Spectral Data Classification And Regression Based On Kernel Density Estimation

This thesis studies the kernel density estimation (KDE) based hyperspectral remotesensing (HSRS) classification and Fourier transform infrared spectroscopy (FTIR)regression respectively. The main difficulties of HSRS classification and FTIR regressionare how to effectively deal with the strong dependence among wave bands of HSRS andhow to accurately recognize the hidden peaks of FTIR. The HSRS classification methodsbased on spectrum matching and support vector machine always neglect the dependencebetween wave bands. And, the least squares fitting methods are sensitive to the hiddenpeaks in FTIR. All these will limit the performances of existing methods focusing onHSRS classification and FTIR regression. Thus, in order to solve these difficulties, thisthesis mainly carries out the KDE based HSRS classification and FTIR regression throughanalyzing the probability density functions (PDF) of HSRS and FTIR data. The mainworks include the following three aspects:(1) The impacts of seven kernels including Gaussian, Uniform, Triangular, Epanechnikov,Biweight, Triweight and Cosine, on the performance of na ve Bayesian classifierbased on the marginal PDF estimation are firstly investigated, where Gaussian kernelis smooth and the other six kernels are non-smooth. Through analyzing the efficienciesof these seven kernels in PDF estimation, the applied conditions of non-smoothkernels are given and meanwhile a flexible na ve Bayesian with equivalent probabilityfor non-smooth kernel (FNBEPNSK) is proposed to relieve the incapability ofnon-smooth kernel. The experimental results on benchmark UCI and realhyperspectral datasets show the application of equivalent probability can effectivelyimprove the classification accuracy of flexible na ve Bayesian.(2) In order to handle the dependence among the condition attributes (wave bands) ofHSRS, a non-na ve Bayesian classifier (NNBC) based on joint PDF estimation isproposed to deal with HSRS classification. A crucial parameter called bandwidth willheavily impact the performance of joint PDF estimation. Thus, a parameter selectioncriterion based on the minimization of mean integrated squared error is designed tofind the optimal bandwidth for NNBC. Then, a theoretical derivation is given to turnout the optimality of joint PDF estimation when the dependence exists amongcondition attributes. Finally, the comparative results with the existing na ve Bayesian classifiers show that our proposed NNBC can not only obtain the better estimationquality but also get higher classification accuracy.(3) A kernel regression ensemble based on fuzzy integral (KREFI) is proposed to improvethe performance of Priestley-Chao kernel estimators, i.e., PCKE1and PCKE2, underthe situation that there is no the optimal bandwidth is selected by PDF estimation. TheChoqet integral is used to fuse the values from different kernel regression estimators.For the application of fuzzy integral, the determination of fuzzy measures is theprimary and fundamental task. Thus, particle swarm optimization (PSO) is introducedto develop a quick and robust determination method for fuzzy measures. The finalexperiments show that our proposed KREFI can obtain the better estimationperformance on the real FTIRs and effectively recognize the hidden peaks of FTIR.