Support Vector Machines with Reject Option for Unequal Costs and Imbalanced Datasets

We consider a binary classification problem based on support vector machines (SVM) with a reject option in nonstandard situations (from the perspective of typical algorithmic assumptions), where it is assumed that misclassification costs differ depending on the class label and that sampling biases exist. In particular, we develop a method for using an SVM with a reject option for handling unequal costs and imbalanced datasets by utilizing a Fisher-consistent surrogate loss function that we propose. Furthermore, we substantiate the proposed method by designing an ��₁-penalty SVM with a reject option (denoted as the modified ��₁-SVMⓇ) for unequal costs and imbalanced datasets. An entire solution path algorithm for the modified ��₁-SVMⓇ is also developed. Experimental results and real data analysis indicate that the proposed method demonstrates good classification performance in the presence of unequal costs and imbalanced datasets.