Qualitative data clustering: a new Integer Linear Programming model

Qualitative data clustering is a fundamental data analysis task, with applications in many areas, like medicine, sociology, and economics. An appealing way to deal with this task is via Integer Linear Programming, as it avoids inappropriate inferences by the final user. This approach has two main advantages: the data are directly used, without the need of being converted to quantitative values, and the optimal number of clusters is automatically obtained by solving the optimization problem. However, it might create large and redundant models, which can limit the size of the problems it can be applied. Recently, models that are more compact and able to avoid some redundancy have been proposed in the literature. These models consume less memory and are faster to obtain the optimal solution set. In this study, a new model is introduced and compared with the state-of-the-art alternatives using datasets from different application domains. Empirical results show that the new model outperforms its predecessors, achieving the optimal solution set with lower computational time and memory consumption.