Mining Periodic Patterns with a MDL Criterion

  • Esther GalbrunEmail author
  • Peggy Cellier
  • Nikolaj Tatti
  • Alexandre Termier
  • Bruno Crémilleux
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11052)


The quantity of event logs available is increasing rapidly, be they produced by industrial processes, computing systems, or life tracking, for instance. It is thus important to design effective ways to uncover the information they contain. Because event logs often record repetitive phenomena, mining periodic patterns is especially relevant when considering such data. Indeed, capturing such regularities is instrumental in providing condensed representations of the event sequences.

We present an approach for mining periodic patterns from event logs while relying on a Minimum Description Length (MDL) criterion to evaluate candidate patterns. Our goal is to extract a set of patterns that suitably characterises the periodic structure present in the data. We evaluate the interest of our approach on several real-world event log datasets. Code related to this paper is available at:


Periodic patterns MDL Sequence mining 



The authors thank Hiroki Arimura and Jilles Vreeken for valuable discussions. This work has been supported by Grenoble Alpes Metropole through the Nano2017 Itrami project, by the QCM-BioChem project (CNRS Mastodons) and by the Academy of Finland projects “Nestor” (286211) and “Agra” (313927).


  1. 1.
    Bellman, R.: On the approximation of curves by line segments using dynamic programming. Commun. ACM 4(6), 284 (1961)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Berberidis, C., Vlahavas, I., Aref, W.G., Atallah, M., Elmagarmid, A.K.: On the discovery of weak periodicities in large time series. In: Elomaa, T., Mannila, H., Toivonen, H. (eds.) PKDD 2002. LNCS, vol. 2431, pp. 51–61. Springer, Heidelberg (2002). Scholar
  3. 3.
    Bhattacharyya, A., Vreeken, J.: Efficiently summarising event sequences with rich interleaving patterns. In: SDM 2017, pp. 795–803. SIAM (2017)Google Scholar
  4. 4.
    Bonchi, F., van Leeuwen, M., Ukkonen, A.: Characterizing uncertain data using compression. In: SDM 2011, pp. 534–545. SIAM (2011)Google Scholar
  5. 5.
    De Raedt, L., Zimmermann, A.: Constraint-based pattern set mining. In: SDM 2007, pp. 237–248. SIAM (2007)Google Scholar
  6. 6.
    Galbrun, E., Cellier, P., Tatti, N., Termier, A., Crémilleux, B.: Mining periodic patterns with a MDL criterion. ArXiv e-prints (2018). arXiv:1807.01706 [cs.DB]
  7. 7.
    Grünwald, P.: Model selection based on minimum description length. J. Math. Psychol. 44(1), 133–152 (2000)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Grünwald, P.: The Minimum Description Length Principle. MIT Press, Cambridge (2007)CrossRefGoogle Scholar
  9. 9.
    Han, J., Dong, G., Yin, Y.: Efficient mining of partial periodic patterns in time series database. In: ICDE 1999, pp. 106–115 (1999)Google Scholar
  10. 10.
    Han, J., Gong, W., Yin, Y.: Mining segment-wise periodic patterns in time-related databases. In: KDD 1998, pp. 214–218 (1998)Google Scholar
  11. 11.
    Heierman III, E.O., Cook, D.J.: Improving home automation by discovering regularly occurring device usage patterns. In: ICDM 2003, pp. 537–540 (2003)Google Scholar
  12. 12.
    Kiernan, J., Terzi, E.: Constructing comprehensive summaries of large event sequences. ACM Trans. Knowl. Discov. Data 3(4), 21:1–21:31 (2009)CrossRefGoogle Scholar
  13. 13.
    Lam, H.T., Moerchen, F., Fradkin, D., Calders, T.: Mining compressing sequential patterns. In: SDM 2012, pp. 319–330. SIAM (2012)Google Scholar
  14. 14.
    Li, Z., Wang, J., Han, J.: Mining event periodicity from incomplete observations. In: KDD 2012, pp. 444–452. ACM (2012)Google Scholar
  15. 15.
    Lopez-Cueva, P., Bertaux, A., Termier, A., Méhaut, J.-F., Santana, M.: Debugging embedded multimedia application traces through periodic pattern mining. In: International Conference on Embedded Software, EMSOFT 2012 (2012)Google Scholar
  16. 16.
    Ma, S., Hellerstein, J.L.: Mining partially periodic event patterns with unknown periods. In: ICDE 2001, pp. 205–214. IEEE Computer Society (2001)Google Scholar
  17. 17.
    Özden, B., Ramaswamy, S., Silberschatz, A.: Cyclic association rules. In: ICDE 1998, pp. 412–421. IEEE Computer Society (1998)Google Scholar
  18. 18.
    Rissanen, J.: Modeling by shortest data description. Automatica 14(5), 465–471 (1978)CrossRefGoogle Scholar
  19. 19.
    Smets, K., Vreeken, J.: Slim: Directly mining descriptive patterns. In: SDM 2012, pp. 236–247. SIAM (2012)Google Scholar
  20. 20.
    Tatti, N., Vreeken, J.: The long and the short of it: summarising event sequences with serial episodes. In: KDD 2012, pp. 462–470. ACM (2012)Google Scholar
  21. 21.
    Vreeken, J., van Leeuwen, M., Siebes, A.: Krimp: mining itemsets that compress. Data Min. Knowl. Discov. 23(1), 169–214 (2011)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Yuan, Q., Zhang, W., Zhang, C., Geng, X., Cong, G., Han, J.: PRED: periodic region detection for mobility modeling of social media users. In: WSDM 2017, pp. 263–272. ACM (2017)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Esther Galbrun
    • 1
    Email author
  • Peggy Cellier
    • 2
  • Nikolaj Tatti
    • 1
    • 4
  • Alexandre Termier
    • 2
  • Bruno Crémilleux
    • 3
  1. 1.Department of Computer ScienceAalto UniversityEspooFinland
  2. 2.Univ. Rennes, {INSA, Inria}, CNRS, IRISARennesFrance
  3. 3.Normandie Univ., UNICAEN, ENSICAEN, CNRS – UMR GREYCCaenFrance
  4. 4.F-SecureHelsinkiFinland

Personalised recommendations