A Novel Discriminant Locality Preserving Projections Method

Locality preserving projections (LPP) is a popular unsupervised dimensionality reduction method based on manifold learning. As a supervised version of the LPP method, discriminant locality preserving projections (DLPP) method has been recently proposed and paid much attention to by researchers. However, the DLPP method has the small-sample-size (SSS) problem. In this paper, in the view of the eigenvalues of scattering matrices of DLPP, they are first mapped to the new values by two polynomial functions, and with the properties of the matrix function of the two polynomial functions, the criterion of the DLPP method is reconstructed; thus, a novel dimensionality reduction method, named polynomial discriminant locality preserving projections (PDLPP) method, is proposed. The proposed PDLPP method has two advantages: one is that it addresses the SSS problem of DLPP, and the other is that, with the nonlinear mapping implied by PDLPP, the distance between inter-class samples is much enlarged and then the better performance of pattern classification is achieved. The experiments are conducted on the COIL-20 database, ORL, Georgia Tech, and AR face datasets, and the results show that the PDLPP is superior to state-of-the-art methods.