模式识别Chapter3CharacterRecognitionFeaturespaceCharacterRecognition模式识别系统宽度PatternRecognitionBayes’theoremingeneral大家学习辛苦了，还是要坚持Bayes’Decision:errorminimumBayes’Decision:riskminimumDiscriminantfunctionsDiscriminantfunctionsDiscriminantfunctionsDiscriminantfunctionsOverviewExampleExampleExampleExampleExampleChapter3Maximum-likelihoodandBayesianparameterestimationIntroductionProbabilityDensityEstimationProbabilityDensityEstimationProbabilityDensityEstimationProbabilityDensityEstimationProbabilityDensityEstimationMaximumLikelihoodEstimationMaximumLikelihoodEstimationMaximumLikelihoodEstimationMaximumLikelihoodEstimationExampleTheGaussiancase:UnknownExampleExampleExample3839BayesEstimation模式识别系统GaussianClassifiers假设独立等方差假设等协方差矩阵Lineardiscriminantfunction(LDF)GaussianClassifiersParameterEstimationofGaussianDensityMaximumLikelihood(ML)ParameterEstimationofGaussianDensityParametric分类器不好用吗--实际中很多类别的概率分布近似Gaussian--即使概率分布偏离Gaussian比较大，当特征维数高而训练样本少(Curseofdimensionality)时，Parametric分类器仍然比较好有时LDF甚至比QDF更好ML估计的好处：--训练计算量小（与类别数和样本数成线性关系）--高维情况下降维（特征选择、变换）经常是有益的Gaussian分类器的改进QDF的问题参数太多：与维数的平方成正比训练样本少时协方差矩阵奇异即使不奇异ML估计的泛化性能也不好Regularizeddiscriminantanalysis(RDA)通过平滑协方差矩阵克服奇异，同时提高泛化性能Wecoulddesignanoptionalclassifierifweknewthepriorprobabilitiesandconditionaldensities.Oneapproachisusethesamplestoestimatetheunknownprobabilitiesanddensities,andthentheresultingestimatesasiftheywerethetruevalues.