CAJ | 학술논문

在小样本条件下,由于离散矩阵的奇异性,作为监督降维的传统线性鉴别分析(LDA)并不能直接计算.许多扩展算法被提出以克服此问题,一般可分为3类:基于类内离散矩阵零空间的方法、基于总体离散矩阵列空间的方法和基于其它子空间的方法.为了深入了解前2类算法的特性,作了计算和理论分析,并得出结论:在满足一定条件下(小样本高维数据一般都满足),基于类内离散矩阵零空间和基于总体离散矩阵列空间的方法具有等价关系,仅最优矢量集的约束条件和实现途径有所区别.在人脸数据库ORL和YALE上的比较实验结果亦证实了上述结论.
재소양본조건하,유우리산구진적기이성,작위감독강유적전통선성감별분석(LDA)병불능직접계산.허다확전산법피제출이극복차문제,일반가분위3류:기우류내리산구진령공간적방법、기우총체리산구진렬공간적방법화기우기타자공간적방법.위료심입료해전2류산법적특성,작료계산화이론분석,병득출결론:재만족일정조건하(소양본고유수거일반도만족),기우류내리산구진령공간화기우총체리산구진렬공간적방법구유등개관계,부최우시량집적약속조건화실현도경유소구별.재인검수거고ORL화YALE상적비교실험결과역증실료상술결론.
In the case of small sample size,classical linear discriminant analysis fails due to the singularity of scatter matrices for supervised dimensionality reduction.Many extensions were proposed in the past to overcome this problem,which in general can be classified into three categories: methods based on the null space of the within-class scatter matrix,ones based on the range space of the total scatter matrix and ones based on other subspace.In order to better understand the characteristics of the algorithms of the former two classes,a computational and theoretical analysis was carried out,and concluded that; under a mild condition which holds in many applications involving high-dimensional data,methods based on the null space of the within-class scatter matrix are equivalent to those based on the range space of the total scatter matrix except two differences of constraints for discriminant vectors and implementation procedure.The comparative results on the face database,ORL and YALE,also confirmed the aforementioned conclusion.