Methods for discovering patterns based on cluster analysis and big data of secondary education institutions

Abstract

Context and relevance. The digitalization of education generates large volumes of learning-activity data containing patterns inaccessible to traditional statistical methods limited to aggregated performance indicators. Deep learning can extract latent patterns from data structure. Objective. To develop and compare student’s vector representation approaches from examination results for cluster analysis and latent-pattern discovery. Hypothesis. Big data on examination results contain patterns not reducible to aggregated performance indicators, and neural-network methods can capture them as vector representations suitable for clustering. Methods and materials. Data from the GIA-9 and GIA-11 examinations for 2023–2025 were used (11 subjects, approximately 5,000 students and 500,000 interactions). Three approaches were compared: a baseline on aggregated scores (Score stats), a variational autoencoder (VAE), and a masked autoencoder (MAE), including a version trained with a contrastive loss. Clustering was performed with HDBSCAN after dimensionality reduction (PCA); quality was assessed with internal metrics (silhouette coefficient, DBCV) and t-SNE visualization. Results. Score stats yields a stable partition reflecting examination type, subject set, and performance. VAE achieves high internal-metric values under aggressive dimensionality reduction, but its clusters are determined by the interaction-sequence length. MAE without a contrastive loss does not produce meaningful clusters; with it, the metrics reach the Score stats level, and the clusters group students by characteristic combinations of jointly chosen examinations. Conclusions. MAE with a contrastive loss extracts latent student characteristics, not reducible to aggregated indicators, from big educational data. The approaches are applicable to state examination data for categorizing students and supporting decision-making.