Max–min distance analysis by making a uniform distribution of class centers for dimensionality reduction

• We present a new method for dimensionality reduction: fractional-step max–min distance analysis (FMMDA).
• We propose a more efficient method: regularized max–min distance analysis (RMMDA).
• We present the speedup version and the kernel version.
• The proposed methods can outperform some state-of-the-art discriminant analysis methods.

Max–min distance analysis (MMDA) for dimensionality reduction has been presented to guarantee class separation. However, class centers may be nonuniformly distributed and thus optimal classification accuracy may not be obtained. In this paper, we first give a novel method based on MMDA, called fractional-step max–min distance analysis (FMMDA), which relaxes max–min pairwise distances in fractional steps. The method can make a relatively uniform distribution of class centers and approximately maintain class separation. Then we present a more efficient method, called regularized max–min distance analysis (RMMDA), which achieves the same effect as FMMDA by integrating the Fisher criterion into MMDA. Moreover, we present the speedup and kernel versions of the methods to accelerate an optimization procedure and deal with the data distribution problem, respectively. Finally, we analyze the computational complexities of our methods. Empirical studies demonstrate that our methods can outperform or be comparable to some state-of-the-art discriminant analysis methods in terms of classification accuracy.