模式识别Chapter 2-2.ppt

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1、1PatternRecognition北京交通大学电子信息工程学院Chapter2BayesianDecisionTheoryIntroductionBayesiandecisiontheory--error/riskminimumClassifiers,discriminantfunctionThenormaldensityDiscriminantfunctionfornormaldensityPatternRecognitionSystemClassifier4DiscriminantfunctionsTheposteriorprobabilitygivestheprobability

2、ofthepatternbelongingtoclassoncewehaveobservedthefeaturevector.Theprobabilityofmisclassificationisminimizedbyselectingtheclasshavingthelargestposteriorprobability,5DiscriminantfunctionsAfeaturevectorxisassignedtoclassifforall6AfeaturevectorxisassignedtoclassifDiscriminantfunctions7Discriminantfunc

3、tionsc类分类问题--把d-维特征空间分成c个决策域。用于表达决策规则的某些函数成为分类函数。决策域的边界面称为决策面。表达决策面的数学方程称为决策面方程。8宽度待分类鱼的长度宽度分布图长度decisionregionsdecisionboundaries9DecisionboundariesApatternclassifierprovidesaruleforassigningeachpointoffeaturespacetooneofcclasses.Wecanthereforeregardthefeaturespaceasbeingdividedupintocdecisionreg

4、ionssuchthatapointfallinginregionisassignedtoclass.Theboundariesbetweentheseregionsareknownasdecisionsurfaceordecisionboundaries.10Decisionboundaries1-D:point2-D:line3-D:planeN-D:hyper-plane11Example:假设在某个局部地区细胞识别中正常和异常两类的先验概率分别为正常：异常：现有一待识别的细胞，其观察值为，从类条件概率密度曲线上查得试对该细胞分类。试给出决策面方程1213Example:假设在某个局

5、部地区细胞识别中正常和异常两类的先验概率分别为正常：异常：现有一待识别的细胞，其观察值为，从类条件概率密度曲线上查得已知风险参数如下：按最小风险贝叶斯决策分类。试给出决策面方程14PatternRecognitionSystem16DiscriminantfunctionfornormaldensityOfthevariousdensityfunctionsthathavebeeninvestigated,nonehasreceivedmoreattentionthanthemulti-variancenormalorGaussiandensityanalyticaltractabilit

6、yappropriatemodelformostsituations17NormalDensityUni-variateDensityExpectedValue,meanVarianceTheuni-variatenormaldensityiscompletelyspecifiedbytwoparameters:itsmeanandvariance.18NormalDensityMulti-variateDensityTheuni-variatenormaldensityiscompletelyspecifiedbytwoparameters:itsmeanvectorandvarianc

7、ematrix.19DiscriminantfunctionsMinimum-errorclassificationcanbeachievedbytheuseofthediscriminantfunction20DiscriminantfunctionsCase1Thesimplestcaseoccurswhenthefeaturesarestatisticallyindependentandwheneachfeatur