Some Research On Support Vector Machine

Statistical learning theory (SLT) is the best of statistical theory of estimation and prediction with small sample at present, which has been considered to be an important complement and development of traditional statistics. Support vector machine (SVM) is a novel machine learning method based on the framework of statistical learning theory by Vapnik etc. Unlike other machine learning algorithms, which are only considered minimizing the empirical risk function, SVM makes use of structural risk minimization principle to train learning machine and measures structure risk by VC -dimension theory. SVM can better solve some practical problems with small sample, non-linearity, high-dimension and local minimization of Neural network algorithm, because of the very simple structure and excellent learning performance, SVM has wide applications in many fields, such as pattern recognition, regression estimation, density estimation and so on.In this paper, statistical learning theory is introduced, which is the foundation of support vector machine. Two problems are mainly discussed here: Firstly, support vector machine' 7th-order smoothing function is studied and the analysis of its approximation accuracy is given, which show that the approximation accuracy of this new smoothing function for further study on the SVM is competitive compared to previous conclusion. Secondly, density function estimation based on Multi-kernel weighted Support Vector Machine is studied using P methods since the density function estimation is an ill-posed problem, and the method we present is better than the standard SVM.