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Other titles in the Adaptive and Learning Systems for Signal Processing, Communications and Control series:

Adaptive and Learning Systems for Signal Processing, Communications and Control #38: Neural Based Orthogonal Data Fitting: The Exin Neural Networks

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Synopses & Reviews

Publisher Comments:

The presentation of a novel theory in orthogonal regression

The literature about neural-based algorithms is often dedicated to principal component analysis (PCA) and considers minor component analysis (MCA) a mere consequence. Breaking the mold, Neural-Based Orthogonal Data Fitting is the first book to start with the MCA problem and arrive at important conclusions about the PCA problem.

The book proposes several neural networks, all endowed with a complete theory that not only explains their behavior, but also compares them with the existing neural and traditional algorithms. EXIN neurons, which are of the authors' invention, are introduced, explained, and analyzed. Further, it studies the algorithms as a differential geometry problem, a dynamic problem, a stochastic problem, and a numerical problem. It demonstrates the novel aspects of its main theory, including its applications in computer vision and linear system identification. The book shows both the derivation of the TLS EXIN from the MCA EXIN and the original derivation, as well as:

  • Shows TLS problems and gives a sketch of their history and applications

  • Presents MCA EXIN and compares it with the other existing approaches

  • Introduces the TLS EXIN neuron and the SCG and BFGS acceleration techniques and compares them with TLS GAO

  • Outlines the GeTLS EXIN theory for generalizing and unifying the regression problems

  • Establishes the GeMCA theory, starting with the identification of GeTLS EXIN as a generalization eigenvalue problem

In dealing with mathematical and numerical aspects of EXIN neurons, the book is mainly theoretical. All the algorithms, however, have been used in analyzing real-time problems and show accurate solutions. Neural-Based Orthogonal Data Fitting is useful for statisticians, applied mathematics experts, and engineers.

Book News Annotation:

As an alternative to the nearly ubiquitous ordinary least squares techniques for modeling systems using linear regression models, the Cirrinciones Giansalve (U. de Picardie--Jules Verne, Amien) and Maurizio (control and signal processing, U. de Technologie de Belfort--Montbéliard, Belfort) explain some iterative total least squares methods that are defined in the literature as neural. Focusing on EXIN neurons, which they created themselves in recent years, they introduce, explain, and analyze them and compare them to the other neural approaches. Their treatment is mainly theoretical, dealing with mathematical and numerical aspects, and even the simulations are selected for illustrating the theory rather than for any practical purpose. Their many applications will appear in the next book. Annotation ©2011 Book News, Inc., Portland, OR (booknews.com)

Synopsis:

Written by two leaders in the field of neural based algorithms, Neural Based Orthogonal Data Fitting proposes several neural networks, all endowed with a complete theory which not only explains their behavior, but also compares them with the existing neural and traditional algorithms. The algorithms are studied from different points of view, including: as a differential geometry problem, as a dynamic problem, as a stochastic problem, and as a numerical problem. All algorithms have also been analyzed on real time problems (large dimensional data matrices) and have shown accurate solutions. Where most books on the subject are dedicated to PCA (principal component analysis) and consider MCA (minor component analysis) as simply a consequence, this is the fist book to start from the MCA problem and arrive at important conclusions about the PCA problem.

Synopsis:

The presentation of a novel theory in orthogonal regression

The literature about neural-based algorithms is often dedicated to principal component analysis (PCA) and considers minor component analysis (MCA) a mere consequence. Breaking the mold, Neural-Based Orthogonal Data Fitting is the first book to start with the MCA problem and arrive at important conclusions about the PCA problem.

