Theoretical and experimental study of SMOTE: limitations and comparisons of rebalancing strategies

Synthetic Minority Oversampling Technique (SMOTE) is a common rebalancing strategy for handling imbalanced data sets. Asymptotically, we prove that SMOTE (with default parameter) regenerates the original distribution by simply copying the original minority samples. We also prove that SMOTE density vanishes near the boundary of the support of the minority distribution, therefore justifying the common BorderLine SMOTE strategy. Then we introduce two new SMOTE-related strategies, and compare them with state-of-the-art rebalancing procedures. We show that rebalancing strategies are only required when the data set is highly imbalanced. For such data sets, SMOTE, our proposals, or undersampling procedures are the best strategies.