Introduction to statistical pattern recognition (2nd ed.)
Introduction to statistical pattern recognition (2nd ed.)
The nature of statistical learning theory
The nature of statistical learning theory
Matrix computations (3rd ed.)
Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
Spectral Grouping Using the Nyström Method
IEEE Transactions on Pattern Analysis and Machine Intelligence
Hyperspectral Target Detection Using Kernel Spectral Matched Filter
CVPRW '04 Proceedings of the 2004 Conference on Computer Vision and Pattern Recognition Workshop (CVPRW'04) Volume 8 - Volume 08
Generalized Discriminant Analysis Using a Kernel Approach
Neural Computation
A mutual information extension to the matched filter
Signal Processing - Special issue: Information theoretic signal processing
On the Choice of Smoothing Parameters for Parzen Estimators of Probability Density Functions
IEEE Transactions on Computers
Expert Systems with Applications: An International Journal
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Given the knowledge of class probability densities, a priori probabilities, and relative risk levels, Bayes classifier provides the optimal minimum-risk decision rule. Specifically, focusing on the two-class (detection) scenario, under certain symmetry assumptions, matched filters provide optimal results for the detection problem. Noticing that the Bayes classifier is in fact a nonlinear projection of the feature vector to a single-dimensional statistic, in this paper, we develop a smooth nonlinear projection filter constrained to the estimated span of class conditional distributions as does the Bayes classifier. The nonlinear projection filter is designed in a reproducing kernel Hilbert space leading to an analytical solution both for the filter and the optimal threshold. The proposed approach is tested on typical detection problems, such as neural spike detection or automatic target detection in synthetic aperture radar (SAR) imagery. Results are compared with linear and kernel discriminant analysis, as well as classification algorithms such as support vector machine, AdaBoost and LogitBoost.