Kernel PCA pattern reconstruction via approximate pre-images.

Schölkopf, B; Mika, S; Smola, AJ; Rätsch, G; Müller, K-R

doi:10.1007/978-1-4471-1599-1_18

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Kernel PCA pattern reconstruction via approximate pre-images.

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Schölkopf, B., Mika, S., Smola, A., Rätsch, G., & Müller, K.-R. (1998). Kernel PCA pattern reconstruction via approximate pre-images. In L. Niklasson, M. Bodén, & T. Ziemke (Eds.), ICANN 98: 8th International Conference on Artificial Neural Networks, Skövde, Sweden, 2–4 September 1998 (pp. 147-152). London, UK: Springer.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-E954-E

Abstract

Algorithms based on Mercer kernels construct their solutions in terms of expansions in a high-dimensional feature space F. Previous work has shown that all algorithms which can be formulated in terms of dot products in F can be performed using a kernel without explicitly working in F. The list of such algorithms includes support vector machines and nonlinear kernel principal component extraction. So far, however, it did not include the reconstruction of patterns from their largest nonlinear principal components, a technique which is common practice in linear principal component analysis.

The present work proposes an idea for approximately performing this task. As an illustrative example, an application to the de-noising of data clusters is presented.