Large margin classifier with graph-based adaptive regularization

TL;DR

This paper proposes a graph-based regularization method with adaptive hyperparameters for binary classifiers, improving outlier handling and class imbalance management through flexible thresholds.

Contribution

It introduces per-class regularization hyperparameters in Gabriel graph classifiers, enhancing robustness and flexibility over fixed-threshold approaches.

Findings

Regularization hyperparameters behave well in margin regions and with outliers.

Adaptive thresholds improve classifier performance in imbalanced scenarios.

Friedman test confirms the effectiveness of flexible thresholds.

Abstract

This paper introduces the use of per-class regularization hyperparameters in Gabriel graph-based binary classifiers. We demonstrate how the quality index used for regularization behaves both in the margin region and in the presence of outliers, and how incorporating this regularization flexibility can lead to solutions that effectively eliminate outliers while training the classifier. We also show how it can address class imbalance by generating higher and lower thresholds for the majority and minority classes, respectively. Thus, rather than having a single solution based on fixed thresholds, flexible thresholds expand the solution space and can be optimized through hyperparameter tuning algorithms. Friedman test shows that flexible thresholds are capable of improving Gabriel graph-based classifiers.