Modelos de programação matemática para aprendizado não supervisionado e suas aplicações na clusterização de dados de escolas brasileiras

The analysis of educational data is essential for understanding the performance of educational institutions and identifying areas for improvement. In this context, data clustering is a widely used tool, particularly with algorithms modeled as mathematical programming problems. This paper proposes the use and implementation of three unsupervised learning algorithms, modeled with Binary Integer Programming and Mixed-Integer Linear Programming, for clustering data on the average performance of Brazilian schools in the National High School Exam, published by the National Institute for Educational Studies and Research Anísio Teixeira. The aim is to validate the models by investigating the characteristics of the institutions in each cluster, comparing their Socio-Economic Level Indicator and their administrative dependence with their school performance. The results found point to the superior performance of federal public schools and private schools when compared to municipal and state public schools.