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Hidden Markov Models, Theory and Applications.Indd HIDDEN MARKOV MODELS, THEORY AND APPLICATIONS Edited by Przemyslaw Dymarski Hidden Markov Models, Theory and Applications Edited by Przemyslaw Dymarski Published by InTech Janeza Trdine 9, 51000 Rijeka, Croatia Copyright © 2011 InTech All chapters are Open Access articles distributed under the Creative Commons Non Commercial Share Alike Attribution 3.0 license, which permits to copy, distribute, transmit, and adapt the work in any medium, so long as the original work is properly cited. After this work has been published by InTech, authors have the right to republish it, in whole or part, in any publication of which they are the author, and to make other personal use of the work. Any republication, referencing or personal use of the work must explicitly identify the original source. Statements and opinions expressed in the chapters are these of the individual contributors and not necessarily those of the editors or publisher. No responsibility is accepted for the accuracy of information contained in the published articles. The publisher assumes no responsibility for any damage or injury to persons or property arising out of the use of any materials, instructions, methods or ideas contained in the book. Publishing Process Manager Ivana Lorkovic Technical Editor Teodora Smiljanic Cover Designer Martina Sirotic Image Copyright Jenny Solomon, 2010. Used under license from Shutterstock.com First published March, 2011 Printed in India A free online edition of this book is available at www.intechopen.com Additional hard copies can be obtained from [email protected] Hidden Markov Models, Theory and Applications, Edited by Przemyslaw Dymarski p. cm. ISBN 978-953-307-208-1 free online editions of InTech Books and Journals can be found at www.intechopen.com Contents Preface IX Part 1 Tutorials and Theoretical Issues 1 Chapter 1 History and Theoretical Basics of Hidden Markov Models 3 Guy Leonard Kouemou Chapter 2 Hidden Markov Models in Dynamic System Modelling and Diagnosis 27 Tarik Al-ani Chapter 3 Theory of Segmentation 51 Jüri Lember, Kristi Kuljus and Alexey Koloydenko Chapter 4 Classification of Hidden Markov Models: Obtaining Bounds on the Probability of Error and Dealing with Possibly Corrupted Observations 85 Eleftheria Athanasopoulou and Christoforos N. Hadjicostis Part 2 Hidden Markov Models in Speech and Time-domain Signals Processing 111 Chapter 5 Hierarchical Command Recognition Based on Large Margin Hidden Markov Models 113 Przemyslaw Dymarski Chapter 6 Modeling of Speech Parameter Sequence Considering Global Variance for HMM-Based Speech Synthesis 131 Tomoki Toda Chapter 7 Using Hidden Markov Models for ECG Characterisation 151 Krimi Samar, Ouni Kaïs and Ellouze Noureddine Chapter 8 Hidden Markov Models in the Neurosciences 169 Blaettler Florian, Kollmorgen Sepp, Herbst Joshua and Hahnloser Richard VI Contents Chapter 9 Volcano-Seismic Signal Detection and Classification Processing Using Hidden Markov Models - Application to San Cristóbal and Telica Volcanoes, Nicaragua 187 Gutiérrez, Ligdamis, Ramírez, Javier, Ibañez, Jesús and Benítez, Carmen Chapter 10 A Non-Homogeneous Hidden Markov Model for the Analysis of Multi-Pollutant Exceedances Data 207 Francesco Lagona, Antonello Maruotti and Marco Picone Part 3 Hidden Markov Models in Image and Spatial Structures Analysis 223 Chapter 11 Continuous Hidden Markov Models for Depth Map-Based Human Activity Recognition 225 Zia Uddin and Tae-Seong Kim Chapter 12 Applications of Hidden Markov Models in Microarray Gene Expression Data 249 Huimin Geng, Xutao Deng and Hesham H Ali Chapter 13 Application of HMM to the Study of Three-Dimensional Protein Structure 269 Christelle Reynès, Leslie Regad, Stéphanie Pérot, Grégory Nuel and Anne-Claude Camproux Chapter 14 Control Theoretic Approach to Platform Optimization using HMM 291 Rahul Khanna, Huaping Liu and Mariette Awad Preface Hidden Markov Models (HMMs), although known for decades, have made a big ca- reer nowadays and are still in state of development. This book presents theoretical is- sues and a variety of HMMs applications. Each of the 14 chapters addresses theoretical problems and refers to some applications, but the more theoretical parts are presented in Part 1 and the application oriented chapters are grouped in Part 2 and 3. Chapter 1 has an introductory character: the basic concepts (e.g. Maximum Likeli- hood, Maximum a Posteriori and Maximum Mutual Information approaches to the HMM training) are explained. Problems of discriminative training are also discussed in1 (2) and (5) – in particular the Large Margin approach. Chapter (3) discusses the united approach to the HMM segmentation (decoding) problem based on statistical learning. The Viterbi training is compared with the Baum-Welch