The solution space for Fisher discriminant analysis and the uniqueness under constraints

This paper studies the solution space of Fisher Criteria. The space is large and it is impossible to find the best solution generally. This paper intends to construct an optimal projection, which solves the Fisher criteria and is the unique solution under nonsingular linear transformation if some constraints are0020given. Therefore a theorem is proposed which shows the feasible for constructing the projection, with a simple way to process the construction from the traditional LDA. Experiment result shows the ability and feasible of the proposed solution.