Cirrincione Neural-Based Orthogonal Data Fitting

The EXIN Neural Networks
1. Auflage 2011
ISBN: 978-0-470-63827-9
Verlag: John Wiley & Sons
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, Band 1, 276 Seiten, E-Book

Reihe: Adaptive and Cognitive Dynamic Systems: Signal Processing, Learning, Communications and Control

The presentation of a novel theory in orthogonal regression
The literature about neural-based algorithms is often dedicatedto principal component analysis (PCA) and considers minor componentanalysis (MCA) a mere consequence. Breaking the mold,Neural-Based Orthogonal Data Fitting is the first book tostart with the MCA problem and arrive at important conclusionsabout the PCA problem.
The book proposes several neural networks, all endowed with acomplete theory that not only explains their behavior, but alsocompares 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 adifferential geometry problem, a dynamic problem, a stochasticproblem, and a numerical problem. It demonstrates the novel aspectsof its main theory, including its applications in computer visionand linear system identification. The book shows both thederivation of the TLS EXIN from the MCA EXIN and the originalderivation, as well as:
* Shows TLS problems and gives a sketch of their history andapplications
* Presents MCA EXIN and compares it with the other existingapproaches
* Introduces the TLS EXIN neuron and the SCG and BFGS accelerationtechniques and compares them with TLS GAO
* Outlines the GeTLS EXIN theory for generalizing and unifying theregression problems
* Establishes the GeMCA theory, starting with the identificationof GeTLS EXIN as a generalization eigenvalue problem
In dealing with mathematical and numerical aspects of EXINneurons, the book is mainly theoretical. All the algorithms,however, have been used in analyzing real-time problems and showaccurate solutions. Neural-Based Orthogonal Data Fitting isuseful for statisticians, applied mathematics experts, andengineers.

Autoren/Hrsg.

Cirrincione, Giansalvo

Cirrincione, Maurizio

Inhaltsverzeichnis

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 NeuralMethods.
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 GeTLSEXIN.
6.4 Rank One Analysis Around the TLS Solution.
6.5 The GeMCA Spectra.
6.6 Qualitative Analysis of the Critical Points of the GeMCAEXIN Error Function.
6.7 Conclusion.
References.
Index.

Über Autor(innen)

GIANSALVO CIRRINCIONE, PHD, is an assistantprofessor at the University of Picardie-Jules Verne, Amiens,France. His current research interests are neural networks, dataanalysis, computer vision, intelligent control, appliedmathematics, brain models, and system identification. E-mailaddress: [e-mail]
MAURIZIO CIRRINCIONE, PHD, is a fullprofessor of control and signal processing at the University ofTechnology of Belfort-Montbéliard, France. His currentresearch interests are neural networks, modeling and control,system identification, data analysis, intelligent control, andelectrical machines and drives. E-mail address:[e-mail]