<FONT face=Verdana>A new algorithm

Laplacian MinMax Discriminant Analysis (LMMDA)

is proposed in this paper for supervised dimensionality reduction. LMMDA 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 samples 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.