Fuzzy Maximum Scatter Discriminant Analysis in Image Segmentation

In this paper, a reformative scatter difference discriminant criterion (SDDC) with fuzzy set theory is studied. The scatter difference between between-class and within-class as discriminant criterion is effective to overcome the singularity problem of the within-class scatter matrix due to small sample size problem occurred in classical Fisher discriminant analysis. However, the conventional SDDC assumes the same level of relevance of each sample to the corresponding class. So, a fuzzy maximum scatter difference analysis (FMSDA) algorithm is proposed, in which the fuzzy k-nearest neighbor (FKNN) is implemented to achieve the distribution information of original samples, and this information is utilized to redefine corresponding scatter matrices which are different to the conventional SDDC and effective to extract discriminative features from overlapping (outlier) samples. Experiments conducted on FERET face databases and in image segmentation demonstrate the effectiveness of the proposed method.