Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
Neural Networks for Pattern Recognition
Neural Networks for Pattern Recognition
Robust De-noising by Kernel PCA
ICANN '02 Proceedings of the International Conference on Artificial Neural Networks
Iterative Kernel Principal Component Analysis for Image Modeling
IEEE Transactions on Pattern Analysis and Machine Intelligence
Denoising using local projective subspace methods
Neurocomputing
Input space versus feature space in kernel-based methods
IEEE Transactions on Neural Networks
An introduction to kernel-based learning algorithms
IEEE Transactions on Neural Networks
The pre-image problem in kernel methods
IEEE Transactions on Neural Networks
Fuzzy peer groups for reducing mixed Gaussian-impulse noise from color images
IEEE Transactions on Image Processing
Constructing sparse KFDA using pre-image reconstruction
ICONIP'10 Proceedings of the 17th international conference on Neural information processing: models and applications - Volume Part II
Finding pre-images via evolution strategies
Applied Soft Computing
Engineering Applications of Artificial Intelligence
Regularized Pre-image Estimation for Kernel PCA De-noising
Journal of Signal Processing Systems
Sparse coding for image denoising using spike and slab prior
Neurocomputing
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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.