Largest center-specific margin for dimension reduction

Dimensionality reduction plays an important role in solving the 'curse of the dimensionality' and attracts a number of researchers in the past decades. In this paper, we proposed a new supervised linear dimensionality reduction method named largest center-specific margin (LCM) based on the intuition that after linear transformation, the distances between the points and their corresponding class centers should be small enough, and at the same time the distances between different unknown class centers should be as large as possible. On the basis of this observation, we take the unknown class centers into consideration for the first time and construct an optimization function to formulate this problem. In addition, we creatively transform the optimization objective function into a matrix function and solve the problem analytically. Finally, experiment results on three real datasets show the competitive performance of our algorithm.