中文摘要：

局部敏感辨别分析（LSDA）只能处理向量型数据，当处理图像等数据时容易产生奇异性问题，为此提出了一种二维局部敏感辨别分析（2DLSDA）方法，可以直接处理二维图像矩阵，能够避免奇异性问题．通过使用矩阵表示，2DLSDA可以有效地利用图像像素间中的空间信息．依据近邻的不同，构造2个分别表示类内近邻关系和类间近邻关系的图，计算2个图上的权重矩阵，基于Schur分解求出2个正交变换矩阵．依据图像的2种展开方式，提出了2种单边2DLSDA算法．在ORL和Yale人脸数据集上的实验结果表明，基于Schur分解的2DLSDA与主成分分析（PCA）、线性辨别分析（LDA）、LSDA相比，能够高效地得到正交变换矩阵，并取得更好的分类效果．

英文摘要：

Locality sensitive discriminant analysis （LSDA） can only deal with vector data, and it is often confronted with singularity problem when dealing with image data. To overcome the limit of LSDA, a method called two-dimensional LSDA （2DLSDA） for image recognition was proposed. 2DLSDA is based directly on 2D image matrices and thus can overcome the singularity problem and utilize the spatial information among pixels more effectively. Firstly, two graphs representing inner-class neighbor relationship and inter-class neighbor relationship respectively were constructed; then, weight matrixes were calculated; finally, two orthogonal transform matrixes were computed based on Schur decomposition. Two unilateral 2DLSDA methods were proposed based on the unfolding way of image matrices. Results of experiments on ORL and Yale datasets demonstrated that the proposed method can obtain the orthogonal transformation matrices efficien discriminant ana tly, and can achieve better performance than principal component analysis （PCA）, linear lysis （LDA） and LSDA.