Kernel Optimization Algorithm For Kernel PCA Based On Non-Gaussianity Estimation

Kernel-based Principle Component Analysis (Kernel PCA) is a newly proposed feature extraction method which generalizes principle component analysis (PCA) to the nonlinear case by use of kernel trick. Kernel PCA can effectively extract nonlinear features of data set. Moreover, compared to PCA, it has no constraint on data distribution in original space and no increase in computational complexity. So Kernel PCA has been widely used in data compression, de-noising and reconstruction.The main problem of Kernel PCA is that its performance is strongly influenced by the parameters in the kernel function used for kernel PCA, and the mapped data, which could not be obtained explicitly, makes the parameter optimization work more difficult. In this paper, we propose a novel parameter optimizing algorithm based on the nongaussian distribution estimation in feature space. Based on the idea that the optimal parameter should lead the mapped data in feature space be as Gaussian as possible, our method analyses the nongaussian structure of the mapped data, and then inversely estimates the degree of its distribution close to the Gaussian one in feature space. The experiments, both on simulated data and real world data, demonstrate excellent results which show effectiveness of the method proposed in this paper.