Research On Bayesian Method In Functional Data Classification

The Bayesian classification model has been widely used in many fields due to its simple structure,fast speed and high classification accuracy.As we all know,Bayesian classifiers need to perform joint probability calculations,and are based on the maximum posterior probability criteria for classification prediction.For functional data with infinite dimensions,strong correlation,and highly degraded covariance matrix,there is no probability density function,which no longer meets the applicable conditions of the traditional Bayesian classifier.In this thesis,the optimal Bayesian classifier proposed by Dai et al.(2017)is the basic research object,and improvements are mainly made from two aspects of dimensionality reduction and projection score density estimation.First,this thesis applies functional principal component analysis(FPCA)and functional partial least squares(FPLS)to reduce the dimensionality of the functional data and then calculate projected scores.Among them,the classifier based on FPLS can relax the assumption of equal eigenfunction between groups proposed by Dai et al.(2017).Secondly,based on the assumption of independence between the projection score variables,kernel density estimation,Gaussian mixture model and the Bayesian nonparametric method are used to solve a series of one-dimensional density estimation to estimate the joint density of projection score variables.Thirdly,the optimization of adjustment parameters is separated from the construction of the classifier to improve the speed of classification.The strong performance of our methodology is demonstrated through simulation and real data examples.