Direct linear discriminant analysis based on column pivoting QR decomposition and economic SVD  

基于列选主QR分解和节约型SVD的直接线性鉴别分析(英文)

作　　者：胡长晖[1,2] 路小波[1,2] 杜一君[1,2] 陈伍军[1,2] 

机构地区：[1]东南大学自动化学院,南京210096 [2]东南大学复杂工程系统测量与控制教育部重点实验室,南京210096

出　　处：《Journal of Southeast University(English Edition)》2013年第4期395-399,共5页东南大学学报（英文版）

基　　金：The National Natural Science Foundation of China (No.61374194)

摘　　要：A direct linear discriminant analysis algorithm based on economic singular value decomposition （DLDA/ESVD） is proposed to address the computationally complex problem of the conventional DLDA algorithm, which directly uses ESVD to reduce dimension and extract eigenvectors corresponding to nonzero eigenvalues. Then a DLDA algorithm based on column pivoting orthogonal triangular （QR） decomposition and ESVD （DLDA/QR-ESVD） is proposed to improve the performance of the DLDA/ESVD algorithm by processing a high-dimensional low rank matrix, which uses column pivoting QR decomposition to reduce dimension and ESVD to extract eigenvectors corresponding to nonzero eigenvalues. The experimental results on ORL, FERET and YALE face databases show that the proposed two algorithms can achieve almost the same performance and outperform the conventional DLDA algorithm in terms of computational complexity and training time. In addition, the experimental results on random data matrices show that the DLDA/QR-ESVD algorithm achieves better performance than the DLDA/ESVD algorithm by processing high-dimensional low rank matrices.针对传统DLDA算法计算复杂的问题,提出了DLDA/ESVD算法,该算法直接使用ESVD降维和提取非零特征值对应的特征向量.然后,为了提高DLDA/ESVD算法处理高维低秩矩阵的性能,提出了DLDA/QR-ESVD算法,该算法使用列选主QR分解降维,使用ESVD提取非零特征值对应的特征向量.在ORL,FERET和YALE数据库上的实验结果表明,所提出的2种算法具有几乎相同的性能,并在计算复杂性和训练时间方面优于传统的DLDA算法.另外,在随机数据矩阵上的实验结果表明,DLDA/QR-ESVD算法处理高维低秩矩阵的性能优于DLDA/ESVD算法.

关 键 词：direct linear discriminant analysis column pivoting orthogonal triangular decomposition economic singular value decomposition dimension reduction feature extraction 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]