Wavelet Kernel Estimation For Projection Pursuit Indices And Curvilinear Distance Analysis

Projection pursuit in statistics and signal processing has received attention because of its potential applications. The purpose of projection pursuit is to discover interesting low-dimensional projections from high-dimensional data set by numerically maximizing a projection index. Therefore, the choice of projection index is very important in projection pursuit.Curvilinear Distance Analysis (CDA) is a nonlinear projection method that can preserve the topology of initial data. In recent years, many authors have shown a good deal of interest in it.This paper proposed the wavelet kernel estimation for projection indices and utilized CDA to reduce the hyperspectral data. And we obtained several results as follows:In chapter 2, we proposed the wavelet kernel estimation for two projection indices, and prove the estimations are asymptotic unbiased estimation and convergence in the mean square.In chapter 3, we give some statistical properties of the multivariate wavelet density estimate -or. And then propose the Multivariate wavelet kernel estimation for projection index. At last we obtain some statistical properties to the estimation.In the last chapter, we obtained a new algorithm to apply on the Hyperspectral image unsupervised classification. The CDA is applied as a pre-processing step to reduce the dimensionally of the dataset. And then ICAMM is used for unsupervised classification.