Skip to main content
SpringerLink
Log in

Recognition of fuzzy time series patterns using evolving classification results

  • Original Paper
  • Published:
Evolving Systems Aims and scope Submit manuscript

Abstract

In some nonstationary time series, where a global model is neither available nor applicable, we may observe recurring patterns that can be extracted to create several local models instead. This article proposes knowledge-based short-time prediction methods for multivariate streaming time series that rely on the early recognition of such local patterns. A parametric fuzzy model for patterns is presented, along with an online, classification-based recognition procedure, which will introduce the notion of evolving classification results. Subsequently, two options are discussed to predict time series employing the fuzzified pattern knowledge, accompanied by an example. Special emphasis is placed on comprehensible models and methods, as well as a seamless interface to data mining algorithms.

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
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18

Similar content being viewed by others

Notes

  1. The datasets—available from Keogh et al. (2006)—were normalised per ensemble to zero mean and unit variance and resampled to L = 100 to achieve higher similarity in order to complicate subsequent examples of this article in Sects. 3.5, 4.3 and 5.4.

  2. The results μab Mutual(t, τ) do not account for the uncertainty and fuzziness of pattern b, and should therefore be regarded as an estimate of the two patterns actual similarity. When necessary, one could alternatively determine degrees of overlap of both patterns’ fuzzy sets instead of classifying the reference course, although the computational costs associated to this will be notably higher.

  3. The common parameters in Fig. 14 were b l = 0.5, b r = 0.8, c l = 10, d l = 8, d r = 2, as well as r = 60, c r = 40 for the ‘Coffee’ pattern and r = 80, c r = 20 for ‘FaceAll’. With this, high values μw are obtained for the desired stages and a rather steep decrease of interest towards lower values of τ.

  4. Ideally, a user should not be burdened with this decision, but be able to rely on the automatic assessment of suitable measures describing the relevant properties of the datasets. While we set this topic aside for future works beyond this article, such measures essentially only have to evaluate the frequency of instances crossing a pattern’s reference (mean) course in order to distinguish “noisy” from “parallel” sets of instances.

  5. At 488 out of 2,100 points of the time series in Fig. 11a, predictions were available with a mean prediction horizon of about 22 samples. The total length of all predictions was 10,572 sample points, from which the results of Tables 1, 2 and 3 were calculated.

  6. The comparison to these approaches is being performed here for the sake of completeness, in view of the fact that the applicability of models for (stationary) time series might not always be given in other cases.

References

  • Aizerman MA, Braverman EM, Rozonoér LI (1964) Theoretical foundations of the potential function method in pattern recognition learning. Autom Remote Control 25:821–837

    Google Scholar 

  • Angelov P, Filev DP, Kasabov N (eds) (2010) Evolving intelligent systems: methodology and applications. Wiley, New York

  • Bocklisch SF (1987) Prozeßanalyse mit unscharfen Verfahren. Technik, Berlin

    Google Scholar 

  • Chatfield C (2003) The analysis of time series: an introduction, 6th edn. Chapman & Hall, London

  • Fuchs E, Gruber T, Nitschke J, Sick B (2009) On-line motif detection in time series with SwiftMotif. Pattern Recognit 42(11):3015–3031

    Article  MATH  Google Scholar 

  • Hempel AJ, Bocklisch SF (2010) Fuzzy pattern modelling of data inherent structures based on aggregation of data with heterogeneous fuzziness. In: Rey GR, Muneta LM (eds) Modelling simulation and optimization, chap 28. INTECH, pp 637–655

  • Herbst G, Bocklisch SF (2009) Online recognition of fuzzy time series patterns. In: Carvalho JP, Dubois D, Kaymak U, Sousa JMC (eds) 2009 International Fuzzy Systems Association World Congress and 2009 European Society for Fuzzy Logic and Technology conference (IFSA-EUSFLAT 2009), pp 974–979

  • Keogh E, Xi X, Wei L, Ratanamahatana CA (2006) The UCR time series classification/clustering homepage. http://www.cs.ucr.edu/~eamonn/time_series_data/

  • Leekwijck WV, Kerre EE (1999) Defuzzification: criteria and classification. Fuzzy Sets Syst 108(2):159–178

    Article  MATH  Google Scholar 

  • Lin J, Keogh E, Lonardi S, Patel P (2002) Finding motifs in time series. In: Proceedings of the second workshop on temporal data mining, pp 53–68

  • Lowe A, Jones RW, Harrison MJ (1999) Temporal pattern matching using fuzzy templates. J Intell Inf Syst 13(1–2):27–45

    Article  Google Scholar 

  • Lughofer E (2008) Evolving fuzzy models: incremental learning, interpretability and stability issues, applications. VDM, Saarbrücken, Germany

  • Mueen A, Keogh E, Zhu Q, Cash S, Westover B (2009) Exact discovery of time series motifs. In: Proceedings of the SIAM international conference on data mining (SDM 2009). American Statistical Association (ASA), pp 473–484

  • Otero A, Félix P, Barro S (2004) MFTP: a model to represent hierarchies of abstraction defined over multiple parameters. In: ECAI Workshop on spatial and temporal reasoning, pp 95–100

  • Päßler M, Bocklisch SF (2000) Fuzzy time series analysis. In: Hampel R, Wagenknecht M, Chaker N (eds) Fuzzy control: theory and practice. Physica, Heidelberg, pp 331–345

  • Povinelli RJ, Feng X (2003) A new temporal pattern identification method for characterization and prediction of complex time series events. IEEE Trans Knowl Data Eng 15(2):339–352

    Article  Google Scholar 

  • Scheunert U (2001) Fuzzy-Mengen-Verknüpfung und Fuzzy-Arithmethik zur Sensor-Daten-Fusion. PhD thesis, Chemnitz University of Technology

  • Slutzky E (1937) The summation of random causes as the sources of cyclic processes. Econometrica 5:105–146

    Article  Google Scholar 

  • Steimann F (1995) Diagnostic monitoring of clinical time series. PhD thesis, Technical University of Vienna

  • Tanaka Y, Iwamoto K, Uehara K (2005) Discovery of time-series motif from multi-dimensional data based on MDL principle. Mach Learn 58(2–3):269–300

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Chemnitz University of Technology, 09107, Chemnitz, Germany

    Gernot Herbst & Steffen F. Bocklisch

Authors
  1. Gernot Herbst
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Steffen F. Bocklisch
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gernot Herbst.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Herbst, G., Bocklisch, S.F. Recognition of fuzzy time series patterns using evolving classification results. Evolving Systems 1, 97–110 (2010). https://doi.org/10.1007/s12530-010-9003-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12530-010-9003-0

Keywords

Search

Navigation