Neighborhood preserving embedding is a widely used manifold reduced dimensionality technique. But NPE has to encounter two problems. One problem is that it suffers from the small-sample-size (SSS) problem. Another is that the performance of NPE is seriously sensitive to the neighborhood size k. To overcome the two problems, an exponential neighborhood preserving embedding (ENPE) is proposed in this paper. The main idea of ENPE is that the matrix exponential is introduced to NPE, then the SSS problem is avoided and low sensitivity to the neighborhood size k is gotten. The experiments are conducted on ORL, Georgia Tech and AR face database. The results show that, ENPE shows advantageous performance over other unsupervised methods, such as PCA, LPP, ELPP and NPE. Another is that ENPE is much less sensitive to the neighborhood parameter k contrasted with the unsupervised manifold learning methods LPP, ELPP and NPE.

As an effective method, exponential discriminant analysis (EDA) has been proposed and widely used to solve the so-called small-sample-size (SSS) problem. In this paper, a simple and effective generalization of EDA is presented and named as GEDA. In GEDA, a general exponential function, where the base of exponential function is larger than the Euler number, is used. Due to the property of general exponential function, the distance between samples belonging to different classes is larger than that of EDA, and then the discrimination property is largely emphasized. The experiment results on the Extended Yale and CMU-PIE face databases show that, GEDA gets more advantageous recognition performance compared to EDA.