A novel local preserving projection scheme for use with face recognition

When locality preserving projection (LPP) is applied to face recognition, it usually suffers from the small sample size (SSS) problem, which means that the eigen-equation of LPP cannot be solved directly. In order to address this issue, we propose a novel LPP scheme. This scheme transforms the objective function of LPP into a new function, which allows the resultant eigen-equation to be directly solved no matter whether the SSS problem occurs or not. Moreover, the fact that the proposed scheme has an adjustable parameter enables us to be able to obtain the best classification accuracy by adjusting the parameter. Our analysis comprehensively reveals the theoretical properties of the proposed scheme and its relationship with other LPP methods. Our analysis also shows that the conventional LPP can be regarded as a special form of the proposed scheme, which also implies that the classification accuracy of the conventional LPP will be lower than the best classification accuracy of the proposed scheme.