Exemplar based Laplacian Discriminant Projection

A new algorithm, exemplar based Laplacian Discriminant Projection (ELDP), is proposed in this paper for supervised dimensionality reduction. ELDP aims at learning a linear transformation which is an extension of Linear Discriminant Analysis combining with clustering technique. Specifically, we define three scatter matrices using similarities based on representative exemplars which are found by Affinity Propagation Clustering. After the transformation, the considered pair-wise samples within the same exemplar subset and the same class are as close as possible, while those exemplars between-classes are as far as possible. The structural information of classes is contained in the exemplar based 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.