对称零空间准则下的LDA特征抽取方法  

Feature Extraction Method of LDA Based on Symmetrical Null Space Criterion

作　　者：宋晓宁[1,2] 郑宇杰[3] 杨静宇[1] 吴小俊[4] 

机构地区：[1]南京理工大学计算机科学与技术学院,南京210094 [2]江苏科技大学计算机科学与工程学院,镇江212003 [3]中国电子科技集团公司第28研究所,南京210007 [4]江南大学信息工程学院,无锡214122

出　　处：《计算机辅助设计与图形学学报》2009年第3期400-405,411,共7页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(60632050,60503026,60572034);国家“八六三”高技术研究发展计划(2006AA01Z119)

摘　　要：小样本问题在利用线性鉴别分析处理高维样本时经常遇到,但是已有方法在如何构造完整的最优子空间,并在其中获得最有效的鉴别分析的过程中始终存在着共同的缺陷.提出一种最优对称零空间准则的鉴别分析方法,通过构造类内和类间散布矩阵的2个零子空间及其互补子空间,获得分布在各子空间中降维样本的最优鉴别信息,可有效地解决传统Fisher线性变换方法中的最终特征维数受类别数限制的问题.在FERET和ORL人脸数据库上的实验结果验证了文中方法的有效性.Linear discriminant analysis often suffers from the small sample size problem when dealing with high dimensional samples. However, a common problem persists for the existing techniques on how to construct a set of complete optimal subspaces and to perform the most efficient discriminant analysis on these constructed subspaces. In this paper, we propose an optimal symmetrical null space analysis to handle this problem. Under the reformulated discriminant criterion, the optimally reduced dimensionality of the sample is discovered to construct a complete subspaee where all the discriminative information is included in the two null subspaces of the within-class and between-class matrices and their corresponding orthogonal complement subspaces. As a result, we may overcome the shortcoming that the final dimension of features obtained by Fisher＇s discriminant analysis is confined by the number of classes. Experimental results conducted on the FERET and ORL face databases demonstrate the effectiveness of the proposed method.

关 键 词：特征抽取 线性鉴别分析 对称零空间 小样本问题 人脸识别 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]