Applied Intelligence

, Volume 42, Issue 1, pp 112–134 | Cite as

Shift density estimation based approximately recurring motif discovery

  • Yasser MohammadEmail author
  • Toyoaki Nishida


Approximately Recurring Motif (ARM) discovery is the problem of finding unknown patterns that appear frequently in real valued timeseries. In this paper, we propose a novel algorithm for solving this problem that can achieve performance comparable with the most accurate algorithms with a speed comparable to the fastest ones. The main idea behind the proposed algorithm is to convert the problem of ARM discovery into a density estimation problem in the single dimensionality shift-space (rather than in the original time-series space). This makes the algorithm more robust to short noise bursts that can dramatically affect the performance of most available algorithms. The paper also reports the results of applying the proposed algorithm to synthetic and three real-world datasets in the domains of gesture discovery and motion primitive discovery.


Data mining Motif discovery HRI 


  1. 1.
    Keogh E, Lin J, Fu A (2005) Hot sax: efficiently finding the most unusual time series subsequence. In: 15th IEEE international conference on data mining, p 8. doi: 10.1109/ICDM.2005.79
  2. 2.
    Mohammad Y, Nishida T, Okada S (2009) Unsupervised simultaneous learning of gestures, actions and their associations for human-robot interaction. In: Proceedings of the 2009 IEEE/RSJ international conference on Intelligent robots and systems, IROS’09. IEEE Press, Piscataway, pp 2537–2544. CrossRefGoogle Scholar
  3. 3.
    Mohammad Y, Nishida T (2013) Tackling the correspondence problem: closed-form solution for gesture imitation by a humanoid’s upper body. In: International conference on active media technology (AMT). WIC and IEEE TF-BI, Maebashi, pp 84–95Google Scholar
  4. 4.
    Mohammad Y, Nishida T (2009) Constrained motif discovery in time series. New Gener Comput 27(4):319–346CrossRefzbMATHGoogle Scholar
  5. 5.
    Minnen D, Starner T, Essa I, Isbell C (2007) Improving activity discovery with automatic neighborhood estimation. In: International joint conference on artificial intelligenceGoogle Scholar
  6. 6.
    Chiu B, Keogh E, Lonardi S (2003) Probabilistic discovery of time series motifs. In: KDD ’03: proceedings of the 9th ACM SIGKDD international conference on knowledge discovery and data mining. ACM, New York, pp 493–498. doi: 10.1145/956750.956808 CrossRefGoogle Scholar
  7. 7.
    Oates T (2002) Peruse: an unsupervised algorithm for finding recurring patterns in time series. In: International conference on data mining, pp 330–337Google Scholar
  8. 8.
    Jensen KL, Styczynxki MP, Rigoutsos I, Stephanopoulos GN (2006) A generic motif discovery algorithm for sequenctial data. BioInformatics 22(1):21–28CrossRefGoogle Scholar
  9. 9.
    Lin J, Keogh E, Lonardi S, Patel P (2002) Finding motifs in time series. In: The 2nd workshop on temporal data mining, at the 8th ACM SIGKDD international, pp 53–68Google Scholar
  10. 10.
    Tang H, Liao SS (2008) Discovering original motifs with different lengths from time series. Know Based Syst 21(7):666–671. doi: 10.1016/j.knosys.2008.03.022 CrossRefGoogle Scholar
  11. 11.
    Buhler J, Tompa M (2001) Finding motifs using random projections. In: 5th international conference on computational biology, pp 69–76Google Scholar
  12. 12.
    Patel P, Keogh E, Lin J, Lonardi S (2002) Mining motifs in massive time series databases. In: IEEE international conference on data mining, pp 370–377. doi: 10.1109/ICDM.2002.1183925.
  13. 13.
    Catalano J, Armstrong T, Oates T (2006) Discovering patterns in real-valued time series. In: Knowledge discovery in databases: PKDD 2006, pp 462–469Google Scholar
  14. 14.
    Mohammad Y, Nishida T (2012) Unsupervised discovery of basic human actions from activity recording datasets. In: Proceedings of the IEEE/SICE international symposium on system integrationGoogle Scholar
  15. 15.
    Mueen A, Keogh EJ, Zhu Q, Cash S, Westover MB (2009) Exact discovery of time series motifs. In: SDM, pp 473–484Google Scholar
  16. 16.
