Presumably correct undersampling

This paper presents a data pre-processing algorithm to tackle class imbalance in classification problems by undersampling the majority class. It relies on a formalism termed Presumably Correct Decision Sets aimed at isolating easy (presumably correct) and difficult (presumably incorrect) instances in a classification problem. The former are instances with neighbors that largely share their class label, while the latter have neighbors that mostly belong to a different decision class. The proposed algorithm replaces the presumably correct instances belonging to the majority decision class with prototypes, and it operates under the assumption that removing these instances does not change the boundaries of the decision space. Note that this strategy opposes other methods that remove pairs of instances from different classes that are each other's closest neighbors. We argue that the training and test data should have similar distribution and complexity and that making the decision classes more separable in the training data would only increase the risks of overfitting. The experiments show that our method improves the generalization capabilities of a baseline classifier, while outperforming other undersampling algorithms reported in the literature.