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贝叶斯分类算法的研究与应用重庆大学硕士学位论文学生姓名：郑默指导教师：刘琼荪教授专业：概率论与数理统计学科门类：理学重庆大学数学与统计学院二O一一年四月ApplicationandResearchonBeyasClassificationAlgorithmAThesisSubmittedtoChongqingUniversityinPartialFulfillmentoftheRequirementfortheDegreeofMasterofScienceByZhengMoSupervisedbyProf.QiongsunLiuMajor:ProbabilityandStatisticsCollegeofMathematicsandStatisticsofChongqingUniversity,Chongqing,ChinaApril2011重庆大学硕士学位论文中文摘要I摘要本文重点研究了数据挖掘中的贝叶斯方法，它具有坚实的数学理论基础,并能综合先验信息和数据样本信息，成为数据挖掘和机器学习研究的热点之一。朴素贝叶斯分类器是一种简单而有效的概率分类方法，然而其属性独立性假设在现实世界中多数不能成立。为了改进该方法的分类性能，近几年已有大量研究成果，许多学者都致力于构建能反映属性之间依赖关系的贝叶斯分类模型。本文简要地介绍了关于朴素贝叶斯分类器和粗糙集的基本理论，包括朴素贝叶斯分类模型，基于属性相关性分析的贝叶斯分类模型，加权贝叶斯分类模型，粗糙集基本理论和属性重要度的构造方法。本文根据RoughSet属性重要度理论，构建了基于互信息的属性子集重要度度量公式，提出属性相关性的加权朴素贝叶斯分类算法(WCB)，该算法同时放宽了朴素贝叶斯算法属性独立性、属性重要性相同的假设。通过数据仿真实验，与基于属性相关相关性分析的贝叶斯(CB)和加权朴素贝叶斯(WNB)两种算法做比较，证明了该算法的有效性。最后对全文的工作进行了总结，并指出有待进一步研究的方向。关键词：朴素贝叶斯分类器，属性重要度，属性相关，加权贝叶斯分类重庆大学硕士学位论文英文摘要IIABSTRACTThisarticlefocusedondataminingmethodofBayesianmethods,ithasasolidtheoreticalfoundationofmathematics,anditcancomprehensiveinformatiananddataforpriorinformation.thereforitbecomesoneofthehotspotsondataminingandmachinelearning.NaiveBayesclassifierisasimpleandeffectiveclassificationmethodonprobabilitytheory,butitsattributeindependenceassumptionisofenviolatedintheworld.ToimprovetheperformanceofBayesclassifiers,inrecentyears,agreatmanyofresearchhasbeendoneonconstructingmodelswhichcanexpressdependenceamongattributes.Somebasictheoriesusedinthisthesisarebrieflyintroduced,includingNaiveBayesianclassificationmodeling,CorrelatedBayesandWeightedNaiveBayes,thebasicthoriesofRoughSet.Basedonthetheoryofroughset,anewNaiveBayesmethodnamedMutualInformation-basedAlgorithmforWeightedNaiveBayes(WCB)wasproposed,whichsynchronouslyloosenNaiveBayesclassifier’sindependenceandequalimportanceoftheattributeassumptions.ComparedwithCorrelatedBayes(CB)andWeightedNaiveBayes(WNB),SimulationresultsonavarietyofUCIdatasetsillustratetheefficiencyofthismethod.Last,wesummarizetheresearchofthisthesisandputforwardsomesuggestionsaboutfurtherstudy.Keywords:NaiveBayesianClassifier,Weightinessofattribute,attributecorrelation,WeightedNaiveBayesclassification重庆大学硕士学位论文目录III目录中文摘要..........................................................................................................................................I英文摘要........................................................................................................................................II1绪论...............................................................................................................................................11.1研究背景和研究现状...........................................................................................................11.1.1研究背景....................................................................................................................11.1.2国内外研究现状........................................................................................................11.2研究内容和目的...................................................................................................................51.2.1研究内容....................................................................................................................51.2.2研究目的....................................................................................................................61.3论文的组织结构...................................................................................................................62朴素贝叶斯分类模型..........................................................................................................72.1贝叶斯理论相关知识...........................................................................................................72.1.1基础知识....................................................................................................................72.1.2贝叶斯决策准则.........................................................................................................72.1.3极大后验假设和极大似然假设................................................................................82.2朴素贝叶斯分类模型...........................................................................................................82.3朴素贝叶斯分类器的优缺点.............................................................................................112.4本章小结.............................................................................................................................113粗糙集理论和加权贝叶斯分类模型........................................................................123.1粗糙集基本理论.................................................................................................................123.1.1粗糙集相关概念......................................................................................................123.1.2知识依赖性的度量..................................................................................................133.1.3属性的重要性..........................................................................................................133.1.4粗糙集中两种度量属性重要度的方法.....................................