Skip to main content
SpringerLink
Log in

State duration and interval modeling in hidden semi-Markov model for sequential data analysis

  • Published:
Annals of Mathematics and Artificial Intelligence Aims and scope Submit manuscript

Abstract

Sequential data modeling and analysis have become indispensable tools for analyzing sequential data, such as time-series data, because larger amounts of sensed event data have become available. These methods capture the sequential structure of data of interest, such as input-output relations and correlation among datasets. However, because most studies in this area are specialized or limited to their respective applications, rigorous requirement analysis of such models has not been undertaken from a general perspective. Therefore, we particularly examine the structure of sequential data, and extract the necessity of “state duration” and “state interval” of events for efficient and rich representation of sequential data. Specifically addressing the hidden semi-Markov model (HSMM) that represents such state duration inside a model, we attempt to add representational capability of a state interval of events onto HSMM. To this end, we propose two extended models: an interval state hidden semi-Markov model (IS-HSMM) to express the length of a state interval with a special state node designated as “interval state node”; and an interval length probability hidden semi-Markov model (ILP-HSMM) which represents the length of the state interval with a new probabilistic parameter “interval length probability.” Exhaustive simulations have revealed superior performance of the proposed models in comparison with HSMM. These proposed models are the first reported extensions of HMM to support state interval representation as well as state duration representation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Esmaeili, M., Gabor, F.: Finding sequential patterns from large sequence data. Int. J. Comput. Sci. Issues (IJSC) 7(1), 43–46 (2010)

    Google Scholar 

  2. Lewis, D.D., Gale, W.A.: A sequential algorithm for training text classifiers. In: Proceedings of ACM the 17th Annual International Conference on Research and Development in Information Retrieval (ACM SIGIR), pp. 3–12 (1994)

  3. Song, J., Nicolae, D.L.: A sequential clustering algorithm with application to gene expression data. J. Korean Stat. Soc. 38(2), 175–184 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  4. Banaee, H., Ahmed, M., Loutfi, A.: Data mining for wearable sensors in health monitoring systems. A review of recent trends and challenges. Sensors 2013 13 (12), 17472–17500 (2013)

    Google Scholar 

  5. Zheng, Y., Niu, R., Varshney, P.K.: Sequential Bayesian estimation with censored data for multi-sensor systems. IEEE Trans. Signal Process. 62(10), 2626–2641 (2014)

    Article  MathSciNet  Google Scholar 

  6. Cheng, H.T.: Learning and Recognizing the Hierarchical and Sequential Structure of Human Activities. PhD thesis, Carnegie Mellon University (2013)

  7. Yu, S.Z.: Hidden semi-markov models. Elsevier Artif. Intell. 174(2), 215–243 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  8. Narimatsu, H., Kasai, H.: Duration and interval hidden Markov model for sequential data analysis. In: Proceedings of International Joint Conference on Neural Networks (IJCNN2015), pp. 3743–2751 (2015)

  9. Sakoe, H., Chiba, S.: A dynamic programming approach to continuous speech recognition. In: Proceedings of 7th International Congress on Acoustics (ICA) 1971, p. C13 (1971)

  10. Vapnik, V.N.: Statistical Learning Theory. Wiley, New York (1995)

    MATH  Google Scholar 

  11. Abe, S.: Support vector machines for pattern classification. Springer Science and Business Media (2010)

  12. Boscardin, W.J., Gelman, A.: Bayesian regression with parametric models for heteroscedasticity. Adv. Econ. 11A, 87–109 (1996)

    Google Scholar 

  13. Cox, D.R.: The regression analysis of binary sequences. J. R. Stat. Soc. 20, 215–242 (1958)

    MathSciNet  MATH  Google Scholar 

  14. Baum, L.E., Petrie, T.: Statistical inference for probabilistic functions of finite state Markov chains. Ann. Math. Stat. 37(6), 1554–1563 (1966)

    Article  MathSciNet  MATH  Google Scholar 

  15. Baum, L.E, Egon, J.A.: An inequality with applications to statistical estimation for probabilistic functions of a Markov process and to a model for ecology. Bull. Am. Math. Soc. 73(3), 360–363 (1967)

    Article  MATH  Google Scholar 

  16. Xue, H., Govindaraju, V.: Hidden Markov models combining discrete symbols and continuous attributes in handwriting recognition. IEEE Trans. Pattern Anal. Machine Intelligence 28(3), 458–462 (2006)

    Article  Google Scholar 

  17. Bengio, Y., Frasconi, P.: Input-output HMM for sequence processing. IEEE Trans. Neural Networks 7(5) (1996)

  18. Salzenstein, F., Collet, C., Lecam, S., Hatt, M.: Non-stationary fuzzy Markov chain. Pattern Recogn. Lett. 28(16), 2201–2208 (2007)

