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

## TL;DR

This paper proposes a modified support vector classifier that adjusts margins based on class variance to better handle imbalanced data, improving classification accuracy.

## Contribution

It introduces a novel SVM formulation with class-specific margins proportional to class standard deviations, enhancing performance on imbalanced datasets.

## Key findings

- Improved classification accuracy on imbalanced datasets
- The modified SVM reduces bias towards the majority class
- The approach generalizes standard SVM when class variances are equal

## Abstract

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.