Segmentation Model With Respect to the Difference in Means

The aim of the paper is to formulate and solve the following segmentation problem. Given is a population described by independent variables: X1, ... , Xn, (both continuous and categorical), the continuous dependent variable Y and the two-level categorical variable $\alpha$ with levels $\alpha = 1$ and $\alpha = 0$. $\bar{Y}_{\alpha=1}$ and $\bar{Y}_{\alpha=0}$ are the means of $Y$ for observations at levels $\alpha=1$ and $\alpha=0$, respectively. The goal is to create the segments of the population, described by the independent variables, that the difference in means $\bar{Y}_{\alpha=1}-\bar{Y}_{\alpha=0}$ is the feature that distinguishes the segments. I. e. the means should be as different as possible between segments and should be similar within the segment. The solution is based on regression trees approach.