Bayesian kernel projections for classifcation of high dimensional data

A Bayesian multi-category kernel classi cation method is proposed. The algorithm performs the classi cation of the projections of the data to the principal axes of the feature space. The advantage of this approach is that the regression coe cients are identi - able and sparse, leading to large computational savings and improved classi cation performance. The degree of sparsity is regulated in a novel framework based on Bayesian decision theory. The Gibbs sampler is implemented to nd 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.