The book proposes several neural networks, all endowed with a complete theory that not only explains their behavior, but also compares them with the existing neural and traditional algorithms. EXIN neurons, which are of the authors' invention, are introduced, explained, and analyzed. Further, it studies the algorithms as a differential geometry problem, a dynamic problem, a stochastic problem, and a numerical problem. It demonstrates the novel aspects of its main theory, including its applications in computer vision and linear system identification. The book shows both the derivation of the TLS EXIN from the MCA EXIN and the original derivation, as well as:

  • Shows TLS problems and gives a sketch of their history and applications

  • Presents MCA EXIN and compares it with the other existing approaches

  • Introduces the TLS EXIN neuron and the SCG and BFGS acceleration techniques and compares them with TLS GAO

  • Outlines the GeTLS EXIN theory for generalizing and unifying the regression problems

  • Establishes the GeMCA theory, starting with the identification of GeTLS EXIN as a generalization eigenvalue problem

In dealing with mathematical and numerical aspects of EXIN neurons, the book is mainly theoretical. All the algorithms, however, have been used in analyzing real-time problems and show accurate solutions. Neural-Based Orthogonal Data Fitting is useful for statisticians, applied mathematics experts, and engineers.

About the Author

GIANSALVO CIRRINCIONE, PHD, is an assistant professor at the University of Picardie-Jules Verne, Amiens, France. His current research interests are neural networks, data analysis, computer vision, intelligent control, applied mathematics, brain models, and system identification. E-mail address: exin@u-picardie.fr

MAURIZIO CIRRINCIONE, PHD, is a full professor of control and signal processing at the University of Technology of Belfort-Montbéliard, France. His current research interests are neural networks, modeling and control, system identification, data analysis, intelligent control, and electrical machines and drives. E-mail address: maurizio.cirrincione@utbm.fr

Table of Contents

Foreword.

Preface.

1 The Total Least Squares Problems.

1.1 Introduction.

1.2 Some TLS Applications.

1.3 Preliminaries.

1.4 Ordinary Least Squares Problems.

1.5 Basic TLS Problem.

1.6 Multidimensional TLS Problem.

1.7 Nongeneric Unidimensional TLS Problem.

1.8 Mixed OLS–TLS Problem.

1.9 Algebraic Comparisons Between TLS and OLS.

1.10 Statistical Properties and Validity.

1.11 Basic Data Least Squares Problem.

1.12 The Partial TLS Algorithm.

1.13 Iterative Computation Methods.

1.14 Rayleigh Quotient Minimization Non Neural and Neural Methods.

2 The MCA EXIN Neuron.

2.1 The Rayleigh Quotient.

2.2 The Minor Component Analysis.

2.3 The MCA EXIN Linear Neuron.

2.4 The Rayleigh Quotient Gradient Flows.

2.5 The MCA EXIN ODE Stability Analysis.

2.6 Dynamics of the MCA Neurons.

2.7 Fluctuations (Dynamic Stability) and Learning Rate.

2.8 Numerical Considerations.

2.9 TLS Hyperplane Fitting.

2.10 Simulations for the MCA EXIN Neuron.

2.11 Conclusions.

3 Variants of the MCA EXIN Neuron.

3.1 High-Order MCA Neurons.

3.2 The Robust MCA EXIN Nonlinear Neuron (NMCA EXIN).

3.3 Extensions of the Neural MCA.

4 Introduction to the TLS EXIN Neuron.

4.1 From MCA EXIN to TLS EXIN.

4.2 Deterministic Proof and Batch Mode.

4.3 Acceleration Techniques.

4.4 Comparison with TLS GAO.

4.5 A TLS Application: Adaptive IIR Filtering.

4.6 Numerical Considerations.

4.7 The TLS Cost Landscape: Geometric Approach.

4.8 First Considerations on the TLS Stability Analysis.

5 Generalization of Linear Regression Problems.

5.1 Introduction.

5.2 The Generalized Total Least Squares (GeTLS EXIN) Approach.

5.3 The GeTLS Stability Analysis.

5.4 Neural Nongeneric Unidimensional TLS.

5.5 Scheduling.

5.6 The Accelerated MCA EXIN Neuron (MCA EXIN+).

5.7 Further Considerations.

5.8 Simulations for the GeTLS EXIN Neuron.

6 The GeMCA EXIN Theory.

6.1 The GeMCA Approach.

6.2 Analysis of Matrix K.

6.3 Analysis of the Derivative of the Eigensystem of GeTLS EXIN.

6.4 Rank One Analysis Around the TLS Solution.

6.5 The GeMCA Spectra.

6.6 Qualitative Analysis of the Critical Points of the GeMCA EXIN Error Function.

6.7 Conclusion.

References.

