Geometrical Bisection Methods In Kernelized Space And Fuzzy Support Vector Machine

Support vector machine is a new learning method developed in recent years based on the foundations of Statistical Learning Theory (SLT). It is gaining popularity due to many attractive features and promising empirical performance in the fields of small-sample statistics, nonlinear and high dimensional pattern recognition. Because of their excellent learning performance, they have successful applications in many fields, such as: face detection, handwriting digit recognition, text auto-categorization, etc.But as a new technique, SVM also have many shortcomings that need to be researched. In this paper, we have proposed several developed SVM algorithms on (Extended) Geometrical Bisection Method (GBM) and Fuzzy Support Vector Machine (FSVM). The main works are as follows:Firstly, Geometric analysis is given on compressed convex hull determined by the EGBM in this paper, and then the corresponding approximately linear separable support vector machine is proposed. This SVM can change the approximately linear separable problem to the strict linear separable problem, and can be generalized to solve the nonlinear separable problem by choosing a proper kernel function, which deduces the corresponding nonlinear SVM based on the EGBM. Thus it shows better generalization of the method.Secondly, we developed two new classifiers: the kernelized geometrical bisection method and its extended version. The derivation of methods is based on the so-called"kernel trick"and GBM (EGBM). The algorithms can solve nonlinearly separable problem, and also improve the training accuracy and the computation robustness even for approximately linearly separable data. Computational experiments show that the proposed algorithms are more competitive and effective than the well-known conventional methods.Finally, a new Fuzzy Support Vector Machine of Dismissing Margin (DMFSVM) based on the idea of class-center is proposed aiming at the outliers and noises appeared in the large quantity samples with fuzzy membership. The new algorithm has weeded out some training samples which isn't possible support vectors and adopted a fuzzy membership function of decreasing semi-Cauchy type, which is suit for the performance of FSVM. Experimental results show that the number of training samples is reduced, which means the consumption of EMS memory is decreased and the amount of computation is reduced, but training speed is increased. And also it can avoid the bad affect of the outliers and noises in the training samples.