A Modified Construction for a Support Vector Classifier to Accommodate Class Imbalances

The classical construction of a Support Vector Classifier as the classifier which iden- tifies a hyperplane maximizing the margin between two classes, given some constraint on slack variables, works well in many common situations. However when there is a difference between classes in their respective variances perpendicular to this hyper- plane, the SVC ends up giving the class with lower variance perpendicular to it an unjustifiably wide berth, while comparatively tightening up on the high-variance class, resulting in a loss to predictive performance. This paper outlines an alternate con- struction, which seeks to adjust the identified hyperplane in such a way that it agrees with the SVC in the event of a class variance balance along the direction perpendicular to the optimal hyperplane, and to examine the impact to the dual representation of the modified constraint equations.