Geometry and invariance in kernel based methods
Advances in kernel methods
Support vector domain description
Pattern Recognition Letters - Special issue on pattern recognition in practice VI
Kernel PCA and de-noising in feature spaces
Proceedings of the 1998 conference on Advances in neural information processing systems II
An introduction to support Vector Machines: and other kernel-based learning methods
An introduction to support Vector Machines: and other kernel-based learning methods
Constructing Boosting Algorithms from SVMs: An Application to One-Class Classification
IEEE Transactions on Pattern Analysis and Machine Intelligence
The Journal of Machine Learning Research
A needle in a haystack: local one-class optimization
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Estimating the Support of a High-Dimensional Distribution
Neural Computation
De-noising by soft-thresholding
IEEE Transactions on Information Theory
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
Kernel Entropy Component Analysis Pre-images for Pattern Denoising
SCIA '09 Proceedings of the 16th Scandinavian Conference on Image Analysis
Reducing the run-time complexity of support vector data descriptions
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
Penalized preimage learning in kernel principal component analysis
IEEE Transactions on Neural Networks
Fast support vector data descriptions for novelty detection
IEEE Transactions on Neural Networks
Dynamic pattern denoising method using multi-basin system with kernels
Pattern Recognition
Finding pre-images via evolution strategies
Applied Soft Computing
Toward supervised anomaly detection
Journal of Artificial Intelligence Research
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The support vector data description (SVDD) is one of the best-known one-class support vector learning methods, in which one tries the strategy of using balls defined on the feature space in order to distinguish a set of normal data from all other possible abnormal objects. The major concern of this letter is to extend the main idea of SVDD to pattern denoising. Combining the geodesic projection to the spherical decision boundary resulting from the SVDD, together with solving the preimage problem, we propose a new method for pattern denoising. We first solve SVDD for the training data and then for each noisy test pattern, obtain its denoised feature by moving its feature vector along the geodesic on the manifold to the nearest decision boundary of the SVDD ball. Finally we find the location of the denoised pattern by obtaining the pre-image of the denoised feature. The applicability of the proposed method is illustrated by a number of toy and real-world data sets.