Kernel Fisher Discriminant Analysis Based on a Regularized Method for Multiclassification and Application in Lithological Identification

This study aimed to construct a kernel Fisher discriminant analysis (KFDA) method from well logs for lithology identification purposes. KFDA, via the use of a kernel trick, greatly improves the multiclassification accuracy compared with Fisher discriminant analysis (FDA). The optimal kernel Fisher projection of KFDA can be expressed as a generalized characteristic equation. However, it is difficult to solve the characteristic equation; therefore, a regularized method is used for it. In the absence of a method to determine the value of the regularized parameter, it is often determined based on expert human experience or is specified by tests. In this paper, it is proposed to use an improved KFDA (IKFDA) to obtain the optimal regularized parameter by means of a numerical method. The approach exploits the optimal regularized parameter selection ability of KFDA to obtain improved classification results. The method is simple and not computationally complex. The IKFDA was applied to the Iris data sets for training and testing purposes and subsequently to lithology data sets. The experimental results illustrated that it is possible to successfully separate data that is nonlinearly separable, thereby confirming that the method is effective

Advances in Optimization and Nonlinear Analysis

The present book focuses on that part of calculus of variations, optimization, nonlinear analysis and related applications which combines tools and methods from partial differential equations with geometrical techniques. More precisely, this work is devoted to nonlinear problems coming from different areas, with particular reference to those introducing new techniques capable of solving a wide range of problems. The book is a valuable guide for researchers, engineers and students in the field of mathematics, operations research, optimal control science, artificial intelligence, management science and economics