    Mohammad Y, Nishida T (2013) Approximately recurring motif discovery using shift density estimation. In: IEA/AIE, pp 141–150Google Scholar
  17. 17.
    Minnen D, Essa I, Isbell CL, Starner T (2007) Detecting subdimensional motifs: an efficient algorithm for generalized multivariate pattern discovery. In: IEEE international conference on data mining (ICDM)Google Scholar
  18. 18.
    Tompa M, Buhler J (2001) Finding motifs using random projections. In: 5th international conference on computational molecular biology, pp 67–74Google Scholar
  19. 19.
    Mueen A (2013) Enumeration of time series motifs of all lengths. In: 2013 IEEE 13th international conference on data mining (ICDM). IEEEGoogle Scholar
  20. 20.
    Nunthanid P, Niennattrakul V, Ratanamahatana C (2011) Discovery of variable length time series motif. In: 2011 8th international conference on electrical engineering/electronics, computer, telecommunications and information technology (ECTI-CON), pp 472 –475. doi: 10.1109/ECTICON.2011.5947877
  21. 21.
    Li Y, Lin J (2010) Approximate variable-length time series motif discovery using grammar inference. In: Proceedings of the 10th international workshop on multimedia data mining. ACM, p 10.
  22. 22.
    Nevill-Manning CG, Witten IH (1997) Identifying hierarchical structure in sequences: a linear-time algorithm. J Artif Intell Res 7(1):67–82. arXiv:9709102 zbMATHGoogle Scholar
  23. 23.
    Lin J, Keogh E, Wei L, Lonardi S (2007) Experiencing SAX: a novel symbolic representation of time series. Data Min Knowl Discov 15(2):107–144. doi: 10.1007/s10618-007-0064-z CrossRefMathSciNetGoogle Scholar
  24. 24.
    Mohammad Y, Nishida T (2009) Robust singular spectrum transform. In: IEA/AIE 2009, pp 253–258Google Scholar
  25. 25.
    Mohammad Y, Nishida T (2011) On comparing SSA-based change point discovery algorithms. In: 2011 IEEE/SICE international symposium on system integration, pp 938–945Google Scholar
  26. 26.
    Mohammad Y, Nishida T (2009) Robust singular spectrum transform. In: The 22nd international conference on industrial, engineering and other applications of applied intelligent systems IEA-AIE 2009, pp 123–132Google Scholar
  27. 27.
    Bro omhead DS, King GP (1986) Extracting qualitative dynamics from experimental data. Physica D 20:217–236CrossRefMathSciNetGoogle Scholar
  28. 28.
    Moskvina V, Zhigljavsky A (2003) An algorithm based on singular spectrum analysis for change-point detection. Commun Stat Simul Comput 32(4):319–352CrossRefMathSciNetzbMATHGoogle Scholar
  29. 29.
    Ide T, Inoue K (2005) Knowledge discovery from heterogeneous dynamic systems using change-point correlations. In: Proceedings SIAM international conference on data miningGoogle Scholar
  30. 30.
  31. 31.
    Mohammad Y, Ohmoto Y, Nishida T (2012) Gstex: Greedy stem extension for free-length constrained motif discovery. In: 25th IEA/AIE conference, pp 417–426Google Scholar
  32. 32.
    Minnen D, Essa I, Isbell C, Starner T (2007) Detecting subdimensional motifs: an efficient algorithm for generalized multivariate pattern discovery. In: IEEE international conference on data mining (ICDM)Google Scholar
  33. 33.
    Mohammad Y, Nishida T (2014) Exact discovery of length-range motifs. In: ACIIDS. SubmittedGoogle Scholar
  34. 34.
    Kulic D, Takano W, Nakamura Y (2008) Incremental learning, clustering and hierarchy formation of whole body motion patterns using adaptive hidden Markov chains. Int J Robot Res 27(7):761–784. doi: 10.1177/0278364908091153. CrossRefGoogle Scholar
  35. 35.
    Pantic M, Pentland A, Nijholt A, Huang T (2007) Machine understanding of human behavior. In: IJCAI 2007 workshop on AI for human computing (AI4HC’07). University of Twente, Centre for Telematics and Information Technology (CTIT), pp 13–24.
  36. 36.
    Vahdatpour A, Amini N, Sarrafzadeh M (2009) Toward unsupervised activity discovery using multi-dimensional motif detection in time series. In: IJCAI, pp 1261–1266Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Faculty of EngineeringAssiut UniversityAsyutEgypt
  2. 2.Graduate School of InformaticsKyoto UniversityKyotoJapan

Personalised recommendations