Input Space Regularization Stabilizes Pre-images for Kernel PCA De-noising

Trine Julie Julie Abrahamsen, Lars Kai Hansen

AbstractSolution of the pre-image problem is key to efficient nonlinear de-noising using kernel Principal Component Analysis. Pre-image estimation is inherently ill-posed for typical kernels used in applications and consequently the most widely used estimation schemes lack stability. For de-noising applications we propose input space distance regularization as a stabilizer for pre-image estimation. We perform extensive experiments on the USPS digit modeling problem to evaluate the stability of three widely used pre-image estimators. We show that the previous methods lack stability when the feature mapping is non-linear, however, by applying a simple input space distance regularizer we can reduce variability with very limited sacrifice in terms of de-noising efficiency.
KeywordsKernel PCA, Pre-image, De-noising
TypeConference paper [With referee]
ConferenceIEEE Workshop on Machine Learning for Signal Processing (MLSP)
BibTeX data [bibtex]
IMM Group(s)Intelligent Signal Processing

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