Discovering frequent chain episodes

  • Avinash AcharEmail author
  • P. S. Sastry
Regular Paper


Frequent episode discovery is a popular framework in temporal data mining with many applications. An episode is a partially ordered set of nodes with each node associated with an event-type. The episodes literature has seen different notions of frequency and a variety of associated discovery algorithms under these different frequencies when the associated partial order is total (serial episode) or trivial (parallel episode). Recently an apriori-based discovery algorithm for mining episodes where the associated partial order has no restriction but the node to event-type association is one–one (general injective episodes) was proposed based on the non-overlapped frequency measure. This work pointed out that frequency alone is not a sufficient indicator of interestingness in the context of episodes with general partial orders and introduced a new measure of interestingness called bidirectional evidence (BE) to address this issue. This algorithm discovers episodes by incorporating both frequency and BE thresholds in the level-wise procedure. In this paper, we extend this BE-based algorithm to a much larger class of episodes that we call chain episodes. This class encompasses all serial and parallel episodes (injective or otherwise) and also many other non-injective episodes with unrestricted partial orders. We first discuss how the BE measure can be generalized to chain episodes and prove the monotonicity property it satisfies in this general context. We then describe our candidate generation step (with correctness proofs) which nicely exploits this new monotonicity property. We further describe the frequency counting (with correctness proofs) and BE computation steps for chain episodes. The experimental results demonstrate the effectiveness of our algorithms.


