Generalization improvement for regularized least squares classification

In the past decades, regularized least squares classification (RLSC) is a commonly used supervised classification method in the machine learning filed because it can be easily resolved through the simple matrix analysis and achieve a close-form solution. Recently, some studies conjecture that the margin distribution is more crucial to the generalization performance. Moreover, from the view of margin distribution, RLSC only considers the first-order statistics (i.e., margin mean) and does not consider the actual higher-order statistics of margin distribution. In this paper, we propose a novel RLSC which takes into account the actual second-order (i.e., variance) information of margin distribution. It is intuitively expected that small margin variance will improve the generalization performance of RLSC from a geometric view. We incorporate the margin variance into the objective function of RLSC and achieve the optimal classifier by minimizing the margin variance. To evaluate the performance of our algorithm, we conduct a series of experiments on several benchmark datasets in comparison with RLSC, kernel minimum squared error, support vector machine and large margin distribution machine. And the empirical results verify the effectiveness of our algorithm and indicate that the margin distribution is helpful to improve the classification performance.