Fuzzy Membership Function Based on Structural Information of Data

Abstract

Membership function based on affinity among samples considers not only the distance between samples and its center, but also the relationship among samples. However it ignores the structural distribution of samples in different classes and the influences of between-class distance on membership. Therefore, this paper proposed an improved membership function, named fuzzy membership function based on structure information of data, which incorporates structural distribution and between-class distance into the calculation of membership. The main idea is to find the optimal hyper-sphere for the positive and negative samples respectively by support vector data description method and give a reduction ratio for samples out of sphere according to the between-class distance. Numerical experiments demonstrate that the proposed membership function is consistent with the practical application, and it can significantly improve the classification performance of fuzzy support vector machine.