Optimal Kernel in a Class of Kernels with an Invariant Metric

Authors:
Akira Tanaka;Hideyuki Imai;Mineichi Kudo;Masaaki Miyakoshi
Affiliations:
Division of Computer Science, Graduate School of Information Science and Technology, Hokkaido University, Sapporo, Japan 060-0814;Division of Computer Science, Graduate School of Information Science and Technology, Hokkaido University, Sapporo, Japan 060-0814;Division of Computer Science, Graduate School of Information Science and Technology, Hokkaido University, Sapporo, Japan 060-0814;Division of Computer Science, Graduate School of Information Science and Technology, Hokkaido University, Sapporo, Japan 060-0814
Venue:
SSPR & SPR '08 Proceedings of the 2008 Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
Year:
2008

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Abstract

Learning based on kernel machines is widely known as a powerful tool for various fields of information science such as pattern recognition and regression estimation. One of central topics of kernel machines is model selection, especially selection of a kernel or its parameters. In this paper, we consider a class of kernels that forms a monotonic classes of reproducing kernel Hilbert spaces with an invariant metric and show that the kernel corresponding to the smallest reproducing kernel Hilbert space including an unknown true function gives the optimal model for the unknown true function.