An Efficient Anomaly Detection in Quasi-Periodic Time Series Data—A Case Study with ECG

  • Goutam ChakrabortyEmail author
  • Takuya Kamiyama
  • Hideyuki Takahashi
  • Tetsuo Kinoshita
Conference paper
Part of the Contributions to Statistics book series (CONTRIB.STAT.)


Anomaly detection from a time series is an important problem with applications to find or predict the development of a fault in a system. Depending on the source of the data, it could be nonperiodic, quasi-periodic, and periodic. Modeling an aperiodic data to detect anomaly is difficult. A pure periodic data seldom happens in nature. Finding anomaly in quasi-periodic time series signals, for example, bio-signals like ECG, heart rate (pulse) data, are important. But, the analysis is computationally complex because of the need for proper window size selection and comparison of every pair of subsequences of window-size duration. In this paper, we proposed an efficient algorithm for anomaly detection of quasi-periodic time series data. We introduced a new concept “mother signal”, which is the average of normal subsequences. Creation of the mother signal is the first step in the process. Finding deviations of subsequences of varied duration (due to quasi-periodicity) from mother signal, is the second step. When this distance crosses a threshold, it is declared as a discord. The algorithm is light enough to work in real-time on computationally weak platforms like a mobile phone. Experiments were done with ECG signals to evaluate the performance. It is shown to be computationally more efficient compared to existing works, and could identify discords with higher rate.


Quasi-periodic time series Anomaly detection Fundamental period Clustering 



Part of this work was carried out under the cooperative research project program of the research institute of electrical communication, Tohoku University, and grant from Sendai Foundation of Applied Information Sciences, Sendai, Japan.


  1. 1.
    Sha, W., Zhu, Y., Huang, T., Qiu, M., Ming, Z., Zhu, Y., Zhang Q.: A multi-order markov chain based scheme for anomaly detection. In: Computer Software and Applications Conference Workshops (COMPSACW), pp. 83–88. Shanghai Jiao TongPages (2013)Google Scholar
  2. 2.
    Ma, J., Perkins, S.: Online novelty detection on temporal sequences. In: KDD’03, Proceedings of the Ninth ACM SIGKDD International Conference on Knowledge Discovery And Data Mining, pp. 613–618 (2003)Google Scholar
  3. 3.
    Rebbapragada, U., Protopapas, P., Brodley, C.E., Alcock, C.: Finding anomalous periodic time series. 74(3) 281–313 (2009)Google Scholar
  4. 4.
    Keogh, E., Lin, J., Fu, A.W., Van Herle, H.: Finding the unusual medical time series, algorithms and applications. EEE Trans. Inf. Technol. Biomed. 10(3), 429–439 (2006)Google Scholar
  5. 5.
    Salvador, S., Chan, P.: Learning states and rules for detecting anomalies in time series. Appl. Intell. 23(3), 241–255 (2005)CrossRefGoogle Scholar
  6. 6.
    Brailovsky, V.L., Kempner, Y.: Application of Piece-wise regression to detecting internal structure of signal. Pattern Recognit. 25(11), 1361–1370 (1992)CrossRefGoogle Scholar
  7. 7.
    Ferrari-Trecate, G., Muselli, M.: A new learning method for piecewise linear regrassion. In: ICANN, Spain 28–30 Aug 2002Google Scholar
  8. 8.
    Chamroukhi, F.: Piecewise regression mixture for simultaneous functional data clustering and optimal segmentation. J. Classif. 33(3), 374–411 (2016)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Basha, R., Ameen, J.R.M.: Unusual sub-sequence identifications in time series with periodicity. Int. J. Innov. Comput. Inf. Control (IJICIC) 3 (2007)Google Scholar
  10. 10.
    Luo W., Gallangher, M.: Faster and parameter free discord search in quasi-periodic time series. In: Huang, J.Z., Cao, L., Srivastave, J. (eds.) PAKDD 2011, Part II, LNAI 6635, pp. 135–145. Springer (2011)Google Scholar
  11. 11.
    Luo, W., Gallangher, M., Janet, W.: Parameter free search of time series discord. J. Comput. Sci. Technol. 28(2), 300–310 (2013)CrossRefGoogle Scholar
  12. 12.
    Sivaraks, H., Ratanamahantana, C.A.: Robust and accurate anomaly detection in ECG artifacts using time series motif discovery. Comput. Math. Methods Med. 2015, 20. Article ID 453214. Scholar
  13. 13.
    Korkmaz, S., Goksuluk, D., Zararsiz, G.: MVN: an R package for assessing multivariate normality. R J. 6(2), 151–162 (2014)Google Scholar
  14. 14.
    Kamiyama, T., Chakraborty, G.: Real-time anomaly detection of continuously monitored periodic bio-signals like ECG. In: Otak, M., et. al. (ed.) LNAI , Springer 10091, pp. 418–427 (2017)CrossRefGoogle Scholar
  15. 15.
    Goldberger, A.L., Amaral, L.A.N., Glass, L., Hausdorff, J.M., Ivanov, P.C.h., Mark, R.G., Mietus, J.E., Moody G.B., Peng, C.-K., Stanley, H.E.: PhysioBank, PhysioToolkit, and PhysioNet: components of a new research resource for complex physiologic signals. Circulation 101(23), 215–220Google Scholar
  16. 16.
    Sugiyama, M., Borgwardt, K.M.: Rapid Distance-Based Outlier Detection via Sampling, NIPS (2013)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Goutam Chakraborty
    • 1
    Email author
  • Takuya Kamiyama
    • 1
  • Hideyuki Takahashi
    • 2
  • Tetsuo Kinoshita
    • 2
  1. 1.Graduate School of Software & Information ScienceIwate Prefectural UniversityTakizawaJapan
  2. 2.Research Institute of Electrical CommunicationTohoku UniversitySendaiJapan

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