Mathematical modeling of clustering based on the results of monitoring the activities of educational institutions of higher education

The article discusses the application of mathematical modeling and cluster analysis methods for processing monitoring data on the activities of educational institutions of higher education. The relevance of the research is determined by the need for an objective assessment of the effectiveness of universities, the identification of problem areas and the development of targeted management solutions. The paper analyzes key indicators, including educational, research, international, financial and economic activities, as well as the salary level of teachers. The main focus is on clustering methods that allow universities to be grouped according to similar characteristics. Hierarchical, centroid, and density algorithms are considered, as well as the specifics of their application in the context of multidimensional educational data. Special importance is attached to the preprocessing of indicators, including normalization and standardization, to ensure the correctness of the results. The clustering quality is assessed using the silhouette index and other metrics, which makes it possible to determine the stability of the selected groups. The results of the study demonstrate that automated clustering of monitoring data helps identify typical university development trajectories, optimize resource management, and develop differentiated support measures. The proposed approach can be integrated into a regular monitoring system, providing operational analytics for management decision-making. The prospects for further research are related to the development of adaptive algorithms, forecasting the dynamics of indicators and the creation of interactive analytical platforms.