Robust Midpoint Classifier (RMC): A Simple and Robust Linear Alternative to Support Vector Machines

Abstract

This paper proposes the Robust Midpoint Classifier (RMC), a simple and interpretable linear classification rule that connects centroid-based methods with margin-based approaches such as Support Vector Machines (SVM). RMC constructs the decision boundary as the perpendicular bisector between robust class centroids obtained via -trimmed means, thereby reducing the influence of outliers while preserving a clear geometric interpretation. We present a unified formulation of RMC as a robustified nearest-centroid rule and analyse its behaviour in mean-shift settings. A simulation study based on repeated experiments compares RMC with a linear SVM under four scenarios: clean Gaussian data, outlier contamination, strong class overlap, and heterogeneous covariance structures. The results show that RMC matches SVM on clean and moderately contaminated data, slightly outperforms SVM in the overlap scenario, and remains competitive when covariances differ. Overall, RMC offers a computationally light and robust alternative for binary linear classification.