Clusterwise Linear Regression with the Least Sum of Absolute Deviations – An MIP Approach

 In this paper, we study the application of mixed-integer programming (MIP) to the clusterwise linear regression (CLR) problem with the least sum of absolute deviations, which is a type of CLR problem that has received both theoretical and practical interests in recent years. We formulate the problem with a big-M formulation and investigate related issues, including the integration of outlier detection into CLR analysis. To improve the global optimization solution, we explore the resolution of breaking the solution symmetry that is prevailing in conventional formulations of many clustering analysis problems. Our numerical studies on randomly generated problem instances and two real data sets offer insights into the computational performance of solving the MIP formulations.