The matrix form for weighted linear discriminant analysis and fractional linear discriminant analysis

In this paper we will extend the recently proposed weighted linear discriminant analysis (W_LDA) and fraction-step linear discriminant analysis (F_LDA) from one dimension vector form to the case of two dimension matrix form, which are called weighted two dimensional linear discriminant analysis (W_2DLDA) and fraction-step two dimension linear discriminant analysis (F_2DLDA), respectively. The motivation of this work is based on the recent research results on two dimensional principal component analysis (2DPCA) and 2DLDA showing that the two dimensional algorithms can save computational costs significantly and thus improve the classifiers performances. First, we derived these numerical algorithms in matrix form and then we implement these two new algorithms on ORL and YALE face databases. The experimentation results show that W_2DLDA produces the best performance among F_2DLDA, F_LDA and W_LDA.