Neural-Based Orthogonal Data Fitting: The EXIN Neural Networks (Adaptive and Cognitive Dynamic Systems: Signal Processing, Learning, Communications and Control) - Hardcover

Cirrincione, Giansalvo; Cirrincione, Maurizio

Hardcover

ISBN 10: 0471322709 ISBN 13: 9780471322702

Publisher: Wiley, 2010

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 this title

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

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.

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.

Edition details

• Publisher: Wiley
• Publication date: 2010
• Language: English
• ISBN 10: 0471322709
• ISBN 13: 9780471322702
• Binding: Hardcover
• Edition number: 1
• Number of pages: 288