We propose a new method of discriminant analysis, called High Di- mensional Discriminant Analysis (HHDA). Our approach is based on the assump- tion that high dimensional data live in different 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 object in real images and its performances are compared to classical classification methods.