关键词: 边界Fisher鉴别分析, 小样本问题, 双子空间, 目标函数

Abstract:

Aiming at the shortcomings that the marginal Fisher discriminant analysis algorithm can not effectively solve the small sample size problem, a complete dual subspace marginal neighborhood discriminant analysis algorithm is proposed. According to the theoretical analysis, the proposed algorithm breaks down the criterion function of the Fisher discriminant analysis into two parts. To solve the criterion function, the algorithm firstly uses PCA to project highdimensional samples into a lowdimensional subspace. In the lowdimensional subspace, the objective function does not lose any effective discriminant information, which is proved by theorem 1 and theorem 2. Secondly, projection matrix from the complementary subspace of withinclass marginal neighborhood is calculated. Finally, the experimental results on face database demonstrate the effectiveness of the proposed algorithm.

Key words: marginal Fisher discriminant analysis;the small sample size problem;dual subspace;the criterion function