Nonlinear Algebra in an ACORNWith Applications to Deep Learning【電子書籍】[ Martin J Lee ]
＜p＞A simple algorithm for solving a set of nonlinear equations by matrix algebra has been discovered recently ー first by transforming them into an equivalent matrix equation and then finding the solution analytically in terms of the inverse matrix of this equation. With this newly developed ACORN (Adaptive Constrained Optimal Robust Nonlinear) algorithm, it is possible to minimize the objective function [constructed from the functions in the nonlinear set of equations] without computing its derivatives.＜/p＞ ＜p＞This book will present the details of ACORN algorithm and how it is used to solve large scale nonlinear equations with an innovative approach ACORN Magic [minimization algorithms gathered in a cloud].＜/p＞ ＜p＞The ultimate motivation of this work is its application to optimization. In recent years, with the advances in big-data, optimization becomes an even more powerful tool in knowledge discovery. ACORN Magic is the perfect choice in this kind of application because of that fact that it is fast, robust and simple enough to be embedded in any type of machine learning program.＜/p＞ ＜p＞＜strong＞Sample Chapter(s)＜/strong＞＜br /＞ ＜a href="www.worldscientific.com/doi/suppl/10.1142/11022/suppl_file/11022_foreword.pdf"＞Foreword＜/a＞＜br /＞ ＜a href="www.worldscientific.com/doi/pdf/10.1142/9789813271524_0001"＞Chapter 1: An Overview of Optimization＜/a＞＜/p＞ ＜p＞＜strong＞Contents:＜/strong＞＜/p＞ ＜ul＞ ＜li＞ ＜p＞An Overview of Optimization＜/p＞ ＜/li＞ ＜li＞ ＜p＞The ACORN Approach to Optimization＜/p＞ ＜/li＞ ＜li＞ ＜p＞Application to Pedagogical Examples＜/p＞ ＜/li＞ ＜li＞ ＜p＞A Data-Modeling Example in Accelerator Physics＜/p＞ ＜/li＞ ＜li＞ ＜p＞Applications to Machine Learning and Neural Networks＜/p＞ ＜/li＞ ＜li＞ ＜p＞＜em＞＜strong＞Appendices:＜/strong＞＜/em＞＜/p＞ ＜ul＞ ＜li＞Code for Plotting the Basin of Attraction (BOA) in Octave＜/li＞ ＜li＞ACORN Code Implementation in Octave＜/li＞ ＜li＞Details for Optimizing the Objective Function in NN8＜/li＞ ＜li＞Details for Optimizing the Objective Function in NN481＜/li＞ ＜/ul＞ ＜/li＞ ＜/ul＞ ＜p＞＜strong＞Readership:＜/strong＞ Students and researchers of optimization in solving nonlinear equations in scientific and engineering problems.＜br /＞ 0＜/p＞画面が切り替わりますので、しばらくお待ち下さい。
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