We propose a new method for discriminant analysis, called High Dimensional Discriminant Analysis (HDDA). Our approach is based on the assumption that high dimensional data live in different subspaces with low dimensionality. We therefore propose a new parameterization of the Gaussian model to classify high-dimensional data. This parameterization takes into account the specific subspace and the intrinsic dimension of each class to limit the number of parameters to estimate. HDDA is applied to recognize object parts in real images and its performance is compared to classical methods.