Investigation And Application Of Kernel Parameter Optimization Algorithm In Kernel PCA

Principle Component Analysis is the multidimensional variable statistical analysis technique which can be used to the data compression and feature extraction. It is supposed that the data submits to Gaussian distribution. By the use of the kernel trick Kernel-based Principle Component Analysis (Kernel PCA) is a newly feature extraction method. It can extract the nonlinear feature of the input data effectively. However, the Kernel PCA performance is dependent on the kernel parameter. Moreover, we cannot analyze the data feature directly because the data in the feature space is invisible.Aiming at optimizing the kernel parameter, first, the thesis presents the background of the Kernel PCA and feature extraction. Then, we address the method that the data can be analyzed in the feature subspace. Lastly, based on the InforMax principle, we propose two algorithms of kernel parameter optimizations using the gauss comparability rule and independent component analysis, and validate the algorithm by the feature extraction and denoising of the handwriting number and face. The main works in this thesis can be introduced as follows:1. By analyzing the how the kernel parameter affect the performance of the feature extraction, we propose the algorithm of the kernel parameter optimization using the gauss comparability rule. First, we analyze the data in the subspace. Then, to estimate comparability of the data distribution and gauss distribution, we address the gauss comparability rule based on the InforMax principle. Moreover, we present the gauss comparability rule of multidimensional variables. Finally, we can obtain the kernel parameter optimization algorithm based on the gauss comparability rule.2. We propose a method the search of the gauss comparability of the mapping data using independent component analysis because the statistic correlation is similar to the gauss firstly. Then, we obtain independent component analysis algorithms based on the multilayer neural networks. Moreover, we seek the gauss comparability of the mapping data using independent component analysis, and therefore gauss comparability value can be obtained. At last, we present the algorithm steps.3. By the feature extraction of the simulated data, denoising of handwriting number and face, we analyze the performance the kernel parameter optimization algorithm. The simulations validate the algorithm based on the gauss comparability rule and independent component analysis. Moreover, the simulated results show that the algorithms can evidently improve the performance of the feature extraction and denoising.