Speaker: Cyril Allauzen
Title: Kernel PCA and De-Noising in Feature Space
Date: 28th February, 2006.

Abstract:
Kernel PCA as a nonlinear feature extractor has proven powerful as a preprocessing step for classification algorithms. But it can also be considered as a natural generalization of linear principal component analysis. This gives rise to the question how to use nonlinear features for data compression, reconstruction, and de-noising, applications common in linear PCA. This is a nontrivial task, as the results provided by kernel PCA live in some high dimensional feature space and need not have pre-images in input space. This work presents ideas for finding approximate pre-images, focusing on Gaussian kernels, and shows experimental results using these pre-images in data reconstruction and de-noising on toy examples as well as on real world data.
Based on the paper by Sebastian Mika, Bernhard Scholkopf, Alex Smola
Klaus-Robert Muller, Matthias Scholz, Gunnar Ratsch
http://sml.nicta.com.au/~smola/papers/MikSchSmoMuletal99.pdf