Finite Mixture Models (Wiley Series in Probability and Statistics)

Book Description

An up-to-date, comprehensive account of major issues in finite mixture modeling
This volume provides an up-to-date account of the theory and applications of modeling via finite mixture distributions. With an emphasis on the applications of mixture models in both mainstream analysis and other areas such as unsupervised pattern recognition, speech recognition, and medical imaging, the book describes the formulations of the finite mixture approach, details its methodology, discusses aspects of its implementation, and illustrates its application in many common statistical contexts.
Major issues discussed in this book include identifiability problems, actual fitting of finite mixtures through use of the EM algorithm, properties of the maximum likelihood estimators so obtained, assessment of the number of components to be used in the mixture, and the applicability of asymptotic theory in providing a basis for the solutions to some of these problems. The author also considers how the EM algorithm can be scaled to handle the fitting of mixture models to very large databases, as in data mining applications. This comprehensive, practical guide:
* Provides more than 800 references-400ublished since 1995
* Includes an appendix listing available mixture software
* Links statistical literature with machine learning and pattern recognition literature
* Contains more than 100 helpful graphs, charts, and tables
Finite Mixture Models is an important resource for both applied and theoretical statisticians as well as for researchers in the many areas in which finite mixture models can be used to analyze data.

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An up-to-date, comprehensive account of major issues in finite mixture modeling This volume provides an up-to-date account of the theory and applications of modeling via finite mixture distributions. With an emphasis on the applications of mixture models in both mainstream analysis and other areas such as unsupervised pattern recognition, speech recognition, and medical imaging, the book describes the formulations of the finite mixture approach, details its methodology, discusses aspects of its implementation, and illustrates its application in many common statistical contexts. Major issues discussed in this book include identifiability problems, actual fitting of finite mixtures through use of the EM algorithm, properties of the maximum likelihood estimators so obtained, assessment of the number of components to be used in the mixture, and the applicability of asymptotic theory in providing a basis for the solutions to some of these problems. The author also considers how the EM algorithm can be scaled to handle the fitting of mixture models to very large databases, as in data mining applications. This comprehensive, practical guide: * Provides more than 800 references-40% published since 1995 * Includes an appendix listing available mixture software * Links statistical literature with machine learning and pattern recognition literature * Contains more than 100 helpful graphs, charts, and tables Finite Mixture Models is an important resource for both applied and theoretical statisticians as well as for researchers in the many areas in which finite mixture models can be used to analyze data.

Customer Reviews:

Not Enough Details - - Assumes use of unavailable Software.......2006-10-29

This title is not up to the high standards set by McLachlan's other books. The text does not get into details which are thoroughly discussed
in McLachlan's excellent "The EM Algorithm and Extensions." Some important points are so condensed and in places so poorly presented that the the discussion is worthless. For example the important section 3.4 "Standard Errors", which underlies much of the discussion contains errors.
The book could be useful to a practioner who is only looking for guidance in fitting mixture models with available software. Unfortanately McLachlan's mixture software referred to in the Appendix, is not available. That's a pity because the advertised software features and design potentially rank it the top choice.
For a user who will use his own EM software to fit mixture models I would recommend highly the McLachlan's EM Algorithm book over the Mixture book.

Excellent!.......2006-07-10

"Finite Mixture Models" is an excellent reading for scientists and researchers working on or interested in finite mixture models. It provides a comprehensive introduction to finite mixture models as well as an extensive survey of the novel finite mixture models presented in the most recent literature on the field in conjunction with the prospective practical applications of them. In addition, the book is very well-written and it has the merit of the use of a consistent mathematical notation throughout the book.

superb update on mixture models.......2001-07-19

McLachlan and Basford (1988) and Titterington, Smith and Makov (1985) were the first well written texts summarizing the diverse lterature and mathematical problems that can be treated through mixture models. Geoff McLachlan is the author of four statistics texts namely (1)McLachlan and Basford (1988) "Mixture Models:Inference and Applications to Clustering", Marcel Dekker, (2) McLachlan (1992) "Discriminant Analysis and Statistical Pattern Recognition", Wiley (3) McLachlan and Krishnan (1997) "The EM Algorithm and Extensions" Wiley and (4) McLachlan and Peel (2000) "Finite Mixture Models" Wiley. These four books are all related to the interesting problems in pattern recognition and clustering. Mixture models and the EM algorithm are tools used to solve problems in clustering and pattern recognition.

