Numerical recipes: the art of scientific computing
Numerical recipes: the art of scientific computing
Elements of statistical computing: numerical computation
Elements of statistical computing: numerical computation
A training algorithm for optimal margin classifiers
COLT '92 Proceedings of the fifth annual workshop on Computational learning theory
Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
Bayesian Classification With Gaussian Processes
IEEE Transactions on Pattern Analysis and Machine Intelligence
Bayesian Learning for Neural Networks
Bayesian Learning for Neural Networks
Pattern Recognition and Neural Networks
Pattern Recognition and Neural Networks
Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
Variational Relevance Vector Machines
UAI '00 Proceedings of the 16th Conference on Uncertainty in Artificial Intelligence
Evaluation of gaussian processes and other methods for non-linear regression
Evaluation of gaussian processes and other methods for non-linear regression
Adaptive Sparseness for Supervised Learning
IEEE Transactions on Pattern Analysis and Machine Intelligence
Sparse bayesian learning and the relevance vector machine
The Journal of Machine Learning Research
Sparse Multinomial Logistic Regression: Fast Algorithms and Generalization Bounds
IEEE Transactions on Pattern Analysis and Machine Intelligence
Input space versus feature space in kernel-based methods
IEEE Transactions on Neural Networks
Moderating the outputs of support vector machine classifiers
IEEE Transactions on Neural Networks
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A Bayesian multi-category kernel classification method is proposed. The algorithm performs the classification of the projections of the data to the principal axes of the feature space. The advantage of this approach is that the regression coefficients are identifiable and sparse, leading to large computational savings and improved classification performance. The degree of sparsity is regulated in a novel framework based on Bayesian decision theory. The Gibbs sampler is implemented to find the posterior distributions of the parameters, thus probability distributions of prediction can be obtained for new data points, which gives a more complete picture of classification. The algorithm is aimed at high dimensional data sets where the dimension of measurements exceeds the number of observations. The applications considered in this paper are microarray, image processing and near-infrared spectroscopy data.