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Publication
KPCA denoising and the pre-image problem revisited
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Advisor(s)
Abstract(s)
Kernel principal component analysis (KPCA) is widely used in classification, feature extraction and denoising applications. In
the latter it is unavoidable to deal with the pre-image problem which constitutes the most complex step in the whole processing
chain. One of the methods to tackle this problem is an iterative solution based on a fixed-point algorithm. An alternative strategy
considers an algebraic approach that relies on the solution of an under-determined system of equations. In this work we present
a method that uses this algebraic approach to estimate a good starting point to the fixed-point iteration. We will demonstrate that
this hybrid solution for the pre-image shows better performance than the other two methods. Further we extend the applicability of
KPCA to one-dimensional signals which occur in many signal processing applications. We show that artefact removal from such
data can be treated on the same footing as denoising. We finally apply the algorithm to denoise the famous USPS data set and to
extract EOG interferences from single channel EEG recordings.
Description
Keywords
Kernel principal component analysis (KPCA) Pre-image Time series analysis Denoising
Citation
Publisher
Elsevier