Fuzzy semi-supervised weighted linear loss twin support vector clustering

Abstract

In this paper, we propose two variants of Weighted Linear Loss Twin Support Vector Clustering (WLL-TWSVC) algorithm for identifying cluster planes. Unlike, Twin Support Vector Clustering (TWSVC) where the solution is obtained by solving a Quadratic Programming Problem (QPP) and a system of linear equations, WLL-TWSVC needs to solve the system of linear equations only. In order to improve the clustering accuracy with the help of limited amount of labeled data, we have extended TWSVC and WLL-TWSVC in the semi-supervised framework which are termed as Laplacian TWSVC (Lap-TWSVC) and Laplacian WLL-TWSVC (Lap-WLL-TWSVC) respectively. Further, to build a robust clustering algorithm which is not sensitive to noise and outliers, we introduce a fuzzy membership matrix and thus extends Lap-WLL-TWSVC to Fuzzy Laplacian WLL-TWSVC. The experimental results on several benchmark UCI datasets indicate that our proposed formulations achieve better clustering accuracy over other state-of-the-art plane-based clustering algorithms with comparatively lesser computational time. As an application to our proposed algorithms, we also perform image segmentation over Berkeley Segmentation dataset.