关键词: 降维, 流形学习, 图嵌入, 人脸识别

Abstract: Based on spectral graph theory and manifold learning，and inspired by Fukunaga-Koontz Transform，the traditional LDA is simplified and improved.FKT has been proved to be the best low-rank approximation to Quadratic Discriminant Analysis.The transform is only used in the two-class classification problem at the early time，and recently has been used in face recognition to solve the Small Sample Size Problem.LDA can transform to a two-stage graph embedding，first it is the PCA，then eigenvalue decomposition of the numerator of the Discriminant in the spaces spanned by the principle eigenvectors of PCA.Both the singularity of the data and the ratio form in Discriminant Analysis are removed.

Key words: dimension reduction, manifold learning, graph embedding, face recognition