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Discriminative analysis of direct linear discriminant
analysis for face recognition |
| ZHAO Wu-feng1,2, SHEN Hai-bin1 ,YAN Xiao-lang1 |
1. Institute of VLSI Design, Zhejiang University, Hangzhou 310027, China;
2.Department of Information Science and Electlonic Engineering,Zhejiang University, Hangzhou 310027, China |
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Abstract Direct linear discriminant analysis (DLDA) is claimed that it can take advantage of all the information, both within and outside of the withinclass scatter matrixs null space. In order to analyze this claims flaw in theory, the discriminative characteristics of DLDA for face recognition was studied. Since the optimal solution of DLDA is inside the range space of the betweenclass scatter matrix, a theoretical analysis was unfold via the following three aspects: the relationship between the withinclass and betweenclass scatter matrixs range space, the relationship between the withinclass scatter matrixs null space and the betweenclass scatter matrixs range space, the characteristics of DLDA under keeping all the discriminative vectors. The results show that: in undersampled cases DLDA nearly can not make use of the information inside the null space of the withinclass scatter matrix, thus some discriminative information may be lost; DLDA is degenerated as PCA of the betweenclass scatter matrix with all nonzero principal components if it keeps the complete discriminative vectors found. The comparative results on the face database, ORL and YALE, indicate that DLDA is inferior to the other extensions of linear discriminant analysis in terms of recognition accuracy. Which is consistent with the theoretical analysis．
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Published: 21 September 2010
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直接LDA在人脸识别中的鉴别力分析
直接线性鉴别分析(DLDA)曾被声明利用类内离散矩阵零空间内外所有鉴别信息,为了分析声明的理论缺陷,对DLDA在人脸识别中的鉴别特性进行了研究.鉴于DLDA是在类间离散矩阵列空间中寻找最优解,理论分析从下面3方面内容展开：类间和类内离散矩阵的列空间之间的关系、类间离散矩阵列空间与类内离散矩阵零空间的关系以及在保留全部鉴别矢量下的DLDA特性,结果表明,在小样本条件下,DLDA几乎没利用零空间内的信息,导致一些有用的鉴别信息的丢失；若保留全部的鉴别矢量,DLDA退化为类间离散矩阵的保留所有非零成分的主成分分析.在人脸数据库ORL和YALE上的比较实验结果显示：DLDA的识别率都次于其它几种线性鉴别分析扩展方法,与理论分析一致.
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