Digital image processing (2nd ed.)
Digital image processing (2nd ed.)
A training algorithm for optimal margin classifiers
COLT '92 Proceedings of the fifth annual workshop on Computational learning theory
The nature of statistical learning theory
The nature of statistical learning theory
Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
Kernel PCA and de-noising in feature spaces
Proceedings of the 1998 conference on Advances in neural information processing systems II
Evolution strategies –A comprehensive introduction
Natural Computing: an international journal
Mustererkennung 1998, 20. DAGM-Symposium
Theoretical Computer Science
Support Vector Data Description
Machine Learning
Kernel Methods for Pattern Analysis
Kernel Methods for Pattern Analysis
Iterative Kernel Principal Component Analysis for Image Modeling
IEEE Transactions on Pattern Analysis and Machine Intelligence
Reconsidering the progress rate theory for evolution strategies in finite dimensions
Proceedings of the 8th annual conference on Genetic and evolutionary computation
Pattern Recognition and Machine Learning (Information Science and Statistics)
Pattern Recognition and Machine Learning (Information Science and Statistics)
Weighted multirecombination evolution strategies
Theoretical Computer Science - Foundations of genetic algorithms
Weakly Supervised Learning on Pre-image Problem in Kernel Methods
ICPR '06 Proceedings of the 18th International Conference on Pattern Recognition - Volume 02
Neural Computation
KPCA denoising and the pre-image problem revisited
Digital Signal Processing
Human-competitive lens system design with evolution strategies
Applied Soft Computing
Penalized preimage learning in kernel principal component analysis
IEEE Transactions on Neural Networks
A Closed-form Solution for the Pre-image Problem in Kernel-based Machines
Journal of Signal Processing Systems
Rate controlling in off line 3D video coding using evolution strategy
IEEE Transactions on Consumer Electronics
Input space versus feature space in kernel-based methods
IEEE Transactions on Neural Networks
The pre-image problem in kernel methods
IEEE Transactions on Neural Networks
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Kernel methods map, usually nonlinearly, the data from input space into a higher-dimensional feature space, in which linear algorithms are performed. In many applications, the inverse mapping is also useful, and the pre-images of some feature vectors need to be found in input space. However, finding pre-images is often a difficult optimization problem. This paper attempts to use evolution strategies (ES) to seek pre-images. This method firstly selects some of the nearest training patterns of an unknown pre-image as the initial group of the ES, then the ES carries out an iterative process to find the pre-images or approximate pre-images. Experimental results based on kernel principal component analysis (KPCA) for pattern denoising show that our proposed method outperforms some conventional techniques, including gradient descent technique, kernel ridge regression, and distance constraint method. Compared to these conventional techniques, the ES-based method is also straightforward to understand, and is easy to implement.