Simple and Robust Locality Preserving Projections Based on Maximum Difference Criterion

Ruisheng Ran, Hao Qin, Shougui Zhang, Bin Fang

Abstract: The locality preserving projections (LPP) method is a hot dimensionality reduction method in the machine learning field. But the LPP method has the so-called small-sample-size problem, and its performance is unstable when the neighborhood size parameter k varies. In this paper, by theoretical analysis and derivation, a maximum difference criterion for the LPP method is constructed, and then a simple and robust LPP method has been proposed, called Locality Preserving Projections based on the approximate maximum difference criterion (LPPMDC). Compared with the existing approaches to solve the small-sample-size problem of LPP, the proposed LPPMDC method has three superiorities: (1) it has no the small-sample-size problem and can get the better performance, (2) it is robust to neighborhood size parameter k, (3) it has low computation complexity. The experiments are performed on the three face databases: ORL, Georgia Tech, and FERET, and the results demonstrate that LPPMDC is an efficient and robust method.