Kernel principal component analysis (KPCA) is a kernelized version of principal component analysis (PCA). A kernel principal component is a superposi-tion of kernel functions. Since the number of kernel functions equals the number of samples, each compo-nent is not a sparse representation. Our purpose is
to sparsify coefficients expressing in linear combina-tion of kernel functions. Two types of sparse kernel principal component are proposed in this paper. The
method for solving the sparse problem is comprised of two steps: (a) we start with the Pythagorean the- orem and derive an explicit regression expression of
KPCA, and (b) two types of regularization, l1-norm or l2;1-norm, are added into the regression expression in order to obtain two different sparsity forms,
respectively.Etc...
Keywords
Principal Component Analysis, Sparse Principal Component Analysis, Kernel Principal Component Analysis, Alternating Direction Method of Multipliers
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