中文摘要：

提取有效特征对高维数据的模式分类起着关键作用．零空间线性判别分析（null—space linear discriminant analysis，NLDA）在数据降维和特征提取上表现出较好的性能，但是该方法本质上仍是一种线性方法．为有效提取数据的非线性特征，提出了零空间核判别分析算法（nuli—space kernel discriminant analysis，NKDA）并将其应用于人脸识别．利用核函数将原始样本隐式地映射到高维特征空间后，采用一次瘦QR分解求核类内散布矩阵的零空间鉴别矢量集，最后再进行一次Cholesky分解求得具正交性的核空间鉴别矢量集．与NLDA相比，NKDA具有更好的识别性能且在大样本情况下也能应用．另外，基于NKDA，提出了增量NKDA算法，当增加新的训练样本时能正确地更新NKDA鉴别矢量集．在ORI．库、Yale库和PIE子库上的实验结果表明了算法的有效性和效率，在有效降维的同时能进一步提高鉴别能力．

英文摘要：

For high-dimensional data, extraeuun recognition. Null-space linear discriminant analysis （NLDA） shows desirable performance, but it is still a linear technique in nature. In order to effectively extract nonlinear features of data set, a novel null-space kernel discriminant analysis （NKDA） is proposed for face recognition. Firstly, the kernel function is used to project the original samples into an implicit space called feature space by nonlinear kernel mapping. Then, the discriminant vectors in the null space of the kernel within-scatter matrix are extracted by only one step of economic QR decomposition. Finally, one step of Cholesky decomposition is used to obtain the orthogonal discriminant vectors in the kernel space. Compared with NI.DA, not only does NKDA achieve better performance, but it is applicable to the large sample size problem. Besides, based on NKDA, the incremental NKDA method is developed, which can accurately update the discriminant vectors of NKDA when new samples are inserted into the training set. Experiments on ORL, Yale face database, and PIE subset demonstrate the effectiveness and efficiency of the algorithms, and show that the algorithm can reduce the dimensions of the data and improve the discriminant ability.