Integer Programming Solution of a Classification Problem

By J. M. Liittschwager, C. Wang. 1978

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Supersparse linear integer models for optimized medical scoring systems (2015, background): “MIP formulations to minimize the 0–1 loss, for instance, were first proposed in Liittschwager and Wang (1978) and Bajgier and Hill (1982), and later refined by Mangasarian (1994), Asparoukhov and Stam (1997) and Glen (1999).”
Solving mixed integer classification problems by decomposition (1997, background): “Although mixed integer classification models were among the earliest introduced [ 19 , 29], the preponderance of the mathematical programming models proposed are linear programs.”
A Mixed-Integer Programming Approach to Multi-Class Data Classification Problem by (2005, background): “There have been several attempts to formulate data classification problems as MILP problems [34-37].”
Mathematical programming formulations for two-group classification with binary variables (1997, methodology): “Among the most widely known MP methods are the minimize the sum of deviations (MSD) method (Freed and Glover [21], Mangasarian [48], Minnick [53], Smith [64]), the minimize the maximum deviation (MMD) method (Freed and Glover [20], Rubin [58]), the minimize the number of misclassifications (MIP) met”