A novel support vector machine with hillside loss and margin distribution

By introducing a hillside loss function for outliers and leveraging the margin distribution of the observations, we establish a novel support vector machine (SVM) optimization model for binary classification. This model possesses the following advantages: First, it incorporates the margin distributions of both classes, thereby making more effective use of the geometric structure of the data; Second, the introduced hillside loss function is smooth and bounded, ensuring that the influence of an outlier on the classifier diminishes as the severity of the outlier increases. By exploiting the structure of the SVM model, we propose a solution method with lower computational complexity which is well-suited for classification problems with a larger number of samples. Computational experiments on both simulated and real-world datasets demonstrate that our classifier effectively ignores outliers, particularly in scenarios where outliers are asymmetrically distributed.