Data mining Episode Apriori-based Non-overlapped frequency Partial order 


Supplementary material


  1. 1.
    Achar A (2010) Discovering Frequent episodes with general partial orders. PhD thesis, Department of Electrical Engineering, Indian Institute of Science, Bangalore, IndiaGoogle Scholar
  2. 2.
    Achar A, Sastry PS (2015) Statistical significance of general partial orders. Inf Sci 296:175–200MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Achar A, Laxman S, Sastry PS (2012) A unified view of the apriori-based algorithms for frequent episode discovery. Knowl Inf Syst 31(2):223–250CrossRefGoogle Scholar
  4. 4.
    Achar A, Ibrahim A, Sastry PS (2013) Pattern-growth based frequent serial episode discovery. Data Knowl Eng 87:91–108CrossRefGoogle Scholar
  5. 5.
    Achar A, Laxman S, Raajay V, Sastry PS (2012) Discovering injective episodes with general partial orders. Data Min Knowl Discov 25(1):67–108MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Achar A, Laxman S, Raajay V, Sastry PS (2009) Discovering general partial orders from event streams. In: Technical report arXiv: 0902.1227v2 [cs.AI]
  7. 7.
    Atallah MJ, Gwadera R, Szpankowski W (2004) Detection of significant sets of episodes in event sequences. In: Proceedings of the 4th IEEE international conference on data mining (ICDM), Brighton, UK, pp 3–10Google Scholar
  8. 8.
    Bouqata B, Caraothers CD, Szymanski BK, Zaki MJ (2006) Vogue: a novel variable order-gap state machine for modeling sequences. In: Proceedings of the 10th European conference on principles and practice of knowledge discovery in databases, vol 4213. Springer, Berlin, pp 42–54Google Scholar
  9. 9.
    Brown EN, Kass RE, Mitra PP (2004) Multiple neuronal spike train data analysis: state of art and future challenges. Nat Neurosci 7(5):456–461CrossRefGoogle Scholar
  10. 10.
    Gan M, Dai H (2012) An efficient one-pass method for discovering bases of recently frequent episodes over online data streams. Int J Innov Comput Inf Control 8(7(A)):4675–4690Google Scholar
  11. 11.
    Gan M, Dai H (2014) Detecting and monitoring abrupt emergences and submergences of episodes over data streams. Inf Syst 39:277–289CrossRefGoogle Scholar
  12. 12.
    Huang K, Chang C (2008) Efficient mining of frequent episodes from complex sequences. Inf Syst 33(1):96–114CrossRefGoogle Scholar
  13. 13.
    Ibrahim A, Sastry S, Sastry PS (2016) Discovering compressing serial episodes from event sequences. Knowl Inf Syst 47(2):405–432CrossRefGoogle Scholar
  14. 14.
    Iwanuma K, Takano Y, Nabeshima H (2004) On anti-monotone frequency measures for extracting sequential patterns from a single very-long sequence. In: Proceedings of the 2004 IEEE conference on cybernetics and intelligent systems, vol 1, pp 213–217Google Scholar
  15. 15.
    Laxman S, Sastry PS, Unnikrishnan KP (2005) Discovering frequent episodes and learning hidden Markov models: a formal connection. IEEE Trans Knowl Data Eng 17:1505–1517CrossRefGoogle Scholar
  16. 16.
    Laxman S, Tankasali V, White RW (2008) Stream prediction using a generative model based on frequent episodes in event sequences. In: Proceedings of the 14th ACM SIGKDD international conference on knowledge discovery and data mining (KDD’08), pp 453–461Google Scholar
  17. 17.
    Luo J, Bridges SM (2000) Mining fuzzy association rules and fuzzy frequent episodes for intrusion detection. Int J Intell Syst 15:687–703CrossRefzbMATHGoogle Scholar
  18. 18.
    Mannila H, Toivonen H, Verkamo AI (1997) Discovery of frequent episodes in event sequences. Data Min Knowl Discov 1(3):259–289CrossRefGoogle Scholar
  19. 19.
    Nag A, Fu AW (2003) Mining frequent episodes for relating financial events and stock trends. In: Proceedings of 7th Pacific-Asia conference on knowledge discovery and data mining (PAKDD 2003). Springer, Berlin, pp 27–39Google Scholar
  20. 20.
    Patnaik D, Sastry PS, Unnikrishnan KP (2008) Inferring neuronal network connectivity from spike data: a temporal data mining approach. Sci Program 16:49–77Google Scholar
  21. 21.
    Patnaik D, Laxman S, Chandramouli B, Ramakrishnan N (2012) Efficient episode mining of dynamic event streams. In: IEEE international conference on data mining, pp 605–614Google Scholar
  22. 22.
    Sastry PS, Unnikrishnan KP (2010) Conditional probability based significance tests for sequential patterns in multi-neuronal spike trains. Neural Comput 22(4):1025–1059CrossRefzbMATHGoogle Scholar
  23. 23.
    Tatti N (2009) Significance of episodes based on minimal windows. In: Proceedings of 2009 IEEE international conference on data miningGoogle Scholar
  24. 24.
    Tatti N (2015) Ranking episodes using a partition model. Data Min Knowl Discov 29(5):1312–1342MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Tatti N, Cule B (2012) Mining closed strict episodes. Data Min Knowl Discov 25(3):34–66MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Tatti N, Cule B (2011) Mining closed episodes with simultaneous events. In: Proceedings of the 17th ACM SIGKDD international conference on knowledge discovery and data mining, pp 1172–1180Google Scholar
  27. 27.
    Tatti N, Cule B (2010) Mining closed strict episodes. In: Proceedings of 2010 IEEE international conference on data mining, pp 501–510Google Scholar
  28. 28.
    Unnikrishnan KP, Shadid BQ, Sastry PS, Laxman S (2009) Root cause diagnostics using temporal datamining, U.S.Patent no. 7509234, 24 MarGoogle Scholar
  29. 29.
    Wang MF, Wu YC, Tsai MF (2008) Exploiting frequent episodes in weighted suffix tree to improve intrusion detection system. In: Proceedings of the 22nd international conference on advanced information networking and applications-workshops. IEEE Computer Society, Washington, pp 1246–1252Google Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.ResearchTata Consultancy ServicesChennaiIndia
  2. 2.Department of Electrical EngineeringIndian Institute of ScienceBangaloreIndia

Personalised recommendations