Optimizing kernel function with applications to kernel principal analysis and locality preserving projection for feature extraction

Kernel learning is a popular research topic in pattern recognition and machine learning. Kernel selection is a crucial problem endured by kernel learning method in the practical applications. Many methods of finding the optimal parameters have been presented, but this kind of methods have no ability of changing the kernel structure, accordingly without changing the data distribution in kernel mapping space. In this paper, we present a uniform framework of kernel optimization based on data-dependent kernel from theory to applications to kernel principal analysis and locality preserving projection for feature extraction. Some experiments are implemented to evaluate the performance and feasibility of this framework.