In each of his books McLachlan has shown an ability to be clear, authoritative, scholarly and thorough. He provides broad coverage of each topic with detailed references. This book is no exception. As he point out in the preface, the literature on mixture models has expanded tremendously since the appearance of his 1988 monograph with Kaye Basford making an updated text very appropriate.

Almost 40% of the 800 references in the text have appeared since 1995. The recent advances covered in the text include identifiability problems with mixture models, the analysis (fitting of mixture models) for real data sets using the EM algorithm and its extensions, properties of maximum likelihood estimators, applicability of asymptotic theory, use of bootstrap methods to assess accuracy of estimates, implimentation of Bayesian approaches through Markov chain Monte Carlo methods and the use of hierarchical mixtures-of-expert models for nonlinear regression as competitors to the MARS and CART algorithms.

This is a great book. Chapter 1 provides a nice overview of the subject with a thorough historical treatment, nicely presented in Section 1.18. In addition to the fact that it covers all the recent advances one can think of. The book also deals with fast implementations of the EM algorithm for data mining and other approaches to modifying the EM algorithm to handle large data sets. There is also a wealth of interesting real problems worked out in detail. These problems come from many disciplines, including interesting medical problems related to diabetes and hemophilia, nuclear test ban data analysis, image processing and competing risk survival analysis. It also covers some interesting aspects of multivariate normal mixture models and their applications.

Wonderful!.......2001-06-17

A wonderful text that functions as well as a reference as it does as an introduction to mixture models. I was surprised by the depth and breadth of the book, which manages to describe almost every mixture model imaginable and then some more, including forms of the models themselves, parameter estimation and fit. Relationships between different models are made clear, lending the text a coherence that isn't undercut by vague generalities. The authors are particularly good at addressing issues of particular importance in mixture modeling, such as fit and model selection. Material is suprisingly recent as well. Overall, a great text that is probably destined to become the standard reference on mixture models.

Job well done.......2001-04-26

Mixture models have become a hot topic in statistics. After you read this book, you will know why.

"Finite Mixture models" have come a long way from classic finite mixture distribution as discused e.g. Titterington et al(1985). A small sample should almost surely entice your taste, with hot items such as hierarchical mixtures-of-experts models, mixtures of GLMs, mixture models for failure-time data, EM algorithms for large data sets, and hidden Markov models. The book gives a lucid overview of recent developments on mixture models since 1990 (the aim of this book in the first place). It expounds on the modern viewpoint that mixtures can be usefully exploited as a mechanism for building flexible statistical models for complex processes, e.g. nonparametric Bayesian models. Balanced attention is given to all three modern approaches to fitting mixture models which include speed-up EM, Bayesian, and stochastic simulation. The whole book is superbly written, and very entertaining---It's hard to put it down once started. It is very update with 45 pages of references and an appendix listing available softwares.

Book Description

In Finite Element Analysis of Electrical Machines the author covers two-dimensional analysis, emphasizing the use of finite elements to perform the most common calculations required of machine designers and analysts. The book explains what is inside a finite element program, and how the finite element method can be used to determine the behavior of electrical machines. The material is tutorial and includes several completely worked out examples. The main illustrative examples are synchronous and induction machines. The methods described have been used successfully in the design and analysis of most types of rotating and linear machines.
Audience: A valuable reference source for academic researchers, practitioners and designers of electrical machinery.

Customer Reviews:

The only book on the subject.......2002-07-31

There are lots of books on finite element analysis. There are a good number of books on finitie element analysis for the electrical engineer. This is the only book devoted solely to the FE method for the analysis of electric machines, so it is kind of hard to say that this is the best because it is the only horse in the race. But I can confidently assert this because it answers most of the questions dealing with the area. Prof. Salon has done a very good job of putting a lot of results in a very slim volume. he has sought to answer most of the question concerning analyzing different machines and he has devoted just enough mathematics to clear up a number of important issues concerning the accuracy of the methods. Most specifically, he dealt with the air gap mesh problem very clearly and succinctly.

He also tells you how to go about calculating the inductance, the flux linkage, and the magnetic flux density from the vector potential. This is a very complete treatment of a very broad subject.

