Kernels' Properties, Tricks And Its Applications On Obstacle Detection

Support Vector Machines(SVMs) , based on the statistical learning theory(STL), have become the important field of machine learning recently. Kernel, which is proposed and developed in the study of SVMs, is a new way of constructing nonlinear map. Good kernels mean good SVMs, so the study of kernel functions is one of the focuses in the research on SVMs.There are two parts in the thesis: the theoretical part and the applied part.In the theoretical part, the thesis focuses on the following three issues: The separability of kernels. Kernels are introduced into SVMs for classifying the nonlinear separated data, but not all of kernels can do it. This thesis presents a sufficient and necessary condition to judge if a kernel can do it. Another operational sufficient condition is also presented. Based on this sufficient condition, a Gaussian kernel is proved to be separable for any given data with a suitable radius parameter chosen. Furthermore, a general method to construct separable kernels for the given data is presented. The selection of kernels. The properties of SVMs will be decided by kernels if the train data are given. This thesis presents two simple methods to select kernel's parameters for classification problems and regression problems respectively. The construction of kernels. The thesis presents a new method to construct a kernel based on interpolation of scattered data. The constructed kernel has the advantage of more generalization and less subjectivity.In the applied part, kernel method is used to improve the method of classification with one class training data. The improved method is combined with ground plane transformation method, so that information from monocular vision and stero vision can be fused effectively. Based on this, a demo system of obstacle detecting in outdoor scenes is developed.