Research On Support Vector Machine Classifier And Its Bayesian Framework

Currently, the support vector machine (SVM) which based on statistical learning theory is a research hotspot. It has many merits, such as good generalization performance, resolving non-linear problem, sparse presentation and global optimal solution etc. But standard classification model and parameters selection should be researched still, and the main work in this thesis is as follow:(1) From support vectors view, the method of pre-extracting support vectors based on concentric hyperspheres division is proposed. The extracted support vectors can be trained instead of total data set, so computational cost will be reduced.(2) The loss function is very important to risk functional of the SVM. Various SVMs can be constructed with different loss functions. In this thesis, some improvements are given for trigonometric function, and the primal and dual problem of corresponding SVM are deduced.(3) Ensemble learning is a research hotspot in machine learning, which can improve generalization performance of classification algorithm. In this thesis, Boosting is introduced to the SVM, and support vector machines combination classifier is proposed.(4) Bayesian framework for support vector machine in classification is theoretically described. Due to the duality between reproducing kernel Hilbert space and stochastic processes, Bayesian framework can be designed for support vector machines with Gaussian process. Therefore, optimal parameters of the SVM can be selected by Bayesian method.