Optimizing Interval Data Classification Through Two-Stage Mixed Integer Programming: A Discriminant Analysis Perspective

Efficient classification of interval data presents considerable challenges, particularly when group overlaps and data uncertainty are prevalent.This study introduces an innovative two-stage Mixed Integer Programming (MIP) framework for discriminant analysis (DA), which is designed to minimize misclassification of vertices while effectively addressing the problem of overlapping groups.By incorporating interval data structures, the proposed model captures both the shared characteristics within groups and the distinct separations between them.The first stage of the model focuses on the identification of group-specific boundaries, while the second stage refines classification by incorporating probabilistic estimates of group memberships.A Monte Carlo simulation is employed to evaluate the robustness of the model under conditions of imprecision and noise, and the results demonstrate its superior capability in handling overlapping data and classifying uncertain observations.Validation through numerical experiments illustrates the model's effectiveness in accurately resolving group overlaps, thereby improving classification performance.The approach offers significant advantages over traditional methods by probabilistically estimating group memberships, thus enhancing decision-making processes in uncertain environments.These findings suggest that the proposed MIP framework holds substantial promise for applications across a range of complex decision-making scenarios, such as those encountered in finance, healthcare, and engineering, where data imprecision is a critical concern.