The Research On SVM Kernel Parameter Selection Based On Convex Estimation

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 kernel parameter selection will impact greatly on the generalization ability, and then on the performance of SVM. Therefore how to select the kernel parameter is an important issue in the SVM research. 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) Proposes an unoptimal way to calculate the generalization error bounds based on the estimation of approximate convex. Most of the existing kernel selection methods gain the optimal kernel parameter by solving the optimization problem, i.e., minimization of the R~2/△~2. However this kind of methods will spend great computation cost, and can't reflect the distributionof training data. The method presented in the thesis computes the radius and margin directly, so it can avoid the solution of the optimization problem and reduce the computation cost. Moreover, it can be used no matter whether the dataset is dense or whether the distribution is uniform.(3) Develops an approximate expression method for R~2/△~2 based on convex approximate. According to the geometric sense of classification problem and starting from dataset, the training data are divided by the degree of a sample and center of the dataset. Then the approximate convex are obtained, and the approximate of R~2/△~2 is so expressed. All these provided the basis of following kernel selection approach based on convex approximate.(4) Provides the SVM kernel selection model and implement algorithm based on convex estimation algorithm. The polynomial kernel and Gauss kernel, as two general kernel functions are testified on the artificial dataset and real dataset respectively.The researches in the thesis are the one of key problem. The research results not only have important theoretical significance, but also direct application value for real-world problems.