    Article  Google Scholar 

  19. Yu, S.Z., Kobayashi, H.: An efficient forward-backward algorithm for an explicit duration hidden Markov model. IEEE Signal Process. Lett. 10(1), 11–14 (2003)

    Article  Google Scholar 

  20. Mitchell, C.D., Jamieson, L.H.: Modeling duration in a hidden Markov model with the exponential family. Proceedings of 1993 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) 2, 331–334 (1993)

    Google Scholar 

  21. Ramesh, P., Wilpon, J.G.: Modeling state duration in hidden Markov models for automatic speech recognition. Proc. of 1992 IEEE International Conference on Acoustic, Speech, and Signal Processing (ICASSP) 1, 381–384 (1992)

    Article  Google Scholar 

  22. Murphy, K.: Dynamic Bayesian Networks: Representation, Inference and Learning. PhD Thesis, Dept. Computer Science, UC Berkeley (2002)

  23. Murphy, K.: Hidden semi-Markov models (hsmms). http://www.cs.ubc.ca/murphyk/papers/segment.pdf,nov.2002.(accessed2017-01-08)

  24. Ferguson, J.D.: Variable duration models for speech. In: Proceedings of the Symposium on the Applications of Hidden Markov Models to Text and Speech, pp. 143–179 (1980)

  25. Guédon, Y., Cocozza Thivent, C.: Explicit state occupancy modelling by hidden semi-Markov models: application of Derin’s scheme. Comput. Speech Lang. 4 (2), 167–192 (1990)

    Article  Google Scholar 

  26. Sansom, J.: Large-scale spatial variability of rainfall through hidden semi-Markov models of breakpoint data. J. Geophys. Res. 104(D24), 31631–31643 (1999)

    Article  Google Scholar 

  27. Sansom, J., Thomson, P.J.: Fitting hidden semi-Markov models to breakpoint rainfall data. J. Appl. Probab. 38A, 142–157 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  28. Guédon, Y.: Estimating hidden semi-Markov chains from discrete sequences. J. Comput. Graph. Stat. 12(3), 604–639 (2003)

    Article  MathSciNet  Google Scholar 

  29. Bulla, J.: Application of Hidden Markov Models and Hidden Semi-Markov Models to Financial Time Series. PhD thesis Georg-August-University of Gottingen (2006)

  30. Bulla, J., Bulla, I.: Stylized facts of financial time series and hidden semi-Markov models. Comput. Stat. Data Anal. 51(4), 2192–2209 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  31. Dong, M., He, D.: Hidden semi-Markov model-based methodology for multi-sensor equipment health diagnosis and prognosis. Eur. J. Oper. Res. 178(3), 858–878 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  32. Dasu, N.A.: Implementation of Hidden semi-Markov Models. PhD thesis, University of Nevada (2011)

  33. Yu, S.Z., Kobayashi, H.: A hidden semi-Markov model with missing data and multiple observation sequences for mobility tracking. Elsevier Science B.V. Signal Process. 83(2), 235–250 (2003)

    Article  MATH  Google Scholar 

  34. Baratchi, M., Meratnia, N., Havinga, P.J.M., Skidmore, A.K., Toxopeus, B.A.K.G.: A hierarchical hidden semi-Markov model for modeling mobility data. In: Proceedings of 2014 ACM International Joint Conference on Pervasive and Ubiquitous Computing (UbiComp 2014), pp. 401–412 (2014)

  35. Eddy, S.R.: Multiple alignment using hidden markov models. Proc. AAAI Third International Conference on Intelligent Systems for Modecular Biology 3, 114–120 (1995)

    Google Scholar 

  36. Kobayashi, H., Yu, S.Z.: Hidden semi-Markov models and efficient forward-backward algorithms. Proc. 2007 Hawaii and SITA Joint Conference on Information Theory 174, 41–46 (2007)

    Google Scholar 

  37. He, Y.: Extended viterbi algorithm for second-order hidden Markov process. In: Proceedings of the IEEE 9th International Conference on Pattern Recognition, pp. 718–720 (1988)

Download references

Author information

Authors and Affiliations

  1. Graduate School of Information Systems, The University of Electro-Communications, Chofugaoka 1-5-1, Chofu-shi, Tokyo, 182-8585, Japan

    Hiromi Narimatsu & Hiroyuki Kasai

Authors
  1. Hiromi Narimatsu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hiroyuki Kasai
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hiromi Narimatsu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Narimatsu, H., Kasai, H. State duration and interval modeling in hidden semi-Markov model for sequential data analysis. Ann Math Artif Intell 81, 377–403 (2017). https://doi.org/10.1007/s10472-017-9561-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10472-017-9561-y

Keywords

Search

Navigation