Fuzzy Support Vector Machine using Hausdorff distance

Abstract

Support Vector Machine (SVM) is one of the most widely used classification algorithms. It is found that soft margin SVM like C-SVM, in the presence of outliers and class imbalance, give suboptimal results. Fuzzy SVM (FSVM) and class imbalance learning (CIL) appears to solve these problems of outliers and class imbalance respectively. The strength of FSVM in absorbing the effect of outliers strongly depends on how well we assign fuzzy membership values to the training samples. In this paper, we present a novel method for assigning these fuzzy membership values. The objective of our method is to assign membership values in the range (0, 1) to only those samples which are possibly outliers and not otherwise. For this, first density based clustering is performed to find the probable outliers and then assign them membership values based on one of the two heuristics. The heuristics use Hausdorff distance of the probable outliers from their own class. The proposed method was evaluated on three real world datasets. The proposed method gave consistently good results as compared to older methods; hence the method can be seen as a potential tool for classifying noisy datasets.