Visibility graph analysis for educational data: potentials and a case study of predicting at-risk online students

This paper introduces visibility graph analysis as a supplementary approach for examining educational time series data, particularly in online learning environments. By converting temporal data into graph representations, we uncover previously hidden patterns and relationships in student interactions, enabling more effective analysis, classification, and prediction of learning outcomes. Through a rigorous case study using the Open University Learning Analytics Dataset, we demonstrate how visibility graph metrics can accurately predict at-risk online students based on their clickstream patterns, achieving classification accuracy exceeding 87% using gradient boosting algorithms. Our novel methodology outperforms several recent deep learning approaches while providing interpretable insights about student behavior through graph-theoretical features such as global efficiency, assortativity coefficient, and betweenness centrality. This research establishes visibility graph analysis as an innovative tool in educational data mining that complements traditional machine learning techniques, opening new avenues for early intervention strategies and personalized learning pathways. However, accurately modeling the problem and selecting the appropriate type of visibility graph for the educational time series data remains dependent on the researcher's knowledge.