Skip to main content
Springer Nature Link
Log in

Improving time series similarity measures by integrating preprocessing steps

  • Published:
Data Mining and Knowledge Discovery Aims and scope Submit manuscript

Abstract

While many application papers involving time series data report about the beneficial application of filters, filtering (and preprocessing in general) plays at best a minor role in the proposals of similarity measures for time series or the studies that compare them. We investigate the performance of basic Euclidean distance with an integrated preprocessing (filtering with automatically derived filters (supervised or unsupervised) and rescaling) and demonstrate that such measures can better respond to typical problems in time series similarity. By accounting for differences in both domains (time and value) we overcome some limitations of elastic measures that focus on time only. Using the proposed measure on real datasets we can achieve performance gains comparable to those of switching from a lock-step measure (Euclidean) to an elastic measure (DTW).

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

Notes

  1. Only the artificial data can be shared: http://public.ostfalia.de/~hoeppnef/tsfilter.html.

  2. We found no reference for the type of the Car dataset, but assume it to be a shape dataset due to its similarity to other datasets of this type, e.g. FISH.

    Fig. 7
    figure 7

    Car (top) and FaceFour (bottom) dataset. For a given reference series (black) several other series (dashed gray) from the same class (left) and another class (right) are filtered and rescaled by LFD (red series) to obtain a higher correspondence with the reference (Color figure online)

    Full size image

References

  • Agrawal R, Faloutsos C, Swami A (1993) Efficient similarity search in sequence databases. In: 4th international conference foundations of data organization and algorithms, Chicago, pp 69–84

  • Argyros T, Ermopoulos C (2003) Efficient subsequence matching in time series databases under time and amplitude transformations. In: IEEE data mining, IEEE computing in society, pp 481–484

  • Batista G, Wang X, Keogh E (2011) A complexity-invariant distance measure for time series. In: Proceedings of international conference on data mining, pp 699–710

    Chapter  Google Scholar 

  • Berndt DJ, Clifford J (1996) Finding patterns in time series: a dynamic programming approach. In: Advances in knowledge discovery and data mining, MITP, pp 229–248

  • Casacuberta F, Vidal E, Rulot H (1987) On the metric properties of dynamic time warping. IEEE Trans Acoust Speech Signal Process 35(11):1631–1633

    Article  Google Scholar 

  • Chen Y, Keogh E, Hu B, Begum N, Bagnall A, Mueen A, Batista G (2011) The UCR time series classification archive. www.cs.ucr.edu/~eamonn/time_series_data

  • Chen L, Ng R (2004) On the marriage of Lp-norms and edit distance. In: International conference on very large databases, pp 792–803

    Chapter  Google Scholar 

  • Chen L, Özsu M, Oria V (2005) Robust and fast similarity search for moving object trajectories. In: Proceedings of ACM SIGMOD, pp 491–502

  • Cleveland WS (1979) Robust locally weighted regression and smoothing scatterplots. J Am Stat Assoc 74(368):829–836. doi:10.2307/2286407

    Article  MathSciNet  MATH  Google Scholar 

  • Dallachiesa M, Nushi B (2012) Uncertain time-series similarity: return to the basics. Proc VLDB 5(11):1662–1673

    Article  Google Scholar 

  • Das G, Gunopulos D, Mannila H (1997) Finding similar time series. In: Proceedings of the conference on principles of knowledge discovery and data mining

  • Elboher E, Werman M (2013) Asymmetric correlation: a noise robust similarity measure for template matching. IEEE Trans Image Process 22(8):3062–3073

    Article  MathSciNet  Google Scholar 

  • Fu TC (2011) A review on time series data mining. Eng Appl Artif Intell 24(1):164–181

    Article  Google Scholar 

  • Górecki T, Łuczak M (2013) Using derivatives in time series classification. Data Min Knowl Discov 26(2):310–331

    Article  MathSciNet  Google Scholar 

  • Höppner F (2014) Less is more: similarity of time series under linear transformations. In: Proceedings of SIAM international conference data mining (SDM), pp 560–568

