Studies Of Several Mathematical Models And Algorithms Of Support Vector Machine

With the development of computer and informational technology, more and more price need to be paid for collecting, storing and processing vast data. Consequently, how to find useful information from sets of data becomes a problem need to be solved imminently. Data mining technology comes into being in this background. KDD is a non-trivial process searching for useful, potential and understandable form from sets of data. It involves a lot of intercross subjects and technologies such as machine learning, mathematical programming, statistics, pattern recognition and so on.Mathematical programming is an important branch of operational research. Its applications can be seen in many areas, such as machine learning, networks problem, mechanics. Especially, combining it with data mining makes it possible to solve large-scale and complicated problems and it has also been successfully applied to feature selection, clustering and regression. Support vector machine is one of the important results of applying mathematical programming to data mining and it is a machine learning method that was brought out by V.Vapnik according to statistic theory.This paper mainly studies two problems of machine learning. One of them is a fundamental problem of machine learning, i.e.,misclassification minimization. Since the objective function is not differentiable, a convex entropy function is used to solve the problem, and the beautiful proximal solution is achieved through the algorithm of the convex programming.Till now, the studies of SVM is mainly on standard model, few issues related to SVM with square cost function, which is the other problem studied in this paper, have been seen. In this paper, the performance of SVM with square cost function is compared with that of the standard SVM, and some results are obtained. When the two-class problem samples are very unbalanced, SVM has a poor performance. According to the analysis of the support vector machine theory, an improved SVM is presented based on one of quasi-Newton algorithms (DFP).