关键词: 模糊线性鉴别分析，特征抽取，小样本问题，离群样本，人脸识别

Abstract: A study was made on the essence of fuzzy Fisher discriminant analysis (FLDA) algorithm in this paper. A reformative FLDA algorithm based on the fuzzy k-nearest neighbor (FKNN) was implemented to achieve the distribution information of every original sample represented with fuzzy membership degree and was incorporated into the redefinition of the scatter matrices. Furthermore, considering the fact that the outlier samples have some adverse influence to the classification result, a relaxed normalized condition in the fuzzy membership degrees was proposed simultaneously,therefore, the limitation from the outlier samples was overcome. Unlike the conventional FLDA algorithm, the proposed method computes its discriminant vectors with fuzzy membership degree from every training sample, which is thcoretically effective to address the small size sample and outlier samples problems. Extensive experimental studies conducted on the ORL and NUST603 face images show the effectiveness of the proposed algorithm.

Key words: Fuzzy linear discriminant analysis, Feature extraction, Small size sample problem, Outlier samples, Face recognition