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IEICE Transactions on Information and Systems 2006 E89-D(7):2243-2249; doi:10.1093/ietisy/e89-d.7.2243
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Copyright © 2006 The Institute of Electronics, Information and Communication Engineers

Regular Section -- Papers -- Pattern Recognition

Constructing Kernel Functions for Binary Regression

Masashi SUGIYAMA1 and Hidemitsu OGAWA2

1 The author is with the Department of Computer Science, Tokyo Institute of Technology, Tokyo, 152–8552 Japan. E-mail: sugi{at}cs.titech.ac.jp, 2 The author is with Toray Engineering Co., Ltd., Otsu-shi, 520–2141 Japan. E-mail: hidemitsu-ogawa{at}kuramae.ne.jp

Kernel-based learning algorithms have been successfully applied in various problem domains, given appropriate kernel functions. In this paper, we discuss the problem of designing kernel functions for binary regression and show that using a bell-shaped cosine function as a kernel function is optimal in some sense. The rationale of this result is based on the Karhunen-Loève expansion, i.e., the optimal approximation to a set of functions is given by the principal component of the correlation operator of the functions.

Key Words: supervised learning, regression, kernel methods, kernel functions, Karhunen-Loève expansion, principal component analysis, binary regression, Gaussian kernel

Manuscript received August 4, 2005. Manuscript revised January 10, 2006.


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