The Study Of The Relevant Techniques In Fuzzy Support Vector Machines

In order to solve the overfitting, unclassifiable regions and time consuming for training in Support Vector Machines (SVMs), four kinds of improved Fuzzy Support Vector Machines(FSVMs) are proposed in this paper.FSVMs based on λ-cut are proposed. The first improved learning machines are the FSVMs based on the edge training data in each class. The learning machines combine FSVMs with the theory of fuzzy set, extract some data from the entire training data to form the reduced training set, and then construct the FSVM on the reduced training set. Firstly, the membership functions are defined with the distances between the training data and their class centers, then the membership functions map training data from each class into a spherical region. The training set becomes the fuzzy training set in which each training datum includes samples' features, label and membership degree. Secondly, the more important training data extracted from the original training set by using the suitable parameter λ are used to form λ - FSVMs. Thirdly, the learning machines are extended to multi-class problems by using the Decision Directed Acyclic Graph (DDAG) strategy.FSVMs based on linear clustering are proposed. The training data close to the hyperplane are extracted to form the improved learning machines by using linear clustering. Firstly, the learning machines select the most typical samples, such as the centers of two classes, to form the coarse classification hyperplane of SVMs named preformed hyperplane. The membership functions are defined with the distances between the training data and the preformed hyperplane, and all the training data are mapped into the zonal area. Secondly, the data closed to the preformed hyperplane by reducing the zonal area are used to form FSVMs. Thirdly, the learning machines are extended to multi-class problems by using one-against-one strategy.FSVMs based on spherical regions are proposed. The reduced training set is used to form the learning machines. Firstly, the center of the spherical region is selected based on the entire training set. Because the training set maybe is imbalance, middle points of two class centers are defined as the center of the spherical region. Secondly, in each class, the membership function is defined with the distance betweenthe training data and the center. Thirdly, the reduced training set obtained by the suitable parameter is used to form the proposed FSVMs.FSVMs based on clustering are proposed. There are many clustering techniques, such as fuzzy c-means (FCM) clustering, density clustering, which can be used in SVMs. In this paper, we select the classic FCM clustering technique to reduce the number of training data. These learning machines partition the training data into many clusters by using FCM clustering. Each cluster is made up of the similar training data. The reduced training set consisting of the centers of these clusters is used to form the improved FSVMs. During clustering, because of sparseness of support vectors, the sparse training data lying in the edge of each class become the center of cluster independently. So the reduced training set affects neither the edge training data nor the performance of FSVMs.