零空间边界Fisher分析法及其在人脸识别中的应用

边界Fisher分析（MFA）是一种有效的特征抽取方法，但在人脸识别的应用中会遭遇小样本问题。基于此，提出一种利用零空间法求解MFA优化准则的算法。该算法通过在MFA的类内散度矩阵的零空间中最大化MFA类问离散度得到最优投影向量，从而避免MFA方法所遇到的小样本问题，同时也保留了包含在类内散度矩阵零空间中的鉴别信息。在标准人脸库上的识别实验结果表明，该算法的识别率高于LDA和MFA，并且较容易选择其最优低维特征空间的维数。

Null Space Marginal Fisher Analysis and Its Application in Face Recognition

Marginal Fisher analysis （MFA） is an efficient linear projection technique for feature extraction. The major drawback of applying MFA to face recognition is that it often encounters the small sample size （SSS） problem. In this paper, a strategy based on null space for solving optimization criteria of MFA is proposed to avoid this issue. It maximizes the class scatter of training samples on null space of within-class scatter matrix （ Sw ） in MFA and reserves the discriminant information contained in null space of S~. The per- formance of this method is tested in both ORL and Yale face databases. Experimental resuhs show that this method is effective and a- chieves higher recognition rate than LDA and MFA. Moreover, it is easy to decide most optimal dimensionality of feature space for this method.