Song Fengxi, Zhang David, Mei Dayong, Guo Zhongwei
New Star Research Institute of Applied Technology, Hefei 230031, China.
IEEE Trans Syst Man Cybern B Cybern. 2007 Dec;37(6):1599-606. doi: 10.1109/tsmcb.2007.906579.
Maximum scatter difference (MSD) discriminant criterion was a recently presented binary discriminant criterion for pattern classification that utilizes the generalized scatter difference rather than the generalized Rayleigh quotient as a class separability measure, thereby avoiding the singularity problem when addressing small-sample-size problems. MSD classifiers based on this criterion have been quite effective on face-recognition tasks, but as they are binary classifiers, they are not as efficient on large-scale classification tasks. To address the problem, this paper generalizes the classification-oriented binary criterion to its multiple counterpart--multiple MSD (MMSD) discriminant criterion for facial feature extraction. The MMSD feature-extraction method, which is based on this novel discriminant criterion, is a new subspace-based feature-extraction method. Unlike most other subspace-based feature-extraction methods, the MMSD computes its discriminant vectors from both the range of the between-class scatter matrix and the null space of the within-class scatter matrix. The MMSD is theoretically elegant and easy to calculate. Extensive experimental studies conducted on the benchmark database, FERET, show that the MMSD out-performs state-of-the-art facial feature-extraction methods such as null space method, direct linear discriminant analysis (LDA), eigenface, Fisherface, and complete LDA.
最大散度差（MSD）判别准则是一种最近提出的用于模式分类的二元判别准则，它利用广义散度差而非广义瑞利商作为类可分性度量，从而在处理小样本量问题时避免了奇异性问题。基于该准则的MSD分类器在人脸识别任务中相当有效，但由于它们是二元分类器，在大规模分类任务中效率不高。为了解决这个问题，本文将面向分类的二元准则推广到其多元对应物——用于面部特征提取的多元MSD（MMSD）判别准则。基于这种新型判别准则的MMSD特征提取方法是一种新的基于子空间的特征提取方法。与大多数其他基于子空间的特征提取方法不同，MMSD从类间散度矩阵的值域和类内散度矩阵的零空间计算其判别向量。MMSD在理论上很优美且易于计算。在基准数据库FERET上进行的大量实验研究表明，MMSD优于诸如零空间方法、直接线性判别分析（LDA）、特征脸、Fisherface和完全LDA等当前最先进的面部特征提取方法。
