基于正态混合模型的贝叶斯分类方法及其应用  

The Bayes Classifier Based on the Normal Mixture Model and Its Application

作　　者：张婧 袁敏 刘妍岩[2] ZHANG JING;YUAN MIN;LIU YANYAN(School of Statistics and Mathematics,Zhongnan University of Economics and Law,Wuhan 430073,China;School of Mathematics and Statistics,Wuhan University,Wuhan 430072,China)

机构地区：[1]中南财经政法大学统计与数学学院,武汉430073 [2]武汉大学数学与统计学院,武汉430072

出　　处：《应用数学学报》2020年第4期742-755,共14页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金面上项目(No.11971362);国家自然科学基金青年项目(No.11901581);中南财经政法大学中央高校基本科研业务费专项资金(No.2722020JCG064)资助.

摘　　要：本文主要研究正态混合模型的贝叶斯分类方法.贝叶斯分类以后验概率最大为准则,后验概率需要估计相关的条件分布.对于连续型数据的分类,其数据由多个类别混合而成,仅用单一分布难以描述,此时混合模型是一个较好的选择,并且可由EM算法获得.模拟实验表明,基于正态混合模型的贝叶斯分类方法是可行有效的.对于特征较多的分类,不同特征对分类的影响不同,本文对每个特征应用基于正态混合模型的贝叶斯分类方法构建基本分类器,然后结合集成学习,用AdaBoost算法赋予每个分类器权重,再线性组合它们得到最终分类器.通过UCI数据库中实际的Wine Data Set验证表明,本文分类方法与集成学习的结合可以得到高准确率和稳定的分类.This paper studies the Bayes classifier based on the normal mixture model.The criterion of Bayes classification is to maximize the posterior probability,which needs to estimate the conditional distribution.For the classification of continuous data,the data is a mixture of multiple categories,thus it's difficult to be described only by a single distribution.Under this situation,mixture model is a good choice and can be obtained by the EM algorithm.The simulation results show that the Bayes classifier based on the normal mixture model is feasible and effective.For the classification which has multi-feature,different features have different effects.Firstly,we build a basic classifier by the Bayes classifier based on the normal mixture model for every feature.Then we use ensemble learning for reference,give a weight for each basic classifier by AdaBoost algorithm.The final classification is a linear combination of these basic classifiers.The validation on the actual wine data set of UCI database shows that our classification method combines with the ensemble learning can get high precision and robust classification.

关 键 词：贝叶斯分类 正态混合模型 EM算法 集成学习 ADABOOST算法 

分 类 号：O212.7[理学—概率论与数理统计]