  Support vector machines (SVMs) are popular learning algorithms to deal with
binary classification problems. They traditionally assume equal
misclassification costs for each class; however, real-world problems may have
an uneven class distribution. This article introduces EBCS-SVM: evolutionary
bilevel cost-sensitive SVMs. EBCS-SVM handles imbalanced classification
problems by simultaneously learning the support vectors and optimizing the SVM
hyperparameters, which comprise the kernel parameter and misclassification
costs. The resulting optimization problem is a bilevel problem, where the lower
level determines the support vectors and the upper level the hyperparameters.
This optimization problem is solved using an evolutionary algorithm (EA) at the
upper level and sequential minimal optimization (SMO) at the lower level. These
two methods work in a nested fashion, that is, the optimal support vectors help
guide the search of the hyperparameters, and the lower level is initialized
based on previous successful solutions. The proposed method is assessed using
70 datasets of imbalanced classification and compared with several
state-of-the-art methods. The experimental results, supported by a Bayesian
test, provided evidence of the effectiveness of EBCS-SVM when working with
highly imbalanced datasets.
