期刊
ANNALS OF OPERATIONS RESEARCH
卷 174, 期 1, 页码 147-168出版社
SPRINGER
DOI: 10.1007/s10479-008-0424-0
关键词
Constrained discriminant analysis; Mixed integer program; Multi-category classification; Multi-group classification; Consistency; Reserved judgment
资金
- National Science Foundation
- Directorate For Engineering
- Div Of Civil, Mechanical, & Manufact Inn [800057] Funding Source: National Science Foundation
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.
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