The Influence of Global Constraints on DTW and LCS Similarity Measures for Time-Series Databases

  • Vladimir Kurbalija
  • Miloš Radovanović
  • Zoltan Geler
  • Mirjana Ivanović
Part of the Advances in Intelligent and Soft Computing book series (AINSC, volume 101)

Abstract

Analysis of time series represents an important tool in many application areas. A vital component in many types of time-series analysis is the choice of an appropriate distance/similarity measure. Numerous measures have been proposed to date, with the most successful ones based on dynamic programming. Being of quadratic time complexity, however, global constraints are often employed to limit the search space in the matrix during the dynamic programming procedure, in order to speed up computation. In this paper, we investigate two representative time-series distance/similarity measures based on dynamic programming, Dynamic Time Warping (DTW) and Longest Common Subsequence (LCS), and the effects of global constraints on them. Through extensive experiments on a large number of time-series data sets, we demonstrate how global constrains can significantly reduce the computation time of DTW and LCS. We also show that, if the constraint parameter is tight enough (less than 10–15% of time-series length), the constrained measure becomes significantly different from its unconstrained counterpart, in the sense of producing qualitatively different 1-nearest neighbour (1NN) graphs. This observation highlights the need for careful tuning of constraint parameters in order to achieve a good trade-off between speed and accuracy.

Keywords

Dynamic Time Warping Global Constraint Longe Common Subsequence Longe Common Subsequence Elastic Measure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Jiawei, H., Micheline, K.: Data Mining: Concepts and Techniques. Morgan Kaufmann Publishers, CA (2005)Google Scholar
  2. 2.
    Faloutsos, C., Ranganathan, M., Manolopoulos, Y.: Fast Subsequence Matching in Time-Series Databases. In: SIGMOD Conference, pp. 419–429 (1994)Google Scholar
  3. 3.
    Keogh, E.J.: A Decade of Progress in Indexing and Mining Large Time Series Databases. In: VLDB, pp. 1268–1268 (2006)Google Scholar
  4. 4.
    Ding, H., Trajcevski, G., Scheuermann, P., Wang, X., Keogh, E.: Querying and Mining of Time Series Data: Experimental Comparison of Representations and Distance Measures. In: VLDB 2008, Auckland, New Zealand, pp. 1542–1552 (2008)Google Scholar
  5. 5.
    Keogh, E.J., Ratanamahatana, C.A.: Exact indexing of dynamic time warping. Knowl. Inf. Syst. 7(3), 358–386 (2005)CrossRefGoogle Scholar
  6. 6.
    Vlachos, M., Gunopulos, D., Kollios, G.: Discovering similar multidimensional trajectories. In: ICDE 2002, pp. 673–684 (2002)Google Scholar
  7. 7.
    Chen, L., Ng, R.T.: On the marriage of lp-norms and edit distance. In: VLDB 2004, pp. 792–803 (2004)Google Scholar
  8. 8.
    Chen, L., Ozsu, M.T., Oria, V.: Robust and fast similarity search for moving object trajectories. In: SIGMOD Conference, pp. 491–502 (2005)Google Scholar
  9. 9.
    Morse, M.D., Patel, J.M.: An efficient and accurate method for evaluating time series similarity. In: SIGMOD Conference, pp. 569–580 (2007)Google Scholar
  10. 10.
    Ratanamahatana, C., Keogh, E.: Three Myths about Dynamic Time Warping. In: proc. of SIAM Inter. Conf. on Data Mining, Newport Beach, CA, April 2005, pp. 506–510 (2005)Google Scholar
  11. 11.
    Kurbalija, V., Radovanović, M., Geler, Z., Ivanović, M.: A framework for time-series analysis. In: Dicheva, D., Dochev, D. (eds.) AIMSA 2010. LNCS, vol. 6304, pp. 42–51. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  12. 12.
    Keogh, E., Xi, X., Wei, L., Ratanamahatana, C.: The UCR Time Series Classification/Clustering Page (2006), http://www.cs.ucr.edu/~eamonn/time_series_data/
  13. 13.
    Agrawal, R., Lin, K.I., Sawhney, H.S., Shim, K.: Fast similarity search in the presence of noise, scaling, and translation in times-series databases. In: Proceedings of the 21st International Conference on Very Large Databases, pp. 490–501 (1995)Google Scholar
  14. 14.
    Chan, K.P., Fu, A., Yu, C.: Haar wavelets for efficient similarity search of time-series: with and without time warping. IEEE Trans. Knowl. Data Eng. 15(3), 686–705 (2003)CrossRefGoogle Scholar
  15. 15.
    Keogh, E., Chakrabarti, K., Pazzani, M., Mehrotra, S.: Dimensionality reduction for fast similarity search in large time series databases. J. Knowl. Inf. Syst. 3(3), 263–286 (2000)CrossRefGoogle Scholar
  16. 16.
    Keogh, E., Chakrabarti, K., Pazzani, M., Mehrotra, S.: Locally adaptive dimensionality reduction for indexing large time series databases. In: Proceedings of ACM SIGMOD Conference on Management of Data, May 2001, pp. 151–162 (2001)Google Scholar
  17. 17.
    Keogh, E.: Exact indexing of dynamic time warping. In: 28th International Conference on Very Large Data Bases, Hong Kong, pp. 406–417 (2002)Google Scholar
  18. 18.
    Xi, X., Keogh, E., Shelton, C., Wei, L., Ratanamahatana, C.A.: Fast time series classification using numerosity reduction. In: Proceedings of the 23rd International Conference on Machine Learning (ICML 2006), pp. 1033-1040. ACM, New York (2006)Google Scholar
  19. 19.
    Berndt, D., Clifford, J.: Using dynamic time warping to find patterns in time series. In: AAAI-1994 Workshop on Knowledge Discovery in Databases, pp. 229–248 (1994)Google Scholar
  20. 20.
    Vlachos, M., Kollios, G., Gunopulos, D.: Discovering Similar Multidimensional Trajectories. In: Proc. of 18th Inter. Conf. on Data Engineering (ICDE), San Jose, CA, pp. 673–684 (2002)Google Scholar
  21. 21.
    Sakoe, H., Chiba, S.: Dynamic programming algorithm optimization for spoken word recognition. IEEE Trans. Acoustics Speech Signal Process ASSP 26, 43–49 (1978)MATHCrossRefGoogle Scholar
  22. 22.
    Itakura, F.: Minimum prediction residual principle applied to speech recognition. IEEE Trans. Acoustics Speech Signal Process ASSP 23, 52–72 (1975)Google Scholar
  23. 23.
    Radovanović, M., Nanopoulos, A., Ivanović, M.: Time-series classification in many intrinsic dimensions. In: Proceedings of SDM, 10th SIAM International Conference on Data Mining, Columbus, Ohio, USA, pp. 677–688 (2010)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Vladimir Kurbalija
    • 1
  • Miloš Radovanović
    • 1
  • Zoltan Geler
    • 2
  • Mirjana Ivanović
    • 1
  1. 1.Department of Mathematics and Informatics, Faculty of ScienceUniversity of Novi SadNovi SadSerbia
  2. 2.Faculty of PhilosophyUniversity of Novi SadNovi SadSerbia

Personalised recommendations