Fractional-step max-min distance analysis for dimension reduction

Dimensionality reduction has been regarded as a key step for high-dimensional data processing and analysis. Max-min distance analysis (MMDA) for dimension reduction is proposed to solve the class separation problem and the minimum pairwise distance between class centers is maximized in the low-dimensional subspace. However, the proposed algorithm ignores the distribution of class centers. Despite of the max-min pairwise distance, the nonuniform distribution of class centers may lead to a suboptimal classification rate. In this paper, we propose a novel method named fractional-step max-min distance analysis (FMMDA). The proposed method maintains excellent class separation and obtains a relatively uniform distribution of class centers by relaxing the max-min pairwise distance in fractional steps. Moreover, we present a dual form of the optimization problem in FMMDA to reduce the computational load of the optimization procedure. Empirical studies demonstrate that the proposed FMMDA significantly outperforms MMDA.