On multi-class classification through the minimization of the confusion matrix norm
Sokol Koço, Cécile Capponi · Asian Conference on Machine Learning · 2013
In imbalanced multi-class classication problems, the misclassication 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 misclassication rate: misclassication costs, ROC-based information, etc. Following this idea of dealing with alternate measures of performance, we propose to address imbalanced classication 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 ne-grain informations contained in the matrix, especially in the case of imbalanced classes. Our rst 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.