中文摘要：

零空间线性鉴别分析NLDA充分利用样本总类内离散度矩阵的零空间信息,能有效克服线性鉴别分析LDA的小样本问题.核方法通过非线性映射,将输入空间样本映射到高维特征空间,再在高维特征空间利用线性特征提取算法.因此,核方法属于非线性特征提取算法.文中结合LDA、NLDA和核方法的优点,引入了核零空间线性鉴别分析KNLDA,导出了KNLDA算法.该算法通过引入核函数,得到低维矩阵,有效避免了直接计算复杂的非线性映射函数,解决了高维类内离散度矩阵的维数灾难问题.同时,将KNLDA算法应用于人脸识别.基于ORL人脸数据库以及ORL与Yale混合人脸数据库的实验结果表明了KNLDA算法的有效性.

英文摘要：

Null space linear discriminant analysis（NLDA）takes full advantage of the null space information of the total within-class scatter matrix of samples,in which the small sample size problem（S3problem）of LDA can be overcome.Through kernel method,the samples in the input space are transformed into a high-dimensional feature space by nonlinear mapping.Then,linear feature extraction algorithm is used in the high-dimensional feature space.Therefore,kernel method belongs to nonlinear feature extraction algorithm.In this paper,combined with the merits of LDA,NLDA and kernel method,kernel null space linear discriminant analysis（KNLDA）is investigated,in which kernel function is introduced and a low-dimensional matrix is obtained.The difficulty is avoided effectively that complex nonlinear mapping function is computed directly,and the problem is solved that there exists dimension disaster to high-dimensional within-class scatter matrix.In the meantime,KNLDA algorithm is applied in face recognition.Experimental results on ORL（Olivetti Research Laboratory）face database,ORL and Yale mixture face database show that KNLDA algorithm is valid in face recognition.