training in (2). The HMM evaluation problem is analyzed in (4), where the probability of classifi cation er- ror in presence of corrupted observations (e.g. caused by sensor failures) is estimated. Chapter (6) presents the Global Variance constrained trajectory training algorithm for the HMMs used for speech signal generation. The Hidden Semi-Markov Models and Hidden Markov Trees are described in (7), the Pair HMMs in (8) and the Non-homo- geneous HMMs in (10). The association of HMMs with other techniques, e.g. wavelet transforms (7) has proved useful for some applications. The HMMs applications concerning recognition, classifi cation and alignment of sig- nals described in time domain are presented in Part 2. In (5) the hierarchical recog- nition of spoken commands and in (6) the HMMs application in the Text-To-Speech synthesis is described. Chapter (7) presents the algorithms of the ECG signal analysis and segmentation. In (8) HMM applications in neurosciences are discussed, i.e. the brain activity modeling, the separation of signals generated by single neurons given a muti-neuron recording and the identifi cation and alignment of birdsong. In (9) the classifi cation of seismic signals is described and in (10) multi-pollutant exceedances data are analyzed. The applications referring to images, spatial structures and other data are presented in Part 3. Moving pictures (in forms of depth silhouett es) are recognized in the Human Ac- tivity Recognition System described in (11). Some applications concern computational 1 Numbers of chapters are referred in parentheses X Preface biology, bioinformatics and medicine. Predictions of gene functions and genetic abnor- malities are discussed in (12), a 3-dimensional protein structure analyzer is described in (13) and a diagnosis of the sleep apnea syndrome is presented in (2). There are also applications in engineering: design of the energy effi cient systems (e.g. server plat- forms) is described in (14) and condition-based maintenance of machines – in (2). I hope that the reader will fi nd this book useful and helpful for their own research. Przemyslaw Dymarski Warsaw University of Technology,Department of Electronics and Information Technology, Institute of Telecommunications Poland Part 1 Tutorials and Theoretical Issues 1 History and Theoretical Basics of Hidden Markov Models Guy Leonard Kouemou EADS Deutschland GmbH, Germany 1. Introduction The following chapter can be understood as one sort of brief introduction to the history and basics of the Hidden Markov Models. Hidden Markov Models (HMMs) are learnable finite stochastic automates. Nowadays, they are considered as a specific form of dynamic Bayesian networks. Dynamic Bayesian networks are based on the theory of Bayes (Bayes & Price, 1763). A Hidden Markov Model consists of two stochastic processes. The first stochastic process is a Markov chain that is characterized by states and transition probabilities. The states of the chain are externally not visible, therefore “hidden”. The second stochastic process produces emissions observable at each moment, depending on a state-dependent probability distribution. It is important to notice that the denomination “hidden” while defining a Hidden Markov Model is referred to the states of the Markov chain, not to the parameters of the model. The history of the HMMs consists of two parts. On the one hand there is the history of Markov process and Markov chains, and on the other hand there is the history of algorithms needed to develop Hidden Markov Models in order to solve problems in the modern applied sciences by using for example a computer or similar electronic devices. 1.1. Brief history of Markov process and Markov chains Andrey Andreyevich Markov (June 14, 1856 – July 20, 1922) was a Russian mathematician. He is best known for his work on the theory of stochastic Markov processes. His research area later became known as Markov process and Markov chains. Andrey Andreyevich Markov introduced the Markov chains in 1906 when he produced the first theoretical results for stochastic processes by using the term “chain” for the first time. In 1913 he calculated letter sequences of the Russian language. A generalization to countable infinite state spaces was given by Kolmogorov (1931). Markov chains are related to Brownian motion and the ergodic hypothesis, two topics in physics which were important in the early years of the twentieth century. But Markov appears to have pursued this out of a mathematical motivation, namely the extension of the law of large numbers to dependent events. Out of this approach grew a general statistical instrument, the so-called stochastic Markov process. In mathematics generally, probability theory and statistics particularly, a Markov process can be considered as a time-varying
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