Abstract: In view of the problems of nonlinear feature extraction and use of a few labeled samples in face recognition, a new algorithm of orthogonal optimal semi-supervised discriminant vectors in a kernel space is proposed. Nonlinear kernel mapping is used to map the face data into an implicit feature space. In this space, the MFA can make use of small amount of labeled samples and the UDP can study a large number of unlabeled samples. The object function is defined using the semi-supervised method. Then optimal projection vector is found using orthogonal approach and face recognition is realized. The effectiveness of the proposed methods is validated through the experimental results on ORL and YALE face databases.

Key words: Marginal Fisher Analysis（MFA）, Unsupervised Discriminant Projection（UDP）, semi-supervised, kernel space, face recognition

摘要： 针对人脸识别中的非线性特征提取和有标记样本不足问题，提出了在核空间具有正交性半监督鉴别矢量的计算方法。算法利用核函数将人脸数据映射到高维非线性空间，在该空间采用边界Fisher判别分析（Marginal Fisher Analysis，MFA）算法将少量有类别标签样本进行降维，同时采用无监督鉴别投影（Unsupervised Discriminant Projection，UDP）对大量无标签样本进行学习，以半监督的方法构造算法的目标函数，在特征值求解时以正交方式找出最优投影向量，进行人脸识别。通过实验，在ORL和YALE人脸数据库上验证了该算法的有效性。

关键词: 边界Fisher判别分析, 无监督鉴别投影, 半监督, 核空间, 人脸识别