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适用于小样本问题的具有类内保持的正交特征提取算法
引用本文:林玉娥,顾国昌,刘海波,沈晶,赵靖. 适用于小样本问题的具有类内保持的正交特征提取算法[J]. 自动化学报, 2010, 36(5): 644-649. DOI: 10.3724/SP.J.1004.2010.00644
作者姓名:林玉娥  顾国昌  刘海波  沈晶  赵靖
作者单位:1.哈尔滨工程大学计算机科学与技术学院 哈尔滨 150001
基金项目:国家自然科学基金(60873036);;国家教育部博士点基金(200702170-51);;中央高校基本科研业务专项资金资助~~
摘    要:在人脸识别中, 具有正交性的特征提取算法是一类有效的特征提取算法, 但受到小样本问题的制约. 本文在正交判别保局投影的基础上, 提出了一种适用于小样本问题的具有类内保持的正交特征提取算法. 算法根据同类样本之间的空间结构信息, 重新定义了类内散度矩阵与类间散度矩阵, 进而给出了一个新的目标函数. 然而新的目标函数对于人脸识别问题, 同样存在着小样本问题. 为此本文将原始数据空间降到一个低维的子空间, 从而避免了总体散度矩阵奇异, 并在理论上证明了在该子空间中求解判别矢量集, 等价于在原空间中求解判别矢量集. 人脸库上的实验结果表明本文算法的有效性.

关 键 词:特征提取   小样本   目标函数   总体散度矩阵
收稿时间:2009-01-04
修稿时间:2009-07-23

An Orthogonal Feature Extraction Method Based on the Within-class Preserving for Small Sample Size Problem
LIN Yu-E, GU Guo-Chang LIU Hai-Bo SHEN Jing ZHAO Jing .College of Computer Science , Technology,Harbin Engineering University,Harbin .School of Computer Science , Engineering,Anhui University of Science , Technology,Huainan. An Orthogonal Feature Extraction Method Based on the Within-class Preserving for Small Sample Size Problem[J]. Acta Automatica Sinica, 2010, 36(5): 644-649. DOI: 10.3724/SP.J.1004.2010.00644
Authors:LIN Yu-E   GU Guo-Chang LIU Hai-Bo SHEN Jing ZHAO Jing .College of Computer Science    Technology  Harbin Engineering University  Harbin .School of Computer Science    Engineering  Anhui University of Science    Technology  Huainan
Affiliation:1.College of Computer Science and Technology, Harbin Engineering University, Harbin 150001;2.School of Computer Science and Engineering, Anhui University of Science and Technology, Huainan 232001
Abstract:Orthogonal feature extraction methods are widely employed to enhance the discriminatory information for the face recognition task, but often suffer the small sample size problem which arises if the number of samples is smaller than the dimensionality of samples. To solve this problem, an orthogonal feature extraction method based on the within-class preserving is proposed. The proposed method redefines the within-class and between-class scatter matrices according to the space information among samples belonging to the same class, and then gives the new objective function. This method may encounter the small size sample problem when it is applied to face recognition task, and so we firstly map the original space into a low dimensional subspace, then the singularity of the total-scatter matrix can be avoided in this low dimensional subspace. It is proved that the discriminant vectors derived in this low dimensional subspace are equal to the discriminant vectors derived in the original space. Experimental results on face database demonstrate the effectiveness of the proposed method.
Keywords:Feature extraction  small size sample  objective function  total-scatter matrix
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