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E-raamat: Hidden Markov Models: Theory and Implementation using MATLAB® [Taylor & Francis e-raamat]

(Instituto Politécnico de Bragança, Portugal), (INESC TEC Technology and Science, Porto, Portugal), (Universidade de Trás-os-Montes e Alto Douro, Escola de Ciências e Tecnologia, Vila Real, Portugal)
  • Formaat: 282 pages
  • Ilmumisaeg: 13-Aug-2019
  • Kirjastus: CRC Press
  • ISBN-13: 9780429261046
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Hidden Markov Models: Theory and Implementation using MATLAB®Suurem pilt
  • Formaat: 282 pages
  • Ilmumisaeg: 13-Aug-2019
  • Kirjastus: CRC Press
  • ISBN-13: 9780429261046
Teised raamatud teemal:
Taylor & Francis e-raamatudRohkem infot Taylor & Francis e-raamatute kohta
Raamatu kodulehekülg: https://www.taylorfrancis.com/books/9780429261046

This book presents, in an integrated form, both the analysis and synthesis of three different types of hidden Markov models. Unlike other books on the subject, it is generic and does not focus on a specific theme, e.g. speech processing. Moreover, it presents the translation of hidden Markov models’ concepts from the realm of formal mathematics into computer codes using MATLAB®. The unique feature of this book is that the theoretical concepts are first presented using an intuition-based approach followed by the description of the fundamental algorithms behind hidden Markov models using MATLAB®. This approach, by means of analysis followed by synthesis, is suitable for those who want to study the subject using a more empirical approach.

Key Selling Points:

  • Presents a broad range of concepts related to Hidden Markov Models (HMM), from simple problems to advanced theory
  • Covers the analysis of both continuous and discrete Markov chains
  • Discusses the translation of HMM concepts from the realm of formal mathematics into computer code
  • Offers many examples to supplement mathematical notation when explaining new concepts
Preface iii
Glossary ix
1 Introduction
1(6)
1.1 System Models
1(3)
1.2 Markov Chains
4(2)
1.3 Book Outline
6(1)
2 Probability Theory and Stochastic Processes
7(22)
2.1 Introduction
7(2)
2.2 Introduction to Probability Theory
9(13)
2.2.1 Events and Random Variables
11(2)
2.2.1.1 Types of variables
13(1)
2.2.2 Probability Definition
14(5)
2.2.3 Axioms and Properties
19(3)
2.3 Probability Density Function
22(2)
2.4 Statistical Moments
24(3)
2.5 Summary
27(2)
3 Discrete Hidden Markov Models
29(128)
3.1 Introduction
29(3)
3.2 Hidden Markov Model Dynamics
32(28)
3.2.1 The Forward Algorithm
37(8)
3.2.2 The Backward Algorithm
45(6)
3.2.3 The Viterbi Algorithm
51(9)
3.3 Probability Transitions Estimation
60(18)
3.3.1 Maximum Likelihood Definition
62(1)
3.3.2 The Baum- Welch Training Algorithm
63(9)
3.3.2.1 Operation conditions for the Baum-Welch algorithm
72(1)
3.3.2.2 Parameter estimation using multiple trials
73(1)
3.3.2.3 Baum-Welch algorithm numerical stability
74(4)
3.4 Viterbi Training Algorithm
78(4)
3.5 Gradient-based Algorithms
82(71)
3.5.1 Partial Derivative of k
82(1)
3.5.1.1 Partial derivative of, in order to bij
82(8)
3.5.1.2 Partial derivative of k in order to bij
90(7)
3.5.2 Partial Derivative of k in order to c
97(2)
3.5.3 Performance Analysis of the Re-estimation Formulas
99(5)
3.5.4 Parameters Coercion by Re-parameterization
104(3)
3.5.5 Rosen's Algorithm
107(3)
3.5.5.1 Linear equality constraints
110(7)
3.5.5.2 Lagrange multipliers and Karush-Kuhn-Tucker conditions
117(18)
3.5.5.3 Linear inequality constraints
135(8)
3.5.5.4 Putting it all together
143(5)
3.5.5.5 Rosen's method applied to hidden Markov models
148(5)
3.6 Architectures for Markov Models
153(1)
3.7 Summary
154(3)
4 Continuous Hidden Markov Models
157(50)
4.1 Introduction
158(4)
4.2 Probability Density Functions and Gaussian Mixtures
162(28)
4.2.1 Gaussian Functions in System Modeling
163(4)
4.2.2 Gaussian Function and Gaussian Mixture
167(23)
4.3 Continuous Hidden Markov Model Dynamics
190(7)
4.3.1 Forward, Backward and Viterbi Algorithms Revisited
192(5)
4.4 Continuous Observations Baum-Welch Training Algorithm
197(7)
4.5 Summary
204(3)
5 Autoregressive Markov Models
207(38)
5.1 Introduction
207(2)
5.2 ARMM Structure
209(4)
5.3 Likelihood and Probability Density for AR Models
213(8)
5.3.1 AR Model Probability Density Function
213(6)
5.3.2 Autoregressive Model Likelihood
219(2)
5.4 Likelihood of an ARMM
221(2)
5.5 ARMM Parameters Estimations
223(11)
5.5.1 Parameters Estimation
226(8)
5.6 Time Series Prediction with ARMM
234(8)
5.6.1 One Step Ahead Time Series Prediction
235(2)
5.6.2 Multiple Steps Ahead Time Series Prediction
237(5)
5.7 Summary
242(3)
6 Selected Applications
245(12)
6.1 Cardiotocography Classification
246(4)
6.2 Solar Radiation Prediction
250(5)
6.3 Summary
255(2)
References 257(4)
Index 261(4)
Color Figures Section 265
João Paulo Coelho is an adjunct professor, and currently the Electrical Engineering course director, at the Polytechnic Institute of Bragança. He is also a researcher at CeDRI and holds a Ph.D. degree in computational intelligence applied to agricultural greenhouses. He has been involved, as a researcher member, in several scientific projects at both the national and European level. His research interests include control systems design, machine learning, electronic instrumentation, embedded systems and discrete-event computer simulation.









Tatiana M. Pinho graduated in Energy Engineering from the University of Trás-os-Montes e Alto Douro (UTAD), Portugal in 2011 and received the MSc degree in Energy Engineering from UTAD in 2013. In 2018, she received the Ph.D. degree in Electrical and Computer Engineering in UTAD and INESC TEC Technology and Science, supported by the FCT. Presently she is a postdoctoral researcher at the INESC TEC and her research interests include systems modeling and adaptive control.



José Boaventura-Cunha graduated in Electronics and Telecommunications Engineering and has a Ph.D. degree in Electrical and Computer Engineering. Presently he is an Associate Professor with habilitation at the UTAD University, a senior researcher at the INESC-TEC and member of IFAC and IEEE. He has coordinated/participated in several national and international research projects aiming the development of new instrumentation, modelling and control technologies applied to agriculture. His research interests include modeling, system identification and adaptive control.
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