High dimensional gaussian classification

High dimensional data analysis is known to be as a challenging problem. In this article, we give a theoretical analysis of high dimensional classification of Gaussian data which relies on a geometrical analysis of the error measure. It links a problem of classification with a problem of nonparametric regression. We give an algorithm designed for high dimensional data which appears straightforward in the light of our theoretical work, together with the thresholding estimation theory. We finally attempt to give a general treatment of the problem that can be extended to frameworks other than gaussian.