A new solution scheme of unsupervised locality preserving projection method for the SSS problem

When locality preserving projection (LPP) method was originally proposed, it takes as the LPP solution the minimum eigenvalue solution of an eigenequation. After that, LPP has been used for image recognition problems such as face recognition. However, almost no researcher realizes that LPP usually encounters several difficulties when applied to the image recognition problem. For example, since image recognition problems are usually small sample size (SSS) problems, the corresponding eigenequation cannot be directly solved. In addition, it seems that even if one can obtain the solution of the eigenequation by using the numerical analysis approach, the obtained conventional LPP solution might produce the 'presentation confusion' problem for samples from different classes, which is disadvantageous for the classification to procedure a high accuracy. In this paper we first thoroughly investigate the characteristics and drawbacks of the conventional LPP solution in the small sample size (SSS) problem in which the sample number is smaller than the data dimension. In order to overcome these drawbacks, we propose a new LPP solution for the SSS problem, which has clear physical meaning and can be directly and easily worked out because it is generated from a non-singular eigenequation. Experimental results the proposed solution scheme can produce a much lower classification error rate than the conventional LPP solution.