A Study On Fuzzy Support Vector Machine

Pattern recognition techniques,traditionally including decision tree,discriminant analysis,neural network,have a lot of applications in many fields such as character recognition,voice recognition,fingerprint recognition,etc.Due to the limitations of small samples,difficulties in finding global optimal solution and nonlinearization,traditional techniques are not always satisfactory in many applications.As a result,support vector machine based on statistical learning theory begins to catch people's attention.Support vector machine has great generalization ability among so many pattern recognition techniques that it performs much better in many small-sample,nonlinear and high-dimension problems than other techniques.Since fuzzy theory was introduced several years ago,the generalization ability of support vector machine has improved.The following is the summarization of this study:(1)Theoretical foundation of statistical learning theory is summarized,and most frequently used support vector machine algorithms in two-class classification problem and the resolution of unclassified regions in multi-class problem are introduced.(2)Nonparametric kernel density estimation method and the solve-the-equation plugin method in its bandwidth estimation are introduced in detail,laying the foundation for studying fuzzy support vector machine.(3)Kernel density estimation method is successfully applied to support vector machine and a new fuzzy support vector machine——density-based fuzzy support vector machine(DBFSVM) is proposed.This method takes the advantage of not knowing the explicit form of nonlinear mappingφ(x) in standard support vector machines and overcomes the shortcoming of using class center as membership function in fuzzy support vector machines.After the numerical study on UCI machine learning database,the generalization ability of the proposed DBFSVM is proved to improve to some extent.