Limes-SVM: A Robust Classification Approach Bridging Soft-Margin and Hard-Margin SVMS

We propose an outlier-robust binary-classification method called LiMES-SVM, which is based on the linearly-involved Moreau-enhanced-over-subspace (LiMES) model (Yukawa et al., 2023). LiMES-SVM involves the Moreau-enhanced hinge loss function which is defined by subtracting the Moreau envelope of the hinge loss from the hinge loss it-self, bridging the soft-margin and hard-margin support vector machines (SVMs) parametrically. While the proposed loss is only weakly convex, the whole cost function remains convex under a mild condition. Numerical examples show that the proposed method exhibits remarkable robustness with respect to the rate and magnitude of outliers.