An unconstrained optimal set of discriminant vectors

Under circumstances of orthogonal constraints, the vectors that make the Fisher discriminant criterion function attain the maximum values are F-S optimal set of discriminant vectors. In this paper, an optimal set of discriminant vectors which need not fill any constraint condition has been presented, together with the solution for the set. In addition, when the number of training samples is smaller than the dimensions of training samples (i.e. small number of training samples problem), the within-class scatter matrix is singular. Under this circumstance, to acquire both F-S optimal set of discriminant vectors and unconstrained optimal set of discriminant vectors presented here becomes unfeasible. To solve this problem, an approved Fisher discriminant function is presented. The results of experiment on ORL face database show that the algorithms presented here have strong ability in discrimination