Analysis of the consistency of a mixed integer programming-based multi-category constrained discriminant model

作者：Brooks J Paul; Lee Eva K^*

来源：Annals of Operations Research, 2010, 174(1): 147-168.

DOI：10.1007/s10479-008-0424-0

• Constrained discriminant analysis
• Mixed integer program
• Multi-category classification
• Multi-group classification
• Consistency
• Reserved judgment

Classification is concerned with the development of rules for the allocation of observations to groups, and is a fundamental problem in machine learning. Much of previous work on classification models investigates two-group discrimination. Multi-category classification is less-often considered due to the tendency of generalizations of two-group models to produce misclassification rates that are higher than desirable. Indeed, producing "good" two-group classification rules is a challenging task for some applications, and producing good multi-category rules is generally more difficult. Additionally, even when the "optimal" classification rule is known, inter-group misclassification rates may be higher than tolerable for a given classification model. We investigate properties of a mixed-integer programming based multi-category classification model that allows for the pre-specification of limits on inter-group misclassification rates. The mechanism by which the limits are satisfied is the use of a reserved judgment region, an artificial category into which observations are placed whose attributes do not sufficiently indicate membership to any particular group. The method is shown to be a consistent estimator of a classification rule with misclassification limits, and performance on simulated and real-world data is demonstrated.

• 出版日期2010-2