关键词: 边界近邻，零空间，目标函数，小样本问题，特征值分解

Abstract: A marginal neighborhood nullspace discriminant analysis was proposed. The proposed method firstly defines the objective function,and then gives the theory analysis and proof of the objective function. Therefore,this paper pointed out that the algorithm must firstly projects high-dimensional samples into low-dimensional subspace by using PCA algorithm as the first step. In the low-dimensional subspace, the objective function does not lose any effective discriminant information. hhis algorithm can effectively not only resolve the small sample size problem but also work out the orthogonality projection matrix only by the three eigenvalue decomposition. Finally, the nonlinear marginal neighborhood nullspace discriminant analysis based on kernel mapping was given. Experimental results on face database demonstrate the effectiveness of the proposed method.

Key words: Marginal neighborhood, Nullspace, Obj ective function, Small sample size problem, Eigenvalue decomposition