The main objective of the work presented here is to introduce a supervised, nonlinear dimensionality reduction technique which, performs well-known linear discriminant analysis in a local way and which is able to provide a powerful mapping with less computational effort than other nonlinear reduction methods. Additionally, because of the close connection of the new approach to Fisher’s LDA, it is more clear that it acts discriminatively, which is not immediately apparent from previous formulations. The method makes use of the optimal scoring framework advocated by Hastie et al. and it is coined local discriminant analysis (eDA).