A Pairwise-frontier-based Classification Method for Two-Group Classification

Mathematical programming-based methods are widely used to generate separating boundaries in two-group classification problems. Nonlinear separating boundaries may have better classification performance than linear separating boundaries, but these require a pre-specification of a nonlinear functional form. This contribution proposes a novel pairwise-frontier-based classification (PFC) method to approximate nonlinear separating boundaries, without predetermining a nonlinear functional form. It consists of two steps that explicitly consider and focus on overlap. The first step is to identify the overlap. Importantly, this contribution proposes to construct frontiers based on background knowledge of classification, thus ensuring that their intersection (i.e., overlap) is not increased by blindly applying commonly used axioms. Depending on the axioms applied, pairwise frontiers can be either convex or nonconvex. The second step minimizes identified overlaps by allowing training observations to be misclassified, but all training observations that have been correctly classified must remain correctly classified. The PFC method with hard frontiers is then extended to the one with soft frontiers. The applicability of the proposed PFC methods is illustrated by simulation studies and real-life data sets. The results show that the proposed method is competitive with some well-established classifiers in the literature and even performs better with unbalanced data sets.