A generalized optimal set of discriminant vectors

摘要

A generalized optimal set of discriminant vectors for linear feature extraction is presented. First, the criteria of selecting the generalized optimal discriminant vectors are introduced, and then a unified solving method is derived to solve the vectors of the generalized optimal set in both cases of a large number of samples and a small number of samples. The experimental results show that the present method is superior to the Foley-Sammon method (Foley and Sammon, IEEE Trans. Comput.24, 281–289 (1975)), the positive pseudoinverse method (Tian et al., Opt. Engng25(7), 834–839 (1986)), the perturbation method (Hong and Yang, Pattern Recognition24, 317–324 (1991)), and the matrix rank decomposition method (Cheng et al., Pattern Recognition25, 101–111 (1992)) in terms of correct classification rate.