Handling imbalanced classification problems with support vector machines via evolutionary bilevel optimization

Salvador Garcia

Abstract:

Support vector machines are popular
learning algorithms to deal with binary classification
problems. They traditionally assume equal misclassifi-
cation costs for each class; however, real-world prob-
lems may have an uneven class distribution. This pa-
per introduces EBCS-SVM: Evolutionary Bilevel Cost-
sensitive Support Vector Machines. EBCS-SVM han-
dles imbalanced classification problems by simultane-
ously learning the support vectors and optimizing the
SVM hyper-parameters, 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 hyper-parameters. This optimization
problem is solved using an evolutionary algorithm at
the upper-level and Sequential Minimal Optimization
at the lower-level. These two methods work in a nested
fashion, i.e., the optimal support vectors help guide
the search of the hyper-parameters, 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.