Index.

Product Details

ISBN:
9780471322702
Subtitle:
The EXIN Neural Networks
Author:
Cirrincione, Giansalvo
Author:
Cirrincione, Maurizio
Author:
Huffel, Sabine van
Publisher:
Wiley
Subject:
Image processing
Subject:
Neural networks (computer science)
Subject:
Numerical analysis
Subject:
Statistics
Subject:
Signal processing
Subject:
Graphics-Image Processing
Copyright:
Edition Description:
WOL online Book (not BRO)
Series:
Adaptive and Learning Systems for Signal Processing, Communications and Control Series
Series Volume:
38
Publication Date:
20110609
Binding:
Online electronic file accessible through online networks
Language:
English
Pages:
255
Dimensions:
240 x 160 x 20 mm 20.4 oz

Related Subjects

Arts and Entertainment » Architecture » Architects
Computers and Internet » Graphics » Image Processing
Engineering » Communications » Radio
Science and Mathematics » Electricity » General Electronics

Adaptive and Learning Systems for Signal Processing, Communications and Control #38: Neural Based Orthogonal Data Fitting: The Exin Neural Networks New Hardcover
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$111.50 Backorder
Product details 255 pages John Wiley & Sons - English 9780471322702 Reviews:
"Synopsis" by , Written by two leaders in the field of neural based algorithms, Neural Based Orthogonal Data Fitting proposes several neural networks, all endowed with a complete theory which not only explains their behavior, but also compares them with the existing neural and traditional algorithms. The algorithms are studied from different points of view, including: as a differential geometry problem, as a dynamic problem, as a stochastic problem, and as a numerical problem. All algorithms have also been analyzed on real time problems (large dimensional data matrices) and have shown accurate solutions. Where most books on the subject are dedicated to PCA (principal component analysis) and consider MCA (minor component analysis) as simply a consequence, this is the fist book to start from the MCA problem and arrive at important conclusions about the PCA problem.
"Synopsis" by , The presentation of a novel theory in orthogonal regression

The literature about neural-based algorithms is often dedicated to principal component analysis (PCA) and considers minor component analysis (MCA) a mere consequence. Breaking the mold, Neural-Based Orthogonal Data Fitting is the first book to start with the MCA problem and arrive at important conclusions about the PCA problem.

The book proposes several neural networks, all endowed with a complete theory that not only explains their behavior, but also compares them with the existing neural and traditional algorithms. EXIN neurons, which are of the authors' invention, are introduced, explained, and analyzed. Further, it studies the algorithms as a differential geometry problem, a dynamic problem, a stochastic problem, and a numerical problem. It demonstrates the novel aspects of its main theory, including its applications in computer vision and linear system identification. The book shows both the derivation of the TLS EXIN from the MCA EXIN and the original derivation, as well as:

  • Shows TLS problems and gives a sketch of their history and applications

  • Presents MCA EXIN and compares it with the other existing approaches

  • Introduces the TLS EXIN neuron and the SCG and BFGS acceleration techniques and compares them with TLS GAO

  • Outlines the GeTLS EXIN theory for generalizing and unifying the regression problems

  • Establishes the GeMCA theory, starting with the identification of GeTLS EXIN as a generalization eigenvalue problem

In dealing with mathematical and numerical aspects of EXIN neurons, the book is mainly theoretical. All the algorithms, however, have been used in analyzing real-time problems and show accurate solutions. Neural-Based Orthogonal Data Fitting is useful for statisticians, applied mathematics experts, and engineers.

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