Some Results Of SVM Parameter Selection Based On Feature Space Theory

Parameter selection is an important problem in Support Vector Machine theory. In great part, it is the parameters who control generalization ability of SVM. This article mainly focuses on how to select optimal SVM parameters under the framework of optimization theory.1. In Chapter 2, the properties of SVM training points in RBF feature space are explored. A framework for theory analysis is founded and the effects of kernel parameters to generalization ability of SVM are presented, especially in extreme cases. The essential meaning of SVM parameters are explained.2. In Chapter 3, a modified model for regulation parameter selection is founded based on the model of K.Schittkowski and Dong. The root of numerical instability of K.Schittkowski's model is analyzed and the need for new methods is justified.3. In Chapter 4, the differences between L₁SVM and L₂-SVM. Based on a new generalization bound, a method to select multiple parameters for L₁-SVM is proposed and numerical experiments are presented. More on algorithm efficiency and development are explored. A stochastic algorithm is presented to select multiple parameters.4. In Chapter 5, a original algorithm to solve SVM model is proposed. It is based on the differential equations theory and calculate the optimal path of SVM parameter. By employing the theorem on existence and uniqueness of solutions, the existence and uniqueness of path is proved. A method of solving ordinary differential equation systems is proposed to get the trajectory of SVM solutions.The existence and uniqueness of parameter path got in Chapter 5 introduces a new way to train SVM. Further, it proves that the process of training is controllable. Numerical experiments show this algorithm works well. Because more efforts still should be made on this direction, in both theory and algorithm, it is hopeful that the method may open a new field in SVM research.