Some Researches On Applications Of Empirical Mode Decomposition And Radial Basis Functions

The researches presented in this thesis belong to the applications of empirical mode decomposition (EMD) and radial basis functions. We mainly focus on the following topics: empirical mode decomposition, radial basis functions, and their applications on similarity analysis of biological sequences. The contents are summarized as follows:In Chapter1, we present the background and development of the researches in this thesis. Some preliminaries are also given.In Chapter2, we study the EMD method and its application on similarity analysis of biological sequences. After introducing the basic knowledge of the EMD method and the graphical representation method of biological sequences, we use the EMD method to divide nonlinear signal sequences converted from the DNA and protein sequences into a group of well-behaved intrinsic mode functions (IMFs) and a residue in order to compare the similarities among the DNA and protein sequences conveniently and intuitively. This work tests the method's suitability by using the mitochondria of four different species and the cytochrome c protein sequences of seven species.In Chapter3, two EMD methods based on the Multi-Quadrics radial basis function (MQ-RBF) quasi-interpolation and the B-spline quasi-interpolation schemes are presented respectively and applied to similarity analysis of DNA sequences. The MQ-RBF quasi-interpolation and the B-spline quasi-interpolation schemes are used to approximate the extrema envelopes respectively during the IMF sifting process. Both of the methods are simple, easy to implement, and do not require solving any linear system of equations. Then we implement the classic EMD method and the two methods respectively. This work verifies our method's suitability and better performance for similarity/dissimilarity analysis among the mitochondria of four different species and the coding sequences of the first exon of β-globin gene of ten different species.In Chapter4, an EMD method based on the reproducing kernel (RK) interpolation is presented and applied to similarity analysis of DNA sequences. The reproducing kernel function is used to interpolate the extrema envelopes during the IMF sifting process. The method is simple, easy to implement, suitable for local similarity analysis of long DNA sequences by using the mitochondria of four different species. In Chapter5, some problems deserve more detailed investigations in future, including the construction of novel MQ quasi-interpolation scheme, the MQ interpolation with variable shape parameter and bivariate interpolation of the reproducing kernel function et al.