Robust Support Vector Machine Using Least Median Loss Penalty

It is found that data points used for training may contain outliers that can generate unpredictable disturbance for some Support Vector Machines (SVMs) classification problems. No theoretical limit for such bad influence is held in traditional convex SVM methods. We present a novel robust misclassification penalty function for SVM which is inspired by the concept of “Least Median Regression”. In our approach, total loss penalty in training is measured by the summation of two median hinge losses, each for a different class. We also propose a “Rank and Convex Procedure” to optimize our tasks. Though our approach is heuristic, it is faster than other known robust methods, such as SVM with Ramp Loss Penalty.