The Research Of Semi-Definite Programming SVM

The selection of model parameters which directly determine the form and complexity of Support Vector Machines classifier and influence the classification accuracy and generalization ability of SVM model is a front-line widely-interested issue in the study of SVM. The traditional kernel parameters selection lacks of theoretical support, needs too much number of iterations and calculated amount, spends too much time, and the actual result is not always desired. This paper focuses on the optimization of SVM using semi-definite programming. Main results of the research are:Firstly, to distinguish the validity of a given set of kernel parameters using semi-definite programming combination coefficients by which we can calculate a better kernel matrix and improve the classification accuracy and generalization ability of SVM, realize the selection of kernel parameters using semi-definite programming.Secondly, an optimization of kernel functions through semi-definite programming is present. It transforms the selection of Heterogeneous or Homogeneous Kernel functions to a semi-definite programming optimization problem, and get a better kernel function by combining simple one with effective kernel parameters. The experimental result shows the generalization ability of Homogeneous Kernel SVM is superior to Heterogeneous kernel SVM.Thirdly, in the study of large-scale datasets, the time consuming and the calculated complexity of solving combination coefficients with semi-definite programming is serious. Against problems above, tow methods to reduce large-scale training datasets of semi-definite programming SVM is proposed. One is through kernel clustering, the other is using interior-point algorithm. They both decrease the scale of solving semi-definite programming problem by extracting margin support vectors and eliminating non support ones. The experiments on the UCI datasets shows the two optimization methods improve the solving efficiency and maintain the classification accuracy of SVM at the same time.