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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 384183, 8 pages
Research Article

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

1College of Management Science, Chengdu University of Technology, Chengdu 610059, China
2College of Geophysics, Chengdu University of Technology, Chengdu 610059, China

Received 19 July 2014; Revised 8 October 2014; Accepted 10 October 2014

Academic Editor: Jun Cheng

Copyright © 2015 Dejiang Luo and Aijiang Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.