Laplacian MinMax Discriminant Projections

A new algorithm, Laplacian minmax discriminant projection (LMMDP), is proposed in this paper for supervised dimensionality reduction. LMMDP aims at learning a linear transformation which is an extension of linear discriminant analysis (LDA). Specifically, we define the within-class scatter and the between-class scatter using similarities which are based on pairwise distances in sample space. After the transformation, the considered pairwise within the same class are as close as possible, while those between classes are as far as possible. The structural information of classes is contained in the within-class and the between-class Laplacian matrices. Thus the discriminant projection subspace can be derived by controlling the structural evolution of Laplacian matrices. The performance on several data sets demonstrates the competence of the proposed algorithm.