Fuzzy Support Vector Machine Based On The New Membership Function

Support vector machine is a kind of new learning method proposed by Vapnik according to the statistical learning theory. The biggest characteristic of SVM is that it overcomes the traditional classification problems including dimension disaster, the local minimization and the over-fitting problem through the structural risk minimization rule. It still provides high generalization ability in the small sample, so that it has attracted a lot of interest.At first, the mathematical model of SVM is introduced. Through the two groups of data, we can find a unique optimal hyperplane. It can make the two groups of sample data in the greatest degree of separate. In order to solve the optimization problem, we can build a quadratic programming. Though the sample training, we can get the decision function. The non-classified sample can be classified by the decision function. If in the model above, we introduce the concept of the membership, it will become the support vector machine formed with the fuzzy information.In the fuzzy support vector machine, membership function plays a very important role and determines the performance of the algorithm to some extent. Support vectors generally are located on the edge of each class and play an important role in the determination of the optimal hyperplane. According to this characteristic, we proposes a new membership function which is combined with the distance and angle so that the sample data closer to the edge of class and normal vector has a larger membership. In addition, based on this idea, we adjust the method of the sample data pretreatment. Then combined with the approach of the minimum sphere radius, we can complement and optimize the model. It can be seen by simulation that the fuzzy support vector machine with the new membership function is accurate, fast and efficient and can improve the original model to some extent. For the uncertain problems, we introduce two solutions:dual membership and posteriori probability. These two methods can classified the existing sample data correctly based on the mathematical model. And it can give the new sample data the right class using the decision function.