Cirrincione, Giansalvo
NeuralBased Orthogonal Data Fitting: The EXIN Neural Networks
The literature about neuralbased algorithms is often dedicated to principal component analysis (PCA) and considers minor component analysis (MCA) a mere consequence. Breaking the mold, NeuralBased 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 realtime problems and show accurate solutions. NeuralBased Orthogonal Data Fitting is useful for statisticians, applied mathematics experts, and engineers.
Keywords: component; literature; orthogonal; often; algorithms; principal; neuralbased; novel theory; dedicated; presentation; regression; mca; important; first; conclusions; book; data; problem; neural; several; networks; theory; behavior, Data Mining Statistics, Applied Mathematics in Science, Data Mining Statistics, Applied Mathematics in Science
 Author(s)
 Cirrincione, Giansalvo
 Cirrincione, Maurizio
 Publisher
 John Wiley and Sons, Inc.
 Publication year
 2010
 Language
 en
 Edition
 1
 Series
 Adaptive and Cognitive Dynamic Systems: Signal Processing, Learning, Communications and Control
 Page amount
 276 pages
 Category
 Natural Sciences
 Format
 Ebook
 eISBN (ePUB)
 9781118097748
 Printed ISBN
 9780471322702