中文摘要：

传统的半监督降维技术中，在原特征空间中定义流形正则化项，但其构造无助于接下来的分类任务．针对此问题，文中提出一种自适应正则化核二维判别分析算法．首先每个图像矩阵经奇异值分解为两个正交矩阵与一个对角矩阵的乘积，通过两个核函数将两个正交矩阵列向量从原始非线性空间映射到一个高维特征空间．然后在低维特征空间中定义自适应正则化项，并将其与二维矩阵非线性方法整合于单个目标函数中，通过交替优化技术，在两个核子空间提取判别特征．最后在两个人脸数据集上的实验表明，文中算法在分类精度上获得较大提升．

英文摘要：

In traditional semi-supervised dimension reduction techniques, the manifold regularization term is defined in the original feature space. However, its construction is useless in the subsequent classification. In this paper, adaptive regularization based kernel two dimensional discriminant analysis （ARKTDDA） is presented. Firstly, each image matrix is transformed as the product of two orthogonal matrices and a diagonal matrix by using the singular value decomposition method. The column vectors of two orthogonal matrices are transformed into high dimensional space by two kernel functions. Then, the adaptive regularization is defined in the low dimensional feature space, and it is integrated with two dimensional matrix nonlinear method into one single objective function. By altering iterative optimization, the discriminative information is extracted in two kernel subspaces. Finally, experimental results on two face datasets demonstrate that the proposed algorithm obtains considerable improvement in classification accuracy.