CAJ | 학술논문

直接线性鉴别分析(DLDA)是一种以克服小样本问题而提出的LDA扩展方法,被声明利用了包含类内散布矩阵零空间外的所有信息.然而,很多反例表明事实并非如此.为了更深入地了解DLDA的特性,该文从理论上对其进行了分析,得出结论:基于传统Fisher准则的DLDA几乎没利用零空间,将丢失一些有用的鉴别信息;而基于广义Fisher准则的DLDA,若满足一定条件(在高维小样本数据应用中一般都满足)且最优鉴别矢量正交约束,则其等价于零空间LDA和正交LDA.在人脸数据库ORL和YALE上的比较实验结果亦与理论分析一致.
직접선성감별분석(DLDA)시일충이극복소양본문제이제출적LDA확전방법,피성명이용료포함류내산포구진령공간외적소유신식.연이,흔다반례표명사실병비여차.위료경심입지료해DLDA적특성,해문종이론상대기진행료분석,득출결론:기우전통Fisher준칙적DLDA궤호몰이용령공간,장주실일사유용적감별신식;이기우엄의Fisher준칙적DLDA,약만족일정조건(재고유소양본수거응용중일반도만족)차최우감별시량정교약속,칙기등개우령공간LDA화정교LDA.재인검수거고ORL화YALE상적비교실험결과역여이론분석일치.
Direct LDA (DLDA) is an extension of Linear Discriminant Analysis (LDA) to deal with the small sample size problem, which is previously claimed to take advantage of all the information, both within and outside of the within-class scatter's null space. However, a lot of counter-examples show that this is not the case. In order to better understand the characteristics of DLDA, this paper presents its theoretical analysis and concludes that: DLDA based on the traditional Fisher criterion nearly does not make use of the information inside the null space, thus some discriminative information may be lost; while one based on other variants of Fisher criterion is equivalent to null-space LDA and orthogonal LDA under the orthogonal constraints among discriminant vectors and a mild condition which holds in many applications involving high-dimensional data. The comparative results on the face database, ORL and YALE, also consistent with the theory analysis.