Manifold based kernel optimization for KPCA

This paper presents a manifold based kernel optimizing algorithm for KPCA which has recently shown effectiveness for pattern recognition and systematic classification based on extracting nonlinear features. However, their performances largely depend on the kernel function. Current methods simply choose the kernel function empirically or experimentally from a given set of candidates. We use manifold learning to improve the kernel function, which is capable to discover the nonlinear degrees of freedom that underlie complex natural observations. In contrast to previous algorithms for kernel optimization, ours efficiently computes a globally optimal solution that is guaranteed to converge asymptotically to the true structure and extracts the nonlinear features better. Experiments show that the method performed well in the field of pattern recognition.