Dimensionality reduction is an important issue for numerous applications including biomedical images analysis and living system analysis. Neighbor embedding, those representing the global and local structure as well as dealing with multiple manifolds, such as the elastic embedding techniques, can go beyond traditional dimensionality reduction methods and find better optima. Nevertheless, existing neighbor embedding algorithms can not be directly applied in classification as suffering from several problems: (1) high computational complexity, (2) nonparametric mappings, and (3) lack of class labels information. We propose a supervised neighbor embedding called discriminative elastic embedding (DEE) which integrates linear projection matrix and class labels into the final objective function. In addition, we present the Laplacian search direction for fast convergence. DEE is evaluated in three aspects: embedding visualization, training efficiency, and classification performance. Experimental results on several benchmark databases present that the proposed DEE exhibits a supervised dimensionality reduction approach which not only has strong pattern revealing capability, but also brings computational advantages over standard gradient based methods.