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JACIII Vol.13 No.4 pp. 416-420
doi: 10.20965/jaciii.2009.p0416
(2009)

Paper:

Kernel Canonical Discriminant Analysis Based on Variable Selection

Seiichi Ikeda and Yoshiharu Sato

Graduate School of Information Science and Technology, Hokkaido University
Kita 9, Nishi 14, Kita-ku, Sapporo 060-0814, Japan

Received:
November 24, 2008
Accepted:
March 10, 2009
Published:
July 20, 2009
Keywords:
AIC, kernel Fisher's discriminant function
Abstract

We have shown that models support vector regression and classification are essentially linear in reproducing kernel Hilbert space (RKHS). To overcome the over fitting problem, a regularization term is added to the optimization process, deciding the coefficient of regularization term involves difficulties. We introduce the variable selection concept to the linear model in RKHS, where the kernel functions is treated as variable transformation when its value is given by observation. We show that kernel canonical discriminant functions for multiclass problems can be discussed under variable selection, which enables us to reduce the number of kernel functions in the discriminant function, i.e., the discriminant function is obtained as linear combinations of sufficiently small numbers of kernel functions, so, we can expect to get reasonable prediction. We discuss variable selection performance in canonical discriminant functions compared to support vector machines.

Cite this article as:
Seiichi Ikeda and Yoshiharu Sato, “Kernel Canonical Discriminant Analysis Based on Variable Selection,” J. Adv. Comput. Intell. Intell. Inform., Vol.13, No.4, pp. 416-420, 2009.
Data files:
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Last updated on Mar. 01, 2021