Weighted Linear Loss Twin Support Vector Clustering

Abstract

Traditional point based clustering methods such as k-means [1], k-median [2], etc. work by partitioning the data into clusters based on the cluster prototype points. These methods perform poorly in case when data is not distributed around several cluster points. In contrast to these, plane based clustering methods such as k-plane clustering [3], local k-proximal plane clustering [4], etc. have been proposed in literature. These methods calculate k cluster center planes and partition the data into k clusters according to the proximity of the datapoints with these k planes. Working on the lines of [5], in this paper, we have presented a Weighted Linear Loss Twin Support Vector Clustering termed as WLL-TWSVC for clustering problems. By introducing the weighted linear loss in the formulation of TWSVC leads to solving system of linear equations with lower computational cost as opposed to solving series of quadratic programming problems along with system of linear equations as in TWSVC. We have also introduces a regularization term in the objective function which takes care of structural risk component along with empirical risk.