James Kwok and Ivor Tsang
In this paper, we address the problem of finding the pre-image of a feature vector in the feature space induced by a kernel. This is of central importance in some kernel applications, such as on using kernel principal component analysis (PCA) for image denoising. Unlike the traditional method in (Mika et al., 1998) which relies on nonlinear optimization, our proposed method directly finds the location of the pre-image based on distance constraints in the feature space. It is non-iterative, involves only linear algebra and does not suffer from numerical instability or local minimum problems. Performance of this method is evaluated on performing kernel PCA and kernel clustering on the USPS data set.