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In this paper we propose a new kernel PCA (KPCA) speed-up algorithm that aims to find a reduced KPCA to approximate the kernel mapping. The algorithm works by greedily choosing a subset of the training samples that minimizes the mean square error of the kernel mapping between the original KPCA and the reduced KPCA. Experimental results have shown that the proposed algorithm is more efficient in computation and effective with lower mapping errors than previous algorithms.