Making use of partial knowledge about hidden states in HMMs: An approach based on belief functions

IEEE Transactions on Fuzzy Systems

Volumn 22, Issue 2, 2014, Pages 395-405

  Ramasso, Emmanuel ^a   Denoeux, Thierry ^b  

^a FEMTO ST INSTITUTE   (France)

^b UNIVERSITÉ DE TECHNOLOGIE DE COMPIÈGNE   (France)

Author keywords

Dempster Shafer theory; evidence theory; evidential expectation maximization (E2M) algorithm; hidden Markov models (HMMs); partially supervised learning; soft labels; uncertain data

Indexed keywords

ALGORITHMS; HIDDEN MARKOV MODELS; MAXIMUM LIKELIHOOD ESTIMATION; UNCERTAINTY ANALYSIS;

DEMPSTER-SHAFER THEORY; EVIDENCE THEORIES; EXPECTATION MAXIMIZATION; HIDDEN MARKOV MODELS (HMMS); PARTIALLY SUPERVISED LEARNING; SOFT LABELS; UNCERTAIN DATAS;

IMAGE SEGMENTATION;

EID: 84897565302     PISSN: 10636706     EISSN: None     Source Type: Journal    
DOI: 10.1109/TFUZZ.2013.2259496     Document Type: Article

References (30)

