A pairwise-frontier-based classification framework for two-group classification

Mathematical programming-based methods are widely used to generate separating boundaries in two-group classification problems. While nonlinear boundaries may often yield better performance, they typically require pre-specifying a nonlinear functional form. This contribution proposes a novel pairwise-frontier-based classification (PFC) framework that approximates nonlinear separating boundaries without the need for such a specification. The proposed PFC framework clarifies the role of axioms in classification, providing a clear basis for axiom selection based on problem characteristics. Building on this, PFC methods with nonconvex (NC) frontiers are developed, ensuring that the overlap is not artificially enlarged. To further minimize overlap, certain training observations are deliberately controlled to misclassify, provided that the total misclassification cost does not increase. This enables the extension from hard frontiers to more stable soft frontiers. The applicability of the proposed PFC methods is validated through simulation studies and real-life datasets. The results show that the proposed PFC methods are competitive with some well-established classifiers. Specifically, the PFC-NCSoft method demonstrates superior average performance and greater stability, making it particularly suitable for imbalanced classification tasks.