A generalized goal programming model for parsimonious robust clusterwise linear regression

In the last decades, clusterwise regression has received considerable attention. Existence of outliers in the dataset and/or usage of unimportant explanatory variables in fitting the regression lines can lead to inaccurate clustering and regression lines. In this paper, we propose a Mixed Integer Programming (MIP) model to obtain a parsimonious robust clusterwise linear regression. The proposed model also can determine the number of homogenous clusters in the dataset and detect the outliers. The proposed model is applied on some datasets and the results are promising. Also, the performance of the model is evaluated using a simulation study.