Fuzzy Support Vector Machine Using Function Linear Membership and Exponential with Mahanalobis Distance

Abstract

Support vector machine (SVM) is one of effective biner classification technic with structural risk minimization (SRM) principle. SVM method is known as one of successful method in classification technic. But the real-life data problem lies in the occurrence of noise and outlier. Noise will create confusion for the SVM when the data is being processed. On this research, SVM is being developed by adding its fuzzy membership function to lessen the noise and outlier effect in data when trying to figure out the hyperplane solution. Distance calculation is also being considered while determining fuzzy value because it is a basic thing in determining the proximity between data elements, which in general is built depending on the distance between the point into the real class mass center. Fuzzy support vector machine (FSVM) uses Mahalanobis distances with the goal of finding the best hyperplane by separating data between defined classes. The data used will be going over trial for several dividing partition percentage transforming into training set and testing set. Although theoretically FSVM is able to overcome noise and outliers, the results show that the accuracy of FSVM, namely 0.017170689 and 0.018668421, is lower than the accuracy of the classical SVM method, which is 0.018838348. The existence of fuzzy membership function is extremely influential in deciding the best hyperplane. Based on that, determining the correct fuzzy membership is critical in FSVM problem.

Keywords

• support vector machine (svm)
• fuzzy support vector machine (fsvm)
• polynomial kernel
• mahalanobis distance