Regularized max-min distance analysis for dimension reduction using the fisher criterion

Under the homoscedastic Gaussian assumption, max-min distance analysis for dimension reduction has been developed to guarantee the separation of class pairs in the subspace. However, the method suffers from two problems. Firstly, close class pairs may still exist and tend to overlap in the subspace. As a result, a suboptimal classification error rate may be obtained. Secondly, local max-min distance analysis achieves better classification performance by applying an iteration technique, but it greatly increases the computations involved. In this paper, regularized max-min distance analysis for dimension reduction is proposed to deal with the above problems by introducing the Fisher criterion. In addition, a kernel trick is used to extend regularized max-min distance analysis to cope with the general case of data distribution. Experimental results on both synthetic data sets and real data sets show that the proposed algorithm can outperform or be comparable to local max-min distance analysis in almost all the cases without resorting to the iteration procedure.