Face recognition using fuzzy maximum scatter discriminant analysis

As we know, classical Fisher discriminant analysis usually suffers from the small sample size problem due to the singularity problem of the within-class scatter matrix. In this paper, a novel fuzzy linear classifier, called fuzzy maximum scatter difference (FMSD) discriminant criterion, is proposed to extract features from samples, especially deals with outlier samples. FMSD takes the scatter difference between between-class and within-class as discriminant criterion, so it will not suffer from the small sample size problem. The conventional scatter difference discriminant criterion (SDDC) assumes the same level of relevance of each sample to the corresponding class. In this paper, the fuzzy set theory is introduced to the conventional SDDC algorithm, where the fuzzy k-nearest neighbor is adopted to achieve the distribution information of original samples. The distribution is utilized to redefine the scatter matrices that are different from the conventional SDDC and effective to extract discriminative features from outlier samples. Experiments conducted on FERET and ORL face databases demonstrate the effectiveness of the proposed method.