Several Improved SVMs

Support Vector Machine or SVM is a new machine learning technique developed from the middle of 1990s. Being different from traditional Neural Network or NN, NN is based on mordern statistics theory, which provides conclusion only for the situation where sample size is tending to infinity, while SVM is based on mordern Statistical Learning Theory or SLT, which is a small-sample statistics and concerns mainly the statistics principles when sample are limited, especially the properties of learning procedure. SLT provides us a new framework for the general learning problem. A large number of experiments have shown that SVM has not only simple structure, but also better performances, especially better generalization ability. SVM can also solve small-sample learning problem better, and through kernel function we can transfer a nonlinear problem to a linear problem. Currently, SVM is becoming a new hot area in the field of machine learning in the world.In this dissertation, we have induced severel developed SVM algorithms. The mian work are as follows: first, we have systematically discussed machine learning problem, which is the basic of SVM, with Statistical Learning Theory or SLT, especially the Vapnik's theory; second, two new SVMs are presented to solve the approximately linear separable problem of pattern recognition, and we compare the new SVMs to the known SVMs through theoretical and practical analysis, and show the advantages and rationality of the new SVMs; third, to the convex hulls having nonequilibrium trainingsets, through compressing or enlarging the two convex hulls, we can get the tangent of them, which seems to be a better separating hyperplane. Finally, we introduce the Bhattacharyya kernel function based on distribution, estimate the parameters of kernel by Bayesian method, and compare the new SVM based on the kernel with the old one.