Linear discriminant analysis based on Zp-norm maximization

In this paper, linear discriminant analysis (LDA) based on L_p-norm (LDA-L_p) optimization method is proposed. The objective function utilizing the L_p-norm with arbitrary p value is studied. By maximizing the L_p-norm-based ratio between the between-class scatter and the within-class scatter, LDA-L_p can construct a set of local optimal projection vectors. Moreover, the optimal projection vectors can be obtained by the gradient ascent method. Experimental results on the two synthetic and fourteen benchmark datasets demonstrate that the better performance of LDA-L_p can be achieved by choosing the optimal value of p.