Revisiting Techniques for Lowerbounding the Dynamic Time Warping Distance

  • Tomáš Bartoš
  • Tomáš Skopal
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7404)


The dynamic time warping (DTW) distance has been used as a popular measure to compare similarities of numeric time series because it provides robust matching that recognizes warps in time, different sampling rate, etc. Although DTW computation can be optimized by dynamic programming, it is still expensive, so there have been many attempts proposed to speedup DTW-based similarity search by distance lowerbounding. Some approaches assume a constrained variant of DTW (i.e., fixed dimensions, warping window constraint, ground distance), while others do not. In this paper, we comprehensively revisit the problem of DTW lowerbounding, define a general form of DTW that fits all the existing variants and goes even beyond. For the constrained variants of general DTW we propose a lowerbound construction generalizing the LB_Keogh that for particular ground distances offers speedup by up to two orders of magnitude. Furthermore, we apply metric and ptolemaic lowerbounding on unconstrained variants of general DTW that beats the few existing competitors up to two orders of magnitude.


Time Series Dynamic Time Warping Query Object Ground Distance Dynamic Time Warping Distance 
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  1. 1.
    Assent, I., Wichterich, M., Krieger, R., Kremer, H., Seidl, T.: Anticipatory dtw for efficient similarity search in time series databases. Proc. VLDB Endow. 2, 826–837 (2009)Google Scholar
  2. 2.
    Berndt, D.J., Clifford, J.: Using Dynamic Time Warping to Find Patterns in Time Series. In: KDD Workshop, pp. 359–370 (1994)Google Scholar
  3. 3.
    Camerra, A., Palpanas, T., Shieh, J., Keogh, E.: iSAX 2.0:indexing and mining one billion time series. In: IEEE International Conf. on Data Mining, pp. 58–67 (2010)Google Scholar
  4. 4.
    Chávez, E., Navarro, G., Baeza-Yates, R., Marroquín, J.L.: Searching in metric spaces. ACM Computing Surveys 33(3), 273–321 (2001)CrossRefGoogle Scholar
  5. 5.
    Hetland, M.L.: Ptolemaic indexing. arXiv:0911.4384 [cs.DS] (2009)Google Scholar
  6. 6.
    Junkui, L., Yuanzhen, W.: Early abandon to accelerate exact dynamic time warping. Int. Arab. J. Inf. Technol. 6(2), 144–152 (2009)Google Scholar
  7. 7.
    Keogh, E.: Exact indexing of dynamic time warping. In: Proceedings of the 28th International Conference on Very Large Data Bases, pp. 406–417 (2002)Google Scholar
  8. 8.
    Keogh, E., Ratanamahatana, C.A.: Exact indexing of dynamic time warping. Knowledge and Information Systems 7, 358–386 (2005), doi:10.1007/s10115-004-0154-9CrossRefGoogle Scholar
  9. 9.
    Keogh, E., Xi, X., Wei, L., Ratanamahatana, C.: The UCR Time Series Classification/Clustering Homepage (2006)Google Scholar
  10. 10.
    Kim, S.-W., Park, S., Chu, W.W.: An index-based approach for similarity search supporting time warping in large sequence databases. In: Proceedings of the 17th International Conference on Data Engineering, pp. 607–614. IEEE Computer Society, Washington, DC (2001)Google Scholar
  11. 11.
    Lokoč, J., Hetland, M.L., Skopal, T., Beecks, C.: Ptolemaic indexing of the signature quadratic form distance. In: Proceedings of the Fourth International Conference on Similarity Search and Applications, pp. 9–16. ACM (2011)Google Scholar
  12. 12.
    Mico, M.L., Oncina, J., Vidal, E.: A new version of the nearest-neighbour approximating and eliminating search algorithm (aesa) with linear preprocessing time and memory requirements. Pattern Recogn. Lett. 15(1), 9–17 (1994)CrossRefGoogle Scholar
  13. 13.
    Rabiner, L., Juang, B.-H.: Fundamentals of speech recognition. Prentice-Hall, Inc., Upper Saddle River (1993)Google Scholar
  14. 14.
    Sakoe, H.: Dynamic programming algorithm optimization for spoken word recognition. IEEE Trans. on Acoustics, Speech, and Signal Processing 26, 43–49 (1978)zbMATHCrossRefGoogle Scholar
  15. 15.
    Shieh, J., Keogh, E.J.: iSAX: disk-aware mining and indexing of massive time series datasets. Data Min. Knowl. Discov. 19(1), 24–57 (2009)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Skopal, T.: On Fast Non-metric Similarity Search by Metric Access Methods. In: Ioannidis, Y., Scholl, M.H., Schmidt, J.W., Matthes, F., Hatzopoulos, M., Böhm, K., Kemper, A., Grust, T., Böhm, C. (eds.) EDBT 2006. LNCS, vol. 3896, pp. 718–736. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  17. 17.
    Skopal, T.: Unified framework for fast exact and approximate search in dissimilarity spaces. ACM Transactions on Database Systems 32(4), 1–46 (2007)CrossRefGoogle Scholar
  18. 18.
    Yi, B.-K., Jagadish, H.V., Faloutsos, C.: Efficient retrieval of similar time sequences under time warping. In: Proceedings of the Fourteenth International Conference on Data Engineering, ICDE 1998, pp. 201–208 (1998)Google Scholar
  19. 19.
    Zezula, P., Amato, G., Dohnal, V., Batko, M.: Similarity Search: The Metric Space Approach (Advances in Database Systems). Advances in Database Systems. Springer-Verlag New York, Inc., Secaucus (2005)Google Scholar

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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Tomáš Bartoš
    • 1
  • Tomáš Skopal
    • 1
  1. 1.SIRET Research Group, Faculty of Mathematics and Physics, Department of Software EngineeringCharles University in PragueCzech Republic

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