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

Abstract: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 ($\beta_0$) 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 $\beta_0$-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 $\beta_0$-based segmentation than in time-based segmentation, reflecting a marked behavioral collapse where engaged learners rapidly disengage. We interpret this as evidence that final-period behavior reflects rather than causes outcomes: students who will pass maintain engagement, while those who will fail disengage. This reframes the value of $\beta_0$: rather than improving prediction, change points identify intervention windows. These are periods where behavioral structure shifts and targeted support may be most effective.

Computers and Society (cs.CY); Machine Learning (cs.LG)

arXiv:2609.32094 [cs.CY]

(or arXiv:2609.32094v1 [cs.CY] for this version)

https://doi.org/10.48550/arXiv.2609.32094 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

Innovations in Analytics of Learning Dynamics (TNA 2026), CCIS vol. 3079, pp. 62-74, Springer, 2026

https://doi.org/10.1007/978-3-032-34157-0_5 Focus to learn more DOI(s) linking to related resources

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