1. L. E. Baum, T. Petrie, G. Soules, and N. Weiss, "A maximization technique occurring in statistical analysis of probabilistic functions of Markov chains," Ann. Math. Stat., vol. 41, pp. 164-171, 1970
2. A. Bendjebbour, Y. Delignon, L. Fouque, V. Samson, and W. Pieczynski, "Multisensor images segmentation using Dempster-Shafer fusion in Markov fields context," IEEE Trans. Geosci. Remote Sens., vol. 39, no. 8, pp. 1789-1798, Aug. 2001 (Pubitemid 32935693)
3. C. M. Bishop, Pattern Recognition and Machine Learning. NewYork, NY, USA: Springer-Verlag, 2006
4. M. Y. Boudaren, E. Monfrini, W. Pieczynski, and A. Assani, "Dempster-Shafer fusion of multisensor signals in nonstationary Markovian context," EURASIP J. Adv. Signal Process., vol. 2012, no. 134, 2012
5. Y.-C. Cheng and S.-T. Li, "Fuzzy time series forecasting with a probabilistic smoothing hidden markov model," IEEE Trans. Fuzzy Syst., vol. 20, no. 2, pp. 291-304, Apr. 2012
6. Z. L. Cherfi, L. Oukhellou, E. Come, T. Denoeux, and P. Aknin, "Partially supervised independent factor analysis using soft labels elicited frommultiple experts: Application to railway track circuit diagnosis," Soft Comput., vol. 16, no. 5, pp. 741-754, 2012
7. E. Come, L. Oukhellou, T. Denoeux, and P. Aknin, "Learning from partially supervised data using mixture models and belief functions," Pattern Recognit., vol. 42, no. 3, pp. 334-348, 2009
8. A. P.Dempster,N. M. Laird, andD. B.Rubin, "Maximum likelihood from incomplete data via the EM algorithm," J. Roy. Statist. Soc., vol. B 39, pp. 1-38, 1977
9. T. Denoeux, "Maximum likelihood estimation from fuzzy data using the fuzzy EM algorithm," Fuzzy Sets Syst., vol. 18, no. 1, pp. 72-91, 2011
10. T. Denoeux, "Maximum likelihood estimation from uncertain data in the belief function framework," IEEE Trans. Knowl. Data Eng., vol. 25, no. 1, pp. 119-130, Jan. 2013
11. M. Dong and D. He, "A segmental hidden semi-Markov model (HSMM)-based diagnostics and prognostics framework and methodology," Mech. Syst. Signal Process., vol. 21, pp. 2248-2266, 2007 (Pubitemid 46566399)
12. G. D. Forney, "The viterbi algorithm," Proc. IEEE, vol. 61, no. 3, pp. 268-278, Mar. 1973
13. L. Fouque, A. Appriou, and W. Pieczynski, "An evidential Markovian model for data fusion and unsupervised image classification," in Proc. 3rd Int. Conf. Inf. Fus., Paris, France, 2000, vol. 1, pp. TuB4-25-TuB4-31
14. L. Hubert and P. Arabie, "Comparing partitions," J. Classification, vol. 2, no. 1, pp. 193-218, 1985
15. P. Lanchantin and W. Pieczynski, "Unsupervised restoration of hidden non stationary Markov chain using evidential priors," IEEE Trans. Signal Process., vol. 53, no. 8, pp. 3091-3098, Aug. 2005 (Pubitemid 41372818)
16. K. P. Murphy, "Dynamic Bayesian networks: Representation, inference and learning," Ph.D. dissertation, Univ. California, Dept. Comput. Sci., Berkeley, CA, USA, 2002
17. W. Pieczynski, "Cha?nes de Markov triplet, triplet Markov chains," Comptes Rendus de lAcademie des Sciences-Mathematique, Serie I, vol. 335, no. 3, pp. 275-278, 2002
18. W. Pieczynski, "Pairwise Markov chains," IEEE Trans. Pattern Anal. Mach. Intell., vol. 25, no. 5, pp. 634-639, May 2003
19. W. Pieczynski, "Multisensor triplet Markov chains and theory of evidence," Int. J. Approx. Reason., vol. 45, pp. 1-16, 2007 (Pubitemid 46617870)
20. L. R. Rabiner, "A tutorial on hidden Markov models and selected applications in speech recognition," Proc. IEEE, vol. 77, no. 2, pp. 257-285, Feb. 1989
21. E. Ramasso, "Contribution of belief functions to HiddenMarkovModels," in Proc. IEEE Worksh. Mach. Learn. Signal Process., Grenoble, France, Oct. 2009, pp. 1-6
22. E. Ramasso, M. Rombaut, and D. Pellerin, "State filtering and change detection using TBM conflict-Application to human action recognition in athletics videos," IEEE Trans. Circuits Syst. Video Technol., vol. 17, no. 7, pp. 944-949, Jul. 2007 (Pubitemid 47159723)
23. E. Ramasso, M. Rombaut, and N. Zerhouni, "Joint prediction of observations and states in time-series based on belief functions," IEEE Trans. Syst., Man Cybern. B: Cybern., vol. 43, no. 1, pp. 37-50, Feb. 2013
24. A. Saxena, K. Goebel, D. Simon, and N. Eklund, "Damage propagation modeling for aircraft engine run-to-failure simulation," in Proc. Int. Conf. Prognost. Health Manag., Denver, CO, USA, 2008, pp. 1-9
25. L. Serir, E. Ramasso, and N. Zerhouni, "Time-sliced temporal evidential networks: the case of evidential HMM with application to dynamical system analysis," in Proc. IEEE Int. Conf. Prognost. Health Manag., Denver, CO, USA, 2011, pp. 1-10
26. G. Shafer, A Mathematical Theory of Evidence. Princeton, NJ, USA: Princeton Univ. Press, 1976
27. H. Soubaras, "On evidential Markov chains," in Proc. Inform. Process. Manage. Uncertainty knowledge-based syst., 2008, pp. 386-393
28. A. J. Viterbi, "Error bounds for convolutional codes and an asymptotically optimal decoding algorithm," IEEE Trans. Inf. Theory, vol. IT-13, no. 2, pp. 260-269, Apr. 1967
29. T. Wang, "Trajectory similarity based prediction for remaining useful life estimation," Ph.D. dissertation, Univ. Cincinnati, Sch. Dynamic Syst., College Eng. Applied Sci., Cincinnati, OH, USA, 2010
30. A. Wilson and A. Bobick, "Hidden Markov models for modeling and recognizing gesture under variation," Int. J. Pattern Recognit. Artif. Intell., vol. 15, no. 1, pp. 123-160, 2001. (Pubitemid 32272688)