A Subspace Learning Based on a Rank Symmetric Relation for Fuzzy Kernel Discriminant Analysis

Classification of nonlinear high-dimensional data is usually not amenable to standard pattern recognition techniques because of an underlying nonlinear small sample size conditions. To address the problem, a novel kernel fuzzy dual discriminant analysis learning based on a rank symmetric relation is developed in this paper. First, dual subspaces with rank symmetric relation on the discriminant analysis are established, by which a set of integrated subspaces of within-class and between-class scatter matrices are constructed, respectively. Second, a reformative fuzzy LDA algorithm is proposed to achieve the distribution information of each sample represented with fuzzy membership degree, which is incorporated into the redefinition of the scatter matrices. Third, considering the fact that the kernel Fisher discriminant is effective to extract nonlinear discriminative information of the input feature space by using kernel trick, a kernel algorithm based on the new discriminant analysis is presented subsequently, which has the potential to outperform the traditional subspace learning algorithms, especially in the cases of nonlinear small sample sizes. Experimental results conducted on the ORL and Yale face database demonstrate the effectiveness of the proposed method.