Centered kernel alignment inspired fuzzy support vector machine

Support vector machine (SVM) is a theoretically well motivated algorithm developed from statistical learning theory which has shown impressive performance in many fields. In spite of its success, it still suffers from the noise sensitivity problem originating from the assumption that each training point has equal importance or weight in the training process. To relax this problem, the SVM was extended to the fuzzy SVM (FSVM) by applying a fuzzy membership to each training point such that different training points can make different contributions to the learning of the decision surface. Although well-determined fuzzy memberships can improve classification performance, there are no general guidelines for their construction. In this paper, inspired by the centered kernel alignment (CKA), which measures the degree of similarity between two kernels (or kernel matrices), we propose a new fuzzy membership function calculation method in which a heuristic function derived from the CKA is used to calculate the dependence between a data point and its associated label. Although the CKA induced FSVM is similar to the kernel target alignment (KTA) induced FSVM, there is actually a critical difference. Without that centering, the definition of alignment does not correlate well with the performance of learning machines. Extensive experiments are performed on real-world data sets from the UCI benchmark repository and the application domain of computational biology which validate the superiority of the proposed FSVM model in terms of several classification performance measures.