Modifying linearly non-separable support vector machine binary classifier to account for the centroid mean vector

This study proposes a modification to the objective function of the support vector machine for the linearly non-separable case of a binary classifier y_i ∈ {-1, 1}. The modification takes into account the position of each data item x_i from its corresponding class centroid. The resulting optimization function involves the centroid mean vector, and the spread of data besides the support vectors, which should be minimized by the choice of hyper-plane β. Theoretical assumptions have been tested to derive an optimal separable hyperplane that yields the minimal misclassification rate. The proposed method has been evaluated using simulation studies and reallife COVID-19 patient outcome hospitalization data. Results show that the proposed method performs better than the classical linear SVM classifier as the sample size increases and is preferred in the presence of correlations among predictors as well as among extreme values.