Discriminant analysis approach using fuzzy fourfold subspaces model

In this paper, some studies have been made on the essence of a novel fuzzy discriminant analysis (FDA) on the fourfold-objective model (FOM). First, a fourfold-objective model on the discriminant analysis is developed, by which a set of integrated subspaces derived from within-class and between-class scatter matrices are constructed, respectively. Second, an improved FDA (IFDA) algorithm based on the relaxed normalized condition is proposed to achieve the distribution information of each sample represented with fuzzy membership grade, which is incorporated into the redefinition of Fisher's scatter matrices. Therefore, the presented algorithm has the potential to outperform the traditional subspace learning algorithms, especially in the cases of small sample size. Experimental results conducted on the ORL, NUST603, FERET and Yale face image databases demonstrate the effectiveness of the proposed method.