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.