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Time series anomaly detection via clustering-based representation

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Abstract

Time series anomaly detection is an important field of data science. Statistical, distance-based, clustering-based, or density-based approaches can detect anomalies. Generally, distance-based methods are relatively straightforward, but the method’s effectiveness depends on how well they handle the distribution of data points. To address the challenge, a preprocessing step is used to convert the underlying time series into a more useful format. In this paper, a novel clustering-based representation of time series is proposed. This representation is then used to compute anomaly scores and detect anomalies. Experimental studies on synthetic and real datasets show that proposed method outperforms other methods by up to 75% for five standard performance metrics.

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Data availibility

Yahoo S5 datasets analyzed during the current study are available at https://webscope.sandbox.yahoo.com/catalog.php?datatype=s&did=70, and the Synthetic datasets generated by https://github.com/KDD-OpenSource/agots repository. The Sin dataset is also generated by Eq. (8).

Notes

  1. For a more formal definition see Definition 1 in Sect. 2.

  2. Piecewise Aggregate Approximation.

  3. Symbolic Aggregate approXimation.

  4. Discrete Fourier Transform.

  5. Discrete Wavelet Transform.

  6. Singular Value Decomposition.

  7. Principal Component Analysis.

  8. Gaussian Mixture Models.

  9. Stochastic Outlier Selection.

  10. Clustering-Based Local Outlier Factor.

  11. Isolation Forest.

  12. It should be noted that the clustering-based representation mechanism is completely different from the clustering-based anomaly detection approaches discussed in Sect. 3.

  13. Optimal Sequence Clustering algorithm.

  14. https://webscope.sandbox.yahoo.com/catalog.php?datatype=s&did=70.

  15. https://github.com/KDD-OpenSource/agots.

  16. https://github.com/ir1979/CUBOID.

  17. https://pyts.readthedocs.io.

  18. https://pycaret.readthedocs.io.

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Authors and Affiliations

  1. School of Mathematics and Computer Sciences, Damghan University, Damghan, 3671641167, Iran

    Elham Enayati, Abdolali Basiri, Javad Ghasemian & Mahmoud Moallem

  2. School of Engineering, Damghan University, Damghan, 3671641167, Iran

    Reza Mortazavi

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  1. Elham Enayati
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  2. Reza Mortazavi
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Correspondence to Reza Mortazavi.

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Appendix: Tables of Scenario 2

Appendix: Tables of Scenario 2

The numerical results in Tables 5, 6, 7, 8 are presented by a confidence interval of 95%.

Table 5 Scenario 2—Performance indices of different methods for Sin dataset
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Table 6 Scenario 2—Performance indices of different methods for Yahoo dataset
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Table 7 Scenario 2—Performance indices of different methods for Synthetic dataset
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Table 8 Scenario 2—\({\text {F-score}}\) indices for all datasets
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Enayati, E., Mortazavi, R., Basiri, A. et al. Time series anomaly detection via clustering-based representation. Evolving Systems 15, 1115–1136 (2024). https://doi.org/10.1007/s12530-023-09543-8

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