Neighborhood MinMax projections

A new algorithm, Neighborhood MinMax Projections (NMMP), is proposed for supervised dimensionality reduction in this paper. The algorithm aims at learning a linear transformation, and focuses only on the pairwise points where the two points are neighbors of each other. After the transformation, the considered pairwise points within the same class are as close as possible, while those between different classes are as far as possible. We formulate this problem as a constrained optimization problem, in which the global optimum can be effectively and efficiently obtained. Compared with the popular supervised method, Linear Discriminant Analysis (LDA), our method has three significant advantages. First, it is able to extract more discriminative features. Second, it can deal with the case where the class distributions aremore complex than Gaussian. Third, the singularity problem existing in LDA does not occur naturally. The performance on several data sets demonstrates the effectiveness of the proposed method.