Structural inequality in higher education performance: unsupervised profiling of 452,020 Colombian Saber Pro students using UMAP and K-means

Abstract This study applies a large-scale unsupervised learning pipeline to Saber Pro microdata from 452,020 Colombian higher education students (2021 to 2023), integrating academic performance across five modules with socioeconomic, financing, labor, digital-asset, and educational-background variables. K-means, Gaussian Mixture Models, DBSCAN, and HDBSCAN were evaluated on UMAP-reduced representations across 128 configurations, using a two-phase design: hyperparameter search on a validated 200,000-record stratified sample, followed by retraining on the full dataset. An ablation study confirmed UMAP’s necessity (4.5× higher Silhouette than the original 32-dimensional space). The selected K-means K = 8 configuration showed internal validity indices (Silhouette = 0.428, Davies-Bouldin = 0.74) indistinguishable from those obtained on permuted null data, and moderate stability under the most conservative replication protocol (mean ARI = 0.506, SD = 0.085, across 15 reruns varying both UMAP seed and fitting subsample); the profiles’ structural meaningfulness is instead supported by their convergence with independently documented regional inequality patterns (geographic external validation). Eight structurally differentiated profiles emerged, ranging from severe digital exclusion in frontier territories (mean score 136.30) to high-performing students (205.28), with intermediate profiles defined by financing dependence, parental education asymmetries, and working-hour constraints. The contrast between DBSCAN’s highest Silhouette (0.828, with 98.8% of observations classified as noise) and the selected solution illustrates the importance of distinguishing statistical optimization from institutional usability. Profile alignment with known regional inequalities, without geographic variables in clustering, provides external validity. Findings support three differentiated intervention tiers: structural equity interventions, preventive academic supports, and enrichment pathways.