Simplicial SMOTE: Oversampling Solution to the Imbalanced Learning Problem

SMOTE (Synthetic Minority Oversampling Technique) is the established geometric approach to random oversampling to balance classes in the imbalanced learning problem, followed by many extensions. Its idea is to introduce synthetic data points of the minor class, with each new point being the convex combination of an existing data point and one of its k-nearest neighbors. In this paper, by viewing SMOTE as sampling from the edges of a geometric neighborhood graph and borrowing tools from the topological data analysis, we propose a novel technique, Simplicial SMOTE, that samples from the simplices of a geometric neighborhood simplicial complex. A new synthetic point is defined by the barycentric coordinates w.r.t. a simplex spanned by an arbitrary number of data points being sufficiently close rather than a pair. Such a replacement of the geometric data model results in better coverage of the underlying data distribution compared to existing geometric sampling methods and allows the generation of synthetic points of the minority class closer to the majority class on the decision boundary. We experimentally demonstrate that our Simplicial SMOTE outperforms several popular geometric sampling methods, including the original SMOTE. Moreover, we show that simplicial sampling can be easily integrated into existing SMOTE extensions. We generalize and evaluate simplicial extensions of the classic Borderline SMOTE, Safe-level SMOTE, and ADASYN algorithms, all of which outperform their graph-based counterparts.