Fuzzy Support Vector Machines

Support vector machines(SVM),which was proposed byVapnik and some others, is a method of machine learning accordingto the statistical learning theory. It is based on VC dimension andstructural risk minimization principle. Kernel function is used to mapthe non-linear separable data into a higher dimensional feature space.So it can be separate in the higher dimensional feature space. Mean-while, using kernel function to calculate inner product that can avoid"dimension disaster". Because SVM has better generalization andlearning power, this technology has turned into the topic of machinelearning, and also gained successful applications in many fields, suchas pattern recognition, image classification, forecasting and so on.But as a new technology, SVM, which still has some limitations.There is lots of fuzzy information in the objective world. If the noisesor outliers exists in the training set of SVM, these"abnormal"samplesalways close to classification surface. So the gained classification sur-face is not the true optimal classification surface. Fuzzy support vectormachines is presented by Lin, then the corresponding membership isgiven according to di?erent input data a?ects on the classification re-sults. So this method e?ectively distinguishes between the noises oroutliers and the valid samples. Although FSVM is perfect than tradi-tional SVM, the definition of membership function is the diffculty ofFSVM.At present, there is not unified method that determine fuzzy mem-bership function, one-class classification algorithm based on liner pro-gramming is used to determine membership in this paper. It not onlythink over the distance between the sample to class center, but alsothink over how much the sample belong to the class. So this methodcan improve classification result. First, structural principle and basictheory of SVM are analyzed and researched in this paper. Second, definitive methods of existing membership are discoursed. On the ba-sis of the one-class classification algorithm of linear programming isproposed to determine membership. At last, contrastive experimentof FSVM classification and traditional SVM classification is given. Ex-perimental results indicate that fuzzy support vector machines yieldsbetter classification result than the traditional SVM, thus the effectsof the noise or outliers can be diminishes.