Skip to main content
SpringerLink
Log in

A Multi-resolution Approximation for Time Series

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

Time series is a common and well-known way for describing temporal data. However, most of the state-of-the-art techniques for analysing time series have focused on generating a representation for a single level of resolution. For analysing of a time series at several levels of resolutions, one would require to compute different representations, one for each resolution level. We introduce a multi-resolution representation for time series based on local trends and mean values. We require the level of resolution as parameter, but it can be automatically computed if we consider the maximum resolution of the time series. Our technique represents a time series using trend-value pairs on each segment belonging to a resolution level. To provide a useful representation for data mining tasks, we also propose dissimilarity measures and a symbolic representation based on the SAX technique for efficient similarity search using a multi-resolution indexing scheme. We evaluate our method for classification and discord discovery tasks over a diversity of data domains, achieving a better performance in terms of efficiency and effectiveness compared with some of the best-known classic techniques. Indeed, for some of the experiments, the time series mining algorithms using our multi-resolution representation were an order of magnitude faster, in terms of distance computations, than the state of the art.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Assent I, Wichterich M, Krieger R, Kremer H, Seidl T (2009) Anticipatory DTW for efficient similarity search in time series databases. Proc VLDB Endow 2(1):826–837

    Google Scholar 

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

    Google Scholar 

  3. Chen Q, Chen L, Lian X, Liu Y, Yu JX (2007) Indexable PLA for efficient similarity search. In: Proceedings of 33rd international conference on very large data bases, VLDB Endowment, pp 435–446

  4. Chen Y, Keogh E, Hu B, Begum N, Bagnall A, Mueen A, Batista G (2015) The UCR time series classification archive. www.cs.ucr.edu/~eamonn/time_series_data/

  5. Dan J, Shi W, Dong F, Hirota K (2013) Piecewise trend approximation: a ratio-based time series representation. Abst Appl Anal 2013:603629. https://doi.org/10.1155/2013/603629

  6. Esmael B, Arnaout A, Fruhwirth RK, Thonhauser G (2012) Multivariate time series classification by combining trend-based and value-based approximations. In: Computational science and its applications—ICCSA 2012, LNCS 7336. Springer, New York, pp 392–403

  7. Fuad MMM (2012) Differential evolution versus genetic algorithms: towards symbolic aggregate approximation of non-normalized time series. In: Proceedings of 16th international database engineering and applications symposium. ACM, pp 205–210

  8. Gullo F, Ponti G, Tagarelli A, Greco S (2009) A time series representation model for accurate and fast similarity detection. Pattern Recognit 42(11):2998–3014

    MATH  Google Scholar 

  9. Keogh E, Kasetty S (2002) On the need for time series data mining benchmarks: A survey and empirical demonstration. In: Proceedings of 8th ACM SIGKDD international conference on knowledge discovery and data mining. ACM, pp 102–111

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

    Google Scholar 

  11. Keogh EJ, Chakrabarti K, Pazzani MJ, Mehrotra S (2001) Dimensionality reduction for fast similarity search in large time series databases. Knowl Inf Syst 3(3):263–286

    MATH  Google Scholar 

  12. Keogh EJ, Chu S, Hart D, Pazzani M (2004) Segmenting time series: a survey and novel approach. In: Last M, Kandel A, Bunke H (eds) Data mining in time series databases, series in machine perception and artificial intelligence, vol 57. World Scientific Publishing Company, Singapore, pp 1–22 chap 1

    Google Scholar 

  13. Keogh EJ, Lin J, Fu AW (2005) HOT SAX: efficiently finding the most unusual time series subsequence. In: Proceedings of 5th IEEE international conference on data mining, pp 226–233

  14. Keogh EJ, Lin J, hee Lee S, Herle HV (2007) Finding the most unusual time series subsequence: algorithms and applications. Knowl Inf Syst 11(1):1–27

    Google Scholar 

  15. Khanh NDK, Anh DT (2012) Time series discord discovery using WAT algorithm and iSAX representation. In: Proceedings of 3rd symposium on information and communication technology. ACM, pp 207–213

  16. Lin J, Keogh E, Lonardi S, Chiu B (2003) A symbolic representation of time series, with implications for streaming algorithms. In: Proceedings of 8th ACM SIGMOD workshop on research issues in data mining and knowledge discovery, pp 2–11

  17. Lin J, Vlachos M, Keogh E, Gunopulos D (2004) Iterative incremental clustering of time series. In: Proceedings of international conference on extending database technology. Springer, New York, pp 106–122

  18. Lin J, Vlachos M, Keogh E, Gunopulos D, Liu J, Yu S, Le J (2005) A MPAA-based iterative clustering algorithm augmented by nearest neighbors search for time-series data streams. In: Ho T, Cheung D, Liu H (eds) Advances in knowledge discovery and data mining, LNCS 3518. Springer, New York, pp 333–342

    Google Scholar 

  19. Lin J, Keogh EJ, Wei L, Lonardi S (2007) Experiencing SAX: a novel symbolic representation of time series. Data Min Knowl Discov 15(2):107–144

    MathSciNet  Google Scholar 

  20. Malinowski S, Guyet T, Quiniou R, Tavenard R (2013) 1d-SAX: a novel symbolic representation for time series. In: Advances in intelligent data analysis XII, LNCS 8207. Springer, New York, pp 273–284

  21. Ordonez P, Armstrong T, Oates T, Fackler J (2011) Classification of patients using novel multivariate time series representations of physiological data. In: Proceedings of 10th international conference on machine learning and applications and workshops, vol 2, pp 172–179

  22. Sanchez H, Bustos B (2017) Multi-resolution time series discord discovery. In: Advances in computational intelligence: 14th international work-conference on artificial neural networks, proceedings, Part II. Springer, New York, pp 116–128

  23. Shieh J, Keogh E (2008) iSAX: indexing and mining terabyte sized time series. In: Proceedings of 14th ACM SIGKDD international conference on knowledge discovery and data mining. ACM, pp 623–631

  24. Wang X, Mueen A, Ding H, Trajcevski G, Scheuermann P, Keogh E (2013) Experimental comparison of representation methods and distance measures for time series data. Data Min Knowl Discov 26(2):275–309

    MathSciNet  Google Scholar 

  25. Wilcoxon F (1945) Individual comparisons by ranking methods. Biom Bull 1(6):80–83

    Google Scholar 

  26. Wu YL, Agrawal D, El Abbadi A (2000) A comparison of DFT and DWT based similarity search in time-series databases. In: Proceedings of 9th international conference on information and knowledge management. ACM, pp 488–495

  27. Yi BK, Faloutsos C (2000) Fast time sequence indexing for arbitrary Lp norms. In: Proceedings of 26th international conference on very large data bases. Morgan Kaufmann Publishers Inc., pp 385–394

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Chile, Santiago, Chile

    Heider Sanchez & Benjamin Bustos

Authors
  1. Heider Sanchez
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Benjamin Bustos
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Benjamin Bustos.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This work was funded by the Millennium Institute for Foundational Research on Data.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sanchez, H., Bustos, B. A Multi-resolution Approximation for Time Series. Neural Process Lett 52, 75–96 (2020). https://doi.org/10.1007/s11063-018-9929-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-018-9929-y

Keywords

Search

Navigation