在2维线性鉴别分析(2DLDA)的基础上，介绍了2维异方差鉴别分析(2DHDA)，并将其应用于人脸识别。2DHDA算法去除了2DLDA算法样本类内协方差相等的约束，克服了异方差鉴别分析(HDA)算法的“小样本”问题。首先，根据2DLDA准则定义2DHDA准则；然后，将2DHDA准则取对数，用梯度下降法求得最优投影矩阵，人脸图像向最优投影矩阵投影提取人脸图像的特征；最后，最小距离分类器完成人脸识别。基于ORL与Yale混合人脸数据库的实验结果表明了2DHDA应用于人脸识别的有效性。

On the basis of two-dimensional linear discriminant analysis(2DLDA), a novel discriminant analysis named two-dimensional heteroscedastic discriminant analysis(2DHDA)is introduced, and is used for face recognition. In 2DHDA, equal within-class covariance constraint is removed and “small sample size” problem of heteroscedastic discriminant analysis(HDA)is solved. Firstly, criterion of 2DHDA is defined according to that of 2DLDA. Secondly, criterion of 2DHDA, log term is taken, and then the optimal projection matrix is solved by gradient descent algorithm. Thirdly, facial images are projected onto the optimal projection matrix, then, 2DHDA features of face images are extracted. Finally, nearest neighbor classifier is selected to perform face recognition. Experimental results based on olivetti research laboratory(ORL)and Yale mixture face database show the validity of 2DHDA for face recognition.