A Modified Construction for a Support Vector Classifier to Accommodate Class Imbalances
This work addresses class imbalance issues in binary classification for machine learning practitioners, offering an incremental improvement over existing SVM methods.
The paper tackles the problem of class imbalance in Support Vector Machines by proposing a modified construction with class-specific margins proportional to each class's standard deviation, which reduces misclassification and improves predictive performance compared to the standard SVM.
Given a training set with binary classification, the Support Vector Machine identifies the hyperplane maximizing the margin between the two classes of training data. This general formulation is useful in that it can be applied without regard to variance differences between the classes. Ignoring these differences is not optimal, however, as the general SVM will give the class with lower variance an unjustifiably wide berth. This increases the chance of misclassification of the other class and results in an overall loss of predictive performance. An alternate construction is proposed in which the margins of the separating hyperplane are different for each class, each proportional to the standard deviation of its class along the direction perpendicular to the hyperplane. The construction agrees with the SVM in the case of equal class variances. This paper will then examine the impact to the dual representation of the modified constraint equations.