An Research Of The Approach Of Determining Kernel Parameters For SVM Based On Scale Space

Support vector machine (SVM) is one type of learning machines that is paid wide attention in recent years. Based on statistical learning theory (SLT), SVM possesses many merits such as concise mathematical form, standard fast training algorithm and excellent generalization performance, so it has been widely applied in data mining problems such as pattern recognition function estimation and time series prediction, et al. At present, there are some hot topics in SVM researches, for example, model selection, fast learning algorithms, et al. Because support vector machine is a kind of learning machines based on kernel, the selection of kernel and corresponding parameter will impact greatly on the generalization ability, and then on the performance of SVM. Therefore, how to select the kernel and corresponding parameter is an important issue. In the thesis, the selections of kernel function and relative parameter for SVM are investigated systematically. The main achievements are concluded in the following:(1) Analyzes the existing methods for kernel selection of SVM.(2) Presents an algorithm for choosing optimal kernel parameters for support vector classification. By defining the data isolation among samples, the optimal kernel parameters and the optimal learning model can be obtained. Because the optimal kernel parameters can be attained before SVM training, the less computation cost is needed. (3) Provides the proof, by KKT condition of optimization problem, that there exist an interval of kernel parameter, within which SVM possesses has good performance.(4) Proves the existence of a certain range of the parameterσof Gaussian kernel, within the range the generalization performance is good, based on the relationship analysis of support vector machine and scale space theory. An appropriateσwithin the range can be achieved via dynamic evaluation.The researches in the thesis are the one of key problems of SVM researches. The research results not only have important theoretical significance, but direct application value for real-world problems as well.