On multi-class learning through the minimization of the confusion matrix norm

TL;DR

This paper introduces a novel approach for imbalanced multi-class classification by optimizing the norm of the confusion matrix, providing a more detailed performance measure than traditional error rates.

Contribution

It demonstrates that optimizing the confusion matrix norm unifies cost-sensitive methods and extends AdaBoost.MM to better handle imbalanced classes.

Findings

The proposed method effectively improves classification performance on imbalanced datasets.

Theoretical analysis confirms the method's desirable properties.

Experimental results show competitive or superior results compared to existing approaches.

Abstract

In imbalanced multi-class classification problems, the misclassification rate as an error measure may not be a relevant choice. Several methods have been developed where the performance measure retained richer information than the mere misclassification rate: misclassification costs, ROC-based information, etc. Following this idea of dealing with alternate measures of performance, we propose to address imbalanced classification problems by using a new measure to be optimized: the norm of the confusion matrix. Indeed, recent results show that using the norm of the confusion matrix as an error measure can be quite interesting due to the fine-grain informations contained in the matrix, especially in the case of imbalanced classes. Our first contribution then consists in showing that optimizing criterion based on the confusion matrix gives rise to a common background for cost-sensitive methods aimed at dealing with imbalanced classes learning problems. As our second contribution, we propose an extension of a recent multi-class boosting method --- namely AdaBoost.MM --- to the imbalanced class problem, by greedily minimizing the empirical norm of the confusion matrix. A theoretical analysis of the properties of the proposed method is presented, while experimental results illustrate the behavior of the algorithm and show the relevancy of the approach compared to other methods.