中文摘要：

研究提出一种模糊双向最大间距准则（fuzzy bidirectional maximum margin criterion,FBMMC）特征提取方法,并将其用于人脸识别。在FBMMC中,首先通过引入原始训练样本集的模糊隶属度矩阵,定义了面向图像的行方向模糊离散度矩阵和行方向模糊最大间距准则,进一步求得行方向最优投影矩阵;然后,对原始训练样本集中的每一个样本,采用行方向最优投影矩阵进行投影变换,从而得到行方向特征训练样本集。同样地,通过引入行方向特征训练样本集的模糊隶属度矩阵,给出了面向图像的列方向模糊离散度矩阵和列方向模糊最大间距准则的定义,进一步求得列方向最优投影矩阵。FBMMC在得到行、列两个方向的最优投影矩阵后,就可以将原始数据空间的样本数据投影到一个相对低维的特征空间,从而完成对原始样本数据的特征提取。在ORL和Yale人脸数据库上的实验结果表明,文中提出的模糊双向最大间距准则特征提取方法用于人脸识别具有较高的识别率。

英文摘要：

This paper proposes a new method for feature extraction and recognition,namely,the fuzzy bidirectional maximum margin criterion（FBMMC）.Through introducing the fuzzy membership grade matrix of the original training sample set,FBMMC defines the row directional fuzzy image scatter matrices and the row directional fuzzy image MMC,and then obtains the row directional optimal projection matrix.Subsequently,each sample in the original training sample set is transformed using the row directional optimal projection matrix,and the row directional feature training sample set can be obtained.Similarly,utilizing the fuzzy membership grade matrix of the row directional feature training sample set,FBMMC defines the formulas of the column directional fuzzy image scatter matrices and the column directional fuzzy image MMC;and then obtains the column directional optimal projection matrix.Having obtained the row and column directional optimal projection matrices,FBMMC can transform the original sample data from original high-dimensional data space to a low-dimensional feature space and complete the feature extraction of the original sample data.Experimental results on the ORL and Yale face database show that the proposed FBMMC method for face recognition has high recognition rate.