Abstract: Feature selection and subspace learning are two key problems in face recognition. To select the rich nonlinear features more accurately in face image and solve the small sample size problem, this paper proposes a new generalized kernel discriminant analysis based on L_2,1-norm regularization (L21GKDA). The proposed method implicitly maps the original samples into feature space by using kernel function, and obtains the generalized kernel Fisher criterion. Then it presents an efficient transformation, transforming its nonlinear model into linear regression model. In order to perform feature selection and subspace learning simultaneously, an L_2,1-norm penalty term is added to the objective function, and the  solution algorithm of the regularization method is also obtained. Due to the feature selection capability of L_2,1-norm penalty term, the recognition performance is greatly improved. Experiments on ORL, AR, PIE standard face databases illustrate that the new method can effectively select the nonlinear features of the face data, and improve the discriminant ability.

Key words: face recognition, feature selection, subspace learning; L_2,1-norm, kernel discriminant analysis

摘要： 特征选取和子空间学习是人脸识别的关键问题。为更准确选取人脸中丰富的非线性特征，并解决小样本问题，提出了一种新的L_2,1范数正则化的广义核判别分析（generalized kernel discriminant analysis based on L_2,1-norm regularization，L21GKDA）。利用核函数将原始样本隐式地映射到高维特征空间中，得到广义核Fisher鉴别准则，再利用一种有效变换将该非线性模型转化为线性回归模型；为了能使特征选取和子空间学习同时进行，在模型中加入了一种L_2,1范数惩罚项，并给出该正则化方法的求解算法。因为方法借助于L_2,1范数惩罚项的特征选取能力，所以它能有效地提高识别率。在ORL、AR和PIE人脸库上的实验结果表明，新算法能有效选取人脸的非线性特征，提高判别能力。

关键词: 人脸识别, 特征选取, 子空间学习, L_2,1范数, 核判别分析