Book Description

This book is an introduction to finite model theory which stresses the computer science origins of the area. In addition to presenting the main techniques for analyzing logics over finite models, the book deals extensively with applications in databases, complexity theory, and formal languages, as well as other branches of computer science. It covers Ehrenfeucht-Fraïssé games, locality-based techniques, complexity analysis of logics, including the basics of descriptive complexity, second-order logic and its fragments, connections with finite automata, fixed point logics, finite variable logics, zero-one laws, and embedded finite models, and gives a brief tour of recently discovered applications of finite model theory.

This book can be used both as an introduction to the subject, suitable for a one- or two-semester graduate course, or as reference for researchers who apply techniques from logic in computer science.

Customer Reviews:

Technical review of this book.......2004-09-21

Model theory is the study of the logical properties of mathematical structures. Finite model theory arises when we focus our attention on finite structures, such as finite graphs (graphs with a finite number of nodes). This book presents the most important results of finite model theory in an extremely readable, yet careful and precise manner. Libkin himself is a master of the art, and this shows in his beautiful presentation of the material.
--Ronald Fagin Manager, Foundations of Computer Science, IBM Almaden Research Center, San Jose, CA

Finite Model Theory (Springer Monographs in Mathematics)

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A nice MATH book on this topic

Finite Model Theory (Springer Monographs in Mathematics)
Heinz-Dieter Ebbinghaus , and Jörg Flum
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 3540287876

Book Description

The book presents the main results of descriptive complexity theory, that is, the connections between axiomatizability of classes of finite structures and their complexity with respect to time and space bounds. The logics that are important in this context include fixed-point logics, transitive closure logics, and also certain infinitary languages; their model theory is studied in full detail. Other topics include DATALOG languages, quantifiers and oracles, 0-1 laws, and optimization and approximation problems. The book is written in such a way that the respective parts on model theory and descriptive complexity theory may be read independently. This second edition is a thoroughly revised and enlarged version of the original text.

Customer Reviews:

A nice MATH book on this topic.......2000-09-06

This book presents many nice topics in finite model theory. The material on infinitary logic and the finite model properties are nicely presented here and not really available elsewhere. The material on Finite Automata and Logic, and on Descriptive Complexity , is available and better done in other books. This entire field is a cross of computer science and math, and this book is strong on the math end, but not on the computer science angle.

Finite Element Method Electromagnetics: Antennas, Microwave Circuits, and Scattering Applications (IEEE Press Series on Electromagnetic Wave Theory)

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Finite Element Method Electromagnetics: Antennas, Microwave Circuits, and Scattering Applications (IEEE Press Series on Electromagnetic Wave Theory)
John L. Volakis , Arindam Chatterjee , and Leo C. Kempel
Manufacturer: Wiley-IEEE Press
ProductGroup: Book
Binding: Paperback

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Similar Items:

The Finite Element Method in Electromagnetics
Computational Electrodynamics: The Finite-Difference Time-Domain Method, Third Edition
Antenna Theory: Analysis and Design, 3rd Edition

ASIN: 0780334256

Book Description

Employed in a large number of commercial electromagnetic simulation packages, the finite element method is one of the most popular and well-established numerical techniques in engineering. This book covers the theory, development, implementation, and application of the finite element method and its hybrid versions to electromagnetics. FINITE ELEMENT METHOD FOR ELECTROMAGNETICS begins with a step-by-step textbook presentation of the finite method and its variations then goes on to provide up-to-date coverage of three dimensional formulations and modern applications to open and closed domain problems. Worked out examples are included to aid the reader with the fine features of the method and the implementation of its hybridization with other techniques for a robust simulation of large scale radiation and scattering. The crucial treatment of local boundary conditions is carefully worked out in several stages in the book.

Book Description

This book gives a comprehensive overview of central themes of finite model theory – expressive power, descriptive complexity, and zero-one laws – together with selected applications relating to database theory and artificial intelligence, especially constraint databases and constraint satisfaction problems. The final chapter provides a concise modern introduction to modal logic, emphasizing the continuity in spirit and technique with finite model theory. This underlying spirit involves the use of various fragments of and hierarchies within first-order, second-order, fixed-point, and infinitary logics to gain insight into phenomena in complexity theory and combinatorics.

The book emphasizes the use of combinatorial games, such as extensions and refinements of the Ehrenfeucht-Fraissé pebble game, as a powerful way to analyze the expressive power of such logics, and illustrates how deep notions from model theory and combinatorics, such as o-minimality and treewidth, arise naturally in the application of finite model theory to database theory and AI.

Students of logic and computer science will find here the tools necessary to embark on research into finite model theory, and all readers will experience the excitement of a vibrant area of the application of logic to computer science.

Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics

Average customer rating:

A decent introduction to theory and methods for FEM
A Good Book To Learn Finite Elements From

Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics
Dietrich Braess
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Paperback

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The Mathematical Theory of Finite Element Methods
Multigrid
The Finite Element Method for Elliptic Problems (Classics in Applied Mathematics)
Domain Decomposition Methods
Finite Elements of Nonlinear Continua

ASIN: 0521011957

Book Description

In this thoroughly revised version of the successful first edition, the author has added new material that will prove useful for research or application of the finite element method. The most important application of finite elements is the numerical solution of elliptic partial differential equations. The author provides thorough coverage of this subject and includes aspects such as saddle point problems that require a more in-depth mathematical treatment.

Customer Reviews:

A decent introduction to theory and methods for FEM.......2006-12-20

I would say I mostly agree with the previous reviewer. The description is pretty clear, despite being a translation, and it has actually proven useful to me during my time in grad school. One minor complaint I have is that some of the proofs he gives are not as clear as I would like them to be. Specifically, I am talking about the sections dealing with the INF-SUP condition. It seems that everyone who writes an FEM book either skirts this whole issue of the INF-SUP condition (which is what a lot of engineering texts do), or they just copy the 'standard' proofs, which suck. But other than that, this is a useful book to have.

A Good Book To Learn Finite Elements From.......2005-06-11

I recently read this book as part of an advanced numerical analysis class in grad school. I found it to be well written and easy to read. It was useful to me in learning about finite elements from both an abstract and practical perspective. I would recommend it to anyone familiar with the concept of a weak solution to an elliptic partial differential equation and with some experience with numerical linear algebra.
This book could have been improved by including some code or pseudo-code to help get novices started. This is not too severe of a drawback since the text is so well written that the reader should be able to implement many of the ideas without any other training in this area.

Model theory for infinitary logic;: Logic with countable conjunctions and finite quantifiers (Studies in logic and the foundations of mathematics)

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Model theory for infinitary logic;: Logic with countable conjunctions and finite quantifiers (Studies in logic and the foundations of mathematics)
H. Jerome Keisler
Manufacturer: North-Holland Pub. Co
ProductGroup: Book
Binding: Hardcover

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Formal Models of Communicating Systems: Languages, Automata, and Monadic Second-Order Logic (Texts in Theoretical Computer Science. An Eatcs Series)

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Formal Models of Communicating Systems: Languages, Automata, and Monadic Second-Order Logic (Texts in Theoretical Computer Science. An Eatcs Series)
Benedikt Bollig
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 3540329226

Book Description

This book studies the relationship between automata and monadic second-order logic, focusing on classes of automata that describe the concurrent behavior of distributed systems. It provides a unifying theory of communicating automata and their logical properties. Based on Hanf's Theorem and Thomas's graph acceptors, it develops a result that allows us to characterize many popular models of distributed computation in terms of the existential fragment of monadic second-order logic. In particular, the book covers finite automata, asynchronous (cellular) automata, communicating finite-state machines, and lossy channel systems. Model behavior is described using graphs and partial orders, leading to the notions of Mazurkiewicz traces, message sequence charts, and live sequence charts. This book is suitable for senior undergraduate and graduate courses on advanced automata theory, concurrency and communication issues. It can also be used as a reference by researchers concerned with the formal modeling of concurrent systems. Some knowledge of automata theory is a prerequisite. Numerous exercises, chapter summaries, and suggested reading allow for self-study, while the book is supported with a website containing course material and solutions.

Numerical Modelling and Design of Electrical Machines and Devices (Advances in Electrical and Electronic Engineering, V. 1)

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Numerical Modelling and Design of Electrical Machines and Devices (Advances in Electrical and Electronic Engineering, V. 1)
Kay Hameyer , and Ronnie Belmanns
Manufacturer: Computational Mechanics, Inc.
ProductGroup: Book
Binding: Hardcover

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ASIN: 1853126268

Book Description

Designed for undergraduates, graduates and practicing engineers, this text provides an up-to-date overview of numerical field computational methods and, in particular, of the finite element method (FEM) in magnetics. Particular attention is paid to the practical use of the FEM in designing electromagnetic devices such as motors, transformers and actuators.

The book is based on the authors' extensive experience teaching numerical techniques to students and design engineers from industry and is ideal for use by anyone who wishes to learn fundamentals and immediately apply these to actual design problems.

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