A Method of Similarity Measure and Visualization for Long Time Series Using Binary Patterns

  • Hailin Li
  • Chonghui Guo
  • Libin Yang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7104)


Similarity measure and visualization are two of the most interesting tasks in time series data mining and attract much attention in the last decade. Some representations have been proposed to reduce high dimensionality of time series and the corresponding distance functions have been used to measure their similarity. Moreover, visualization techniques are often based on such representations. One of the most popular time series visualization is time series bitmaps using chaos-game algorithm. In this paper, we propose an alternative version of the long time series bitmaps of which the number of the alphabets is not restricted to four. Simultaneously, the corresponding distance function is also proposed to measure the similarity between long time series. Our approach transforms long time series into SAX symbolic strings and constructs a non-sparse matrix which stores the frequency of binary patterns. The matrix can be used to calculate the similarity and visualize the long time series. The experiments demonstrate that our approach not only can measure the long time series as well as the “bag of pattern” (BOP), but also can obtain better visual effects of the long time series visualization than the chaos-game based time series bitmaps (CGB). Especially, the computation cost of pattern matrix construction in our approach is lower than that in CGB.


Time series visualization Binary patterns Symbol representation Similarity measure 


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  1. 1.
    Agrawal, R., Lin, K.I., Sawhney, H.S., Shim, K.: Fast similarity search in the presence of noise, scaling and translation in time-series databases. In: Proceedings of Very Large DataBase (VLDB), pp. 490–501 (1995)Google Scholar
  2. 2.
    Berndt, D.J., Clifford, J.: Finding patterns in time series: A dynmaic programming approach. In: Advances in Knowledge Discovery and Data Mining, pp. 229–248 (1996)Google Scholar
  3. 3.
    Cao, L.: In-depth Behavior Understanding and Use: the Behavior Informatics Approach. Information Science 180(17), 3067–3085 (2010)CrossRefGoogle Scholar
  4. 4.
    Rabiner, L., Juang, B.H.: Fundamentals of speech recognition, Englewood Cliffs, N.J (1993)Google Scholar
  5. 5.
    Keogh, E.: Exact indexing of dynamic time warping. In: Proceedings of the 28th VLDB Conference, Hong Kong, China, pp. 1–12 (2002)Google Scholar
  6. 6.
    Popivanov, I., Miller, R.J.: Similarity search over time-series data using wavelets. In: Proceedings of the 18th International Conference on Data Engineering, pp. 212–221 (2002)Google Scholar
  7. 7.
    Iyer, M.A., Harris, M.M., Watson, L.T., Berry, M.W.: A performance comparison of piecewise linear estimation methods. In: Proceedings of the 2008 Spring Simulation Multi-Conference, pp. 273–278 (2008)Google Scholar
  8. 8.
    Lin, J., Keogh, E., Wei, L., Lonardi, S.: Experiencing SAX: a novel symbolic representation of time series. Data Mining and Knowledge Discovery 15, 107–144 (2007)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Lin, J., Keogh, E., Lonardi, S., Chiu, B.: A symbolic representation of time series with implications for streaming algorithms. In: Proceedings of the 8th ACM SIGMOD Workshop on Research Issues in Data Mining and Knowledge Discovery, pp. 2–11 (2003)Google Scholar
  10. 10.
    Keogh, E., Lin, J., Fu, A.: Hot SAX: efficiently finding the most unusual time series subsequence. In: Proceedings of the 5th IEEE International Conference on Data Mining, pp. 226–233 (2005)Google Scholar
  11. 11.
    Theodoridis, S., Koutroumbas, K.: Pattern Recognition, 4th edn., pp. 323–409 (2009)Google Scholar
  12. 12.
    Faloutsos, C., Ranganathan, M., Manolopoulos, Y.: Fast subsequence matching in time series databases. In: Proceedings of the ACM SIGMOD International Conference on Management of Data, pp. 419–429 (1994)Google Scholar
  13. 13.
    Lin, J., Li, Y.: Finding Structural Similarity in Time Series Data using Bag of Patterns Representation. In: Winslett, M. (ed.) SSDBM 2009. LNCS, vol. 5566, pp. 461–477. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  14. 14.
    Lin, J., Keogh, E., et al.: VizTree: a tool for visually mining and monitoring massive time series databases. In: Proceedings 2004 VLDB Conference, pp. 1269–1272. Morgan Kaufmann, St Louis (2004)Google Scholar
  15. 15.
    Lin, J., Keogh, E., et al.: Visually mining and monitoring massive time series. In: Proceedings of the 10th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Seattle, WA, USA, pp. 460–469 (2004)Google Scholar
  16. 16.
    Kumar, N., Lolla, V.N., et al.: Time-series bitmaps: a practical visualization tool for working with large time series databases. In: SIAM 2005 Data Mining Conference, pp. 531–535 (2005)Google Scholar
  17. 17.
    Fu, T.C., Chung, F.L., Kwok, K., Ng, C.M.: Stock time series visualization based on data point importance. Engineering Applications of Artificial Intelligence 21(8), 1217–1232 (2008)CrossRefGoogle Scholar
  18. 18.
    Barnsley, M.F.: Fractals everywhere, 2nd edn. Academic Press (1993)Google Scholar
  19. 19.
    Ekambaram, A., Montagne, E.: An Alternative Compress Storage Format for Sparse Matrices. In: Yazıcı, A., Şener, C. (eds.) ISCIS 2003. LNCS, vol. 2869, pp. 196–203. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  20. 20.
    Stock.: Stock data web page (2005),

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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Hailin Li
    • 1
  • Chonghui Guo
    • 1
  • Libin Yang
    • 2
  1. 1.Institute of Systems EngineeringDalian University of TechnologyDalianChina
  2. 2.College of Mathematics and Computer ScienceLongyan UniversityLongyanChina

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