适用于小样本问题的具有类内保持的正交特征提取算法

An Orthogonal Feature Extraction Method Based on the Within-class Preserving for Small Sample Size Problem

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.

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.