关键词: Mallow&rsquo, s Cp准则, Logistic模型, 模型选择, 粗糙集, 泛化能力

Abstract: Rough set selection is a key step in empirical research of rough sets. Misclassification rate is often used as an optimal criterion of rough set evaluation. In view that the misclassification rate criterion does not consider the complexity of the rough set, thus there is over-fitting risk, and the rough set with the least misclassification rate in a test set does not always have the best generalization ability, the Mallow’s Cp criterion is introduced as a new rough set selection criterion. The Mallow’s Cp selection algorithm for rough set expresses the nonlinear rough set classification rules as linear form by Logistic model, the Cp value of the rough set is defined as the Cp value of the Logistic model, and rough set is selected according to Cp value. Empirical research results show that the Mallow’s Cp selection algorithm for rough set can choose out rough set with better generalization ability, and the selection frequency of rough set with best generalization ability is higher than misclassification rate criterion. Especially when there is small difference of misclassification rate among rough sets, new approach is more likely to choose rough set with the best generalization ability than misclassification criterion. The Mallow’s Cp selection algorithm for rough set combines the classification accuracy and complexity of rough rules and is better at choosing rough set with the best generalization ability.

Key words: Mallow’s Cp criterion, Logistic model, model selection, rough set, generalization ability