The nature of statistical learning theory
The nature of statistical learning theory
An introduction to support Vector Machines: and other kernel-based learning methods
An introduction to support Vector Machines: and other kernel-based learning methods
Kernel Methods for Pattern Analysis
Kernel Methods for Pattern Analysis
Subspace Information Criterion for Model Selection
Neural Computation
Optimal Kernel in a Class of Kernels with an Invariant Metric
SSPR & SPR '08 Proceedings of the 2008 Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
An introduction to kernel-based learning algorithms
IEEE Transactions on Neural Networks
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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. An appropriate model selection is required in order to obtain desirable learning results. In our previous work, we discussed a class of kernels forming a nested class of reproducing kernel Hilbert spaces with an invariant metric and proved that the kernel corresponding to the smallest reproducing kernel Hilbert space, including an unknown true function, gives the best model. In this paper, we relax the invariant metric condition and show that a similar result is obtained when a subspace with an invariant metric exists.