An Interpretable Data Envelopment Analysis–Discriminant Analysis Framework for Imbalanced Classification: Economic Constraints, Maximum-Margin Extensions, and a Financial Risk Early Warning Application

Data envelopment analysis–discriminant analysis (DEA–DA) offers interpretable classification, but is limited by fixed cumulative-weight assumptions, class imbalance, unspecified indicator directions, and sensitivity to extreme observations. We develop a unified DEA–DA framework with alternative cumulative-weight regimes, class-specific error weights, prespecified input–output directions, a cardinality bound on selected indicators, and an overlap-focused second stage that retains Stage-1 weights. A maximum-margin extension (Meta) is treated separately for linearly separable data and data that are not linearly separable. Under linear separability and the L1-normalized one-sided directional specification, (Model 5) induces a constrained hard-margin L1SVM representation. For data that are not linearly separable, minimum class-specific discrimination errors are relaxed within nonnegative budgets before maximizing the score-space separation parameter η and processing overlap observations. The empirical application uses 2017–2023 feature-year data linked to the same fixed 2024 ST-status label and is therefore interpreted as retrospective fixed-target-year discrimination rather than independent prospective multi-horizon forecasting. Under repeated paired evaluation conditional on prespecified annual Meta settings, Meta achieves 67.84% balanced accuracy versus 50.66% for traditional DEA–DA and is statistically indistinguishable from L1SVM and L2SVM. Contamination and K-sensitivity analyses support coefficient stability and a transparent sparsity–class-balance trade-off. The main contribution is an interpretable, economically constrained, imbalance-aware DEA–DA framework rather than universal performance dominance.