    Chapter  Google Scholar 

  • Höppner F (2015) Optimal filtering for time series classification. In: Proceedings of 16th internatinal conference intelligent data engineering and automated learning, pp 26–35

    Chapter  Google Scholar 

  • Höppner F, Klawonn F (2009) Compensation of translational displacement in time series clustering using cross correlation. In: Proceedings of 8th international symposium intelligent data analysis, no. 5772 in LNCS, pp 71–82

    Chapter  Google Scholar 

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

    Article  Google Scholar 

  • Kay SM (1993) Fundamentals of statistical signal processing. Prentice-Hall, Englewood Cliffs

    MATH  Google Scholar 

  • Keogh E (2003) Efficiently finding arbitrarily scaled patterns in massive time series databases. In: Knowledge discovery in databases (PKDD), pp 253–265

    Chapter  Google Scholar 

  • Keogh E, Kasetty S (2003) On the need for time series data mining benchmarks: a survey and empirical demonstration. Data Min Knowl Discov 7(4):349–371. doi:10.1023/A:1024988512476

    Article  MathSciNet  Google Scholar 

  • Keogh E, Pazzani M (2001) Derivative dynamic time warping. In: SDM, pp 5–7

  • Kullback S, Leibler RA (1951) On information and sufficiency. Ann Math Stat 22(1):79–86

    Article  MathSciNet  Google Scholar 

  • Last M, Klein Y, Kandel A (2001) Knowledge discovery in time series databases. IEEE Trans Syst Man Cybern 31(01):160–169

    Article  Google Scholar 

  • Marteau PF (2009) Time warp edit distance with stiffness adjustment for time series matching. IEEE Trans Pattern Anal Mach Intell 31(2):306–318

    Article  Google Scholar 

  • Müller M (2007) Information retrieval for music and motion. Springer, New York

    Book  Google Scholar 

  • Navarro G (2001) A guided tour to approximate string matching. ACM Comput Surv 33(1):31–88

    Article  Google Scholar 

  • Ramsay JO, Silverman BW (1997) Functional data analysis. Springer series in statistics. Springer, New York

    Book  Google Scholar 

  • Ratanamahatana C, Keogh E (2004) Everything you know about dynamic time warping is wrong. In: Third workshop on mining temporal and sequential data

  • Sakoe H, Chiba S (1978) Dynamic programming algorithm optimization for spoken word recognition. IEEE Trans Acoust Speech Signal Process 26(1):43–49

    Article  Google Scholar 

  • Schäfer P (2014) The BOSS is concerned with time series classification in the presence of noise. Data Min Knowl Discov 29(6):1505–1530

    Article  MathSciNet  Google Scholar 

  • Serrà J, Arcos JL (2014) An empirical evaluation of similarity measures for time series classification. Knowl Based Syst 67:305–314

    Article  Google Scholar 

  • Taylor JR (1997) An introduction to error analysis. University Science Books, New York

    Google Scholar 

  • Tversky A (1977) Features of similarity. Psychol Rev 84(4):327–352

    Article  Google Scholar 

  • Wang X, Mueen A, Ding H, Trajcevski G, Scheuermann P, Keogh E (2012) Experimental comparison of representation methods and distance measures for time series data. Data Min Knowl Discov 26(2):275–309

    Article  MathSciNet  Google Scholar 

  • Ye L, Keogh E (2010) Time series shapelets: a novel technique that allows accurate, interpretable and fast classification. Data Min Knowl Discov 22(1–2):149–182

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

I would like to thank the reviewers for their useful comments.

Author information

Authors and Affiliations

  1. Department of Computer Science, Ostfalia University of Applied Sciences, Wolfenbüttel, Germany

    Frank Höppner

Authors
  1. Frank Höppner
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Frank Höppner.

Additional information

Responsible editor: Eamonn Keogh.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Höppner, F. Improving time series similarity measures by integrating preprocessing steps. Data Min Knowl Disc 31, 851–878 (2017). https://doi.org/10.1007/s10618-016-0490-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10618-016-0490-x

Keywords