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2015 | OriginalPaper | Chapter

5. Hidden Markov Models

Author : Luis Enrique Sucar

Published in: Probabilistic Graphical Models

Publisher: Springer London

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Abstract

Markov chains and hidden Markov models (HMMs) are particular types of PGMs that represent dynamic processes. After a brief introduction to Markov chains, this chapter focuses on hidden Markov models. The algorithms for solving the basic problems: evaluation, optimal sequence, and parameter learning are presented. The chapter concludes with a description of several extensions to the basic HMM, and two applications: the “PageRank” procedure used by Google and gesture recognition.

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Footnotes
1
Do not confuse a state diagram, where a node represents each state—a specific value of a random variable—and the arcs transitions between states, with a graphical model diagram, where a node represents a random variable and the arcs represent probabilistic dependencies.
 
2
This is a particular case of the Most Probable Explanation or MPE problem, which will be discussed in Chap. 7.
 
3
If we have some domain knowledge this could provide a good initialization for the parameters; otherwise, we can set them to uniform probabilities.
 
4
Hidden Markov models, including these extensions, are particular types of dynamic Bayesian networks, a more general model that is described in Chap. 9.
 
Literature
1.
go back to reference Aviles, H., Sucar, L.E., Mendoza C.E.: Visual recognition of similar gestures. In: 18th International Conference on Pattern Recognition, pp. 1100–1103 (2006) Aviles, H., Sucar, L.E., Mendoza C.E.: Visual recognition of similar gestures. In: 18th International Conference on Pattern Recognition, pp. 1100–1103 (2006)
2.
go back to reference Aviles, H., Sucar, L.E., Mendoza, C.E., Pineda, L.A.: A Comparison of dynamic naive Bayesian classifiers and hidden Markov models for gesture recognition. J. Appl. Res. Technol. 9(1), 81–102 (2011) Aviles, H., Sucar, L.E., Mendoza, C.E., Pineda, L.A.: A Comparison of dynamic naive Bayesian classifiers and hidden Markov models for gesture recognition. J. Appl. Res. Technol. 9(1), 81–102 (2011)
4.
go back to reference Kemeny, J.K., Snell, L.: Finite Markov Chains. Van Nostrand, Princeton (1965) Kemeny, J.K., Snell, L.: Finite Markov Chains. Van Nostrand, Princeton (1965)
5.
go back to reference Langville, N., Carl, D., Meyer, C.D.: Google’s PageRank and Beyond: The Science of Search Engine Rankings. Princeton University Press, Princeton (2012) Langville, N., Carl, D., Meyer, C.D.: Google’s PageRank and Beyond: The Science of Search Engine Rankings. Princeton University Press, Princeton (2012)
6.
go back to reference Page, L., Brin, S., Motwani, R., Winograd, T.: The PageRank Citation Ranking: Bringing Order to the Web. Stanford Digital Libraries Working Paper (1998) Page, L., Brin, S., Motwani, R., Winograd, T.: The PageRank Citation Ranking: Bringing Order to the Web. Stanford Digital Libraries Working Paper (1998)
7.
go back to reference Rabiner, L.E.: A tutorial on hidden Markov models and selected applications in speech recognition. In: Waibel, A., Lee, K. (eds.) Readings in Speech Recognition, pp. 267–296. Morgan Kaufmann, San Francisco (1990) Rabiner, L.E.: A tutorial on hidden Markov models and selected applications in speech recognition. In: Waibel, A., Lee, K. (eds.) Readings in Speech Recognition, pp. 267–296. Morgan Kaufmann, San Francisco (1990)
8.
go back to reference Rabiner, L., Juang, B.H.: Fundamentals on Speech Recognition. Prentice-Hall Signal Processing Series, New Jersey (1993) Rabiner, L., Juang, B.H.: Fundamentals on Speech Recognition. Prentice-Hall Signal Processing Series, New Jersey (1993)
9.
go back to reference Wilson, A., Bobick, A.: Using hidden Markov models to model and recognize gesture under variation. Int. J. Pattern Recognit. Artif. Intell., Spec. Issue Hidden Markov Models Comput. Vis. 15(1), 123–160 (2000)CrossRef Wilson, A., Bobick, A.: Using hidden Markov models to model and recognize gesture under variation. Int. J. Pattern Recognit. Artif. Intell., Spec. Issue Hidden Markov Models Comput. Vis. 15(1), 123–160 (2000)CrossRef
Metadata
Title
Hidden Markov Models
Author
Luis Enrique Sucar
Copyright Year
2015
Publisher
Springer London
DOI
https://doi.org/10.1007/978-1-4471-6699-3_5

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