Análisis topológico del indicador socioeconómico de los estudiantes de Escuela Superior Politécnica del Litoral

Abstract

CONDITION FOR PROJECT PUBLICATION. This research analyzes the socioeconomic structure of students at the Escuela Superior Politécnica del Litoral (ESPOL) using Topological Data Analysis (TDA) tools. The central objective is to propose a vulnerability indicator that captures nonlinear relationships and complex structures, overcoming the limitations of traditional statistical methods. The study is justified by the need to identify atypical student profiles to optimize the design of institutional welfare policies. For this work, data from the institutional socioeconomic survey were processed. Persistent homology was applied to identify structural invariants, and the G-Mapper algorithm was used to visualize the topological network. The process included Anderson-Darling normality tests for optimized interval selection and the Isolation Forest algorithm for anomaly detection. The results demonstrated that geographic variables such as place of residence act as fundamental pillars of the model, as their omission led to the disappearance of significant topological cycles. Furthermore, the proposed approach identified vulnerability niches that remained hidden beneath the conventional statistical average. It is concluded that Topological Data Analysis constitutes a robust tool for detailed population segmentation, facilitating a more precise institutional intervention. Keywords: Topological Data Analysis, G-Mapper, Socioeconomic Vulnerability, Isolation Forest, Persistent Homology.