Abstract: In this paper, we address the pre-image problem in kernel principal component analysis (PCA), which is central in using kernel PCA for denoising. While the traditional method proposed by Mika etal. relies on gradient descent and iteration, our proposed approach directly finds the location of the pre-image based on the distance constraints in the feature space. It involves only standard linear algebra, requires no iteration and does not suffer from numerical instability or local minimum problems. Moreover, preliminary experimental results on image denoising show significant improvements over the traditional method.
6th Annual Workshop On Kernel Machines, NIPS*2002, Whistler, Canada, December 2002.