Weighted L-1-Norm Support Vector Machine for the Classification of Highly Imbalanced Data

The support vector machine has been successfully applied to various classification areas due to its flexibility and a high level of classification accuracy. However, when analyzing imbalanced data with uneven class sizes, the classification accuracy of SVM may drop significantly in predicting minority class because the SVM classifiers are undesirably biased toward the majority class. The weighted L-2-norm SVM was developed for the analysis of imbalanced data; however, it cannot identify irrelevant input variables due to the characteristics of the ridge penalty. Therefore, we propose the weighted L-1-norm SVM, which uses lasso penalty to select important input variables and weights to differentiate the misclassification of data points between classes. We demonstrate the satisfactory performance of the proposed method through simulation studies and a real data analysis.