Approximations of the standard principal components analysis and kernel PCA

作者：Zhang, Rui; Wang, Wenjian^*; Ma, Yichen

来源：Expert Systems with Applications, 2010, 37(9): 6531-6537.

DOI：10.1016/j.eswa.2010.02.133

• PCA
• KPCA
• Kernel space
• Orthogonal projection

Principal component analysis (PCA) is a powerful technique for extracting structure from possibly high-dimensional data sets, while kernel PCA (KPCA) is the application of PCA in a kernel-defined feature space. For standard PCA and KPCA, if the size of dataset is large, it will need a very large memory to store kernel matrix and a lot of time to calculate eigenvalues and corresponding eigenvectors. The aim of this paper is to learn linear and nonlinear principal components by using a few partial data points and determine which data points can be used. To verify the performance of the proposed approaches, a series of experiments on artificial datasets and UCI benchmark datasets are accomplished. Simulation results demonstrate that the proposed approaches can compete with or outperform the standard PCA and KPCA in generalization ability but with much less memory and time consuming.

• 出版日期2010-9
• 单位山西大学; 山东理工大学; 西安交通大学