New bundle method for clusterwise linear regression utilizing support vector machines

Abstract

<p>Clusterwise linear regression (CLR) aims to simultaneously partition a data into a given number of clusters and find regression coefficients for each cluster. In this paper, we propose a novel approach to solve the CLR problem. The main idea is to utilize the support vector machine (SVM) approach to model the CLR problem by using the SVM for regression to approximate each cluster. This new formulation of CLR is represented as an unconstrained nonsmooth optimization problem, where the objective function is a difference of convex (DC) functions. A method based on the combination of the incremental algorithm and the double bundle method for DC optimization is designed to solve it. Numerical experiments are made to validate the reliability of the new formulation and the efficiency of the proposed method. The results show that the SVM approach is beneficial in solving CLR problems, especially, when there are outliers in data.<br /></p>