Subset kernel principal component analysis

Kernel principal component analysis (kernel PCA or KPCA) has been used widely for non-linear feature extraction, dimensionally reduction, and classification problems. However, KPCA is known to have high computational complexity, that is the eigenvalue decomposition of which size equals to the number of samples n. Moreover, in order to calculate projection of vector onto the subspace obtained by KPCA, we have to store all n samples and evaluate the kernel function n times. In order to overcome these problems, we propose subset KPCA that minimizes a residual error for all samples using limited number of them, and we provide its solution. Experimental results using synthetic and real data show that the proposed method gives almost the same result as KPCA even if the size of the problem is one-tenth of KPCA.