Period Segmentation in Transition Network Analysis: A Topological Data Analysis Approach

Hitoshi Inoue, Koichi Yasutake

Temporal dynamics in learning behavior can be revealed through period segmentation in Transition Network Analysis (TNA). Cristea et al. demonstrated that segmenting courses into halves and quarters reveals how learning strategies evolve and relate to academic performance. Building on this approach, we investigate whether Topological Data Analysis (TDA), specifically connected components ($β_0$) change points from Zigzag Persistent Homology, can provide data-driven period boundaries that identify intervention windows. Analyzing 22 courses from the Open University Learning Analytics Dataset, we find that $β_0$-based segmentation captures greater between-period variation than time-based segmentation (median variance ratio (VR) = 4.10$\times$; 21/22 courses show VR $>$ 1.1). Permutation tests confirmed significance ($p < 0.05$) in 18% of individual courses, with 73% showing positive improvement over random breakpoints. Only one course showed better performance with time-based segmentation. However, analysis of academic outcomes reveals a key insight: final-period behavior shows lower correlation with outcomes in $β_0$-based segmentation than in time-based segmentation, reflecting a…