We propose a new method of discriminant analysis, called High Dimensional Discriminant Analysis (HHDA). Our approach is based on the assumption that high dimensional data live in di erent subspaces with low dimensionality. Thus, HDDA reduces the dimension for each class independently and regularizes class conditional covariance matrices in order to adapt the Gaussian framework to high dimensional data. This regularization is achieved by assuming that classes are spherical in their eigenspace. HDDA is applied to recognize objects in real images and its performances are compared to classical classi cation methods.