An 0ptimal Linear Discriminant Analysis for Pattern Recognition

This paper introduces the conception of efficient projection vector by transforming Foley-Sammon discriminant analysis into a bi-objective constrained optimization problem. The conditions for the efficient projection vector are obtained through the necessary conditions for multi-objective optimization. The efficient projection vector is prove to be the eigen-vector of eigen-equation corresponding to the largest eigen-value, providing a method finding the set of efficient projection vectors. Here the non-singularity of the within scatter matrix is not essential. The results of the experiments show that the computational time is greatly reduced if the proposed method is used for feature extraction and the fuction of recognition is superior to other methods.