Neural Based Orthogonal Data Fitting: The EXIN Neural Networks (Hardcover)

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.

《正交回歸中的新理論呈現》是一本關於神經網絡算法的文獻，通常專注於主成分分析（PCA），並將次要成分分析（MCA）視為僅僅是一個結果。然而，《基於神經網絡的正交數據擬合》打破了這一模式，首次從MCA問題入手，並對PCA問題提出了重要結論。

該書提出了幾種神經網絡，並配備了完整的理論，不僅解釋了它們的行為，還將它們與現有的神經和傳統算法進行了比較。作者創造的EXIN神經元被引入、解釋和分析。此外，該書將算法視為微分幾何問題、動態問題、隨機問題和數值問題進行研究。它展示了其主要理論的新穎方面，包括在計算機視覺和線性系統識別中的應用。該書展示了從MCA EXIN到TLS EXIN的推導過程以及原始推導過程，並且還：

• 展示了TLS問題並概述了其歷史和應用




• 介紹了MCA EXIN並將其與其他現有方法進行比較




• 介紹了TLS EXIN神經元以及SCG和BFGS加速技術，並將其與TLS GAO進行比較




• 概述了GeTLS EXIN理論，用於泛化和統一回歸問題




• 建立了GeMCA理論，從識別GeTLS EXIN作為一個泛化特徵值問題開始

在處理EXIN神經元的數學和數值方面，該書主要是理論性的。然而，所有的算法都已被用於分析實時問題並提供準確的解決方案。《基於神經網絡的正交數據擬合》對統計學家、應用數學專家和工程師都是有用的。