to Marc Dupont .

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Editors and Affiliations

  1. Lab. d'Informatique de Grenoble, Université Grenoble, Grenoble, France

    Ahlame Douzal-Chouakria

  2. Universidade da Coruna, Coruna, Spain

    José A. Vilar

  3. IRISA, Université de Bretagne-Sud, Vannes, France

    Pierre-François Marteau

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Dupont, M., Marteau, PF. (2016). Coarse-DTW for Sparse Time Series Alignment. In: Douzal-Chouakria, A., Vilar, J., Marteau, PF. (eds) Advanced Analysis and Learning on Temporal Data. AALTD 2015. Lecture Notes in Computer Science(), vol 9785. Springer, Cham. https://doi.org/10.1007/978-3-319-44412-3_11

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  • DOI: https://doi.org/10.1007/978-3-319-44412-3_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-44411-6

  • Online ISBN: 978-3-319-44412-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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