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

Asynchronous online learning offers temporal flexibility at a structural cost: learning communities tend to fragment rather than cohere. $β_0$, the number of disconnected behavioral clusters from Zigzag Persistent Homology, serves as a cohort-level indicator of this structure. Two questions remained unverified at scale: (1) does apparent $β_0$ convergence reflect genuine behavioral alignment or learner dropout? and (2) do assessment deadlines produce reproducible fragmentation-convergence cycles? We address both across all 22 OULAD courses (N > 22,000; 857 week-pairs). Changes in $β_0$ strongly co-vary with active learner changes (pooled r = 0.387; median per-course r_delta = 0.459, 20/22 courses), identifying $β_0$ as a participation-sensitive indicator: $β_0$ and active learner counts co-respond to deadline events rather than one causing the other. Deadlines produced fragmentation in 82.6% of assessments and the full Fragment First, Converge Later (FFCL) cycle in 60.2%. 3-phase analysis confirmed structural fragmentation as the dominant long-term trajectory (90.9% of courses), moderated by curriculum structure. These findings establish $β_0$ as a participation-sensitive structural indicator with direct implications for AI-augmented learning analytics design.

Student dropout is a persistent concern in Learning Analytics, yet comparative studies frequently evaluate predictive models under heterogeneous protocols, prioritizing discrimination over temporal interpretability and calibration. This study introduces a survival-oriented benchmark for temporal dropout risk modelling using the Open University Learning Analytics Dataset (OULAD). Two arms are compared: Family A: Dynamic Weekly, with models in person-period representation, and Family B: Static Early-Window, with an expanded roster of families: tree-based survival, parametric, and neural models. The evaluation protocol integrates four analytical layers: predictive performance, ablation, explainability, and calibration. Results are reported within each family separately, because a single numerical cross-family ranking would conflate genuine model differences with artifacts of temporal representation, to which survival metrics are known to be sensitive. Within Family B, Random Survival Forest showed the highest point estimates for time-dependent concordance and the lowest Brier scores across all three horizons; within Family A, Poisson Piecewise-Exponential showed the lowest point estimate for integrated Brier score within a tight five-model cluster. No-refit bootstrap resampling qualifies these positions as directional signals, not claims of strict superiority. Ablation and explainability analyses converged, across all models, on a shared finding: the dominant predictive signal was not primarily demographic or structural, but temporal and behavioral. Calibration corroborated this pattern in the better-discriminating models, except for XGBoost AFT, the sole outlier (analyzed in the Discussion). These results support unified, multi-dimensional benchmarking in Learning Analytics and situate dropout risk as a temporal-behavioral process rather than a function of static background attributes.

Learning analytics often treats unsupervised clusters of intelligent tutoring system (ITS) logs as learner types that should predict learning. We test that assumption on EdNet-KT3. Clustering study-strategy features (resource use, revision, video, problem practice) for 5{,}000 active learners yields a silhouette-selected parent cut ($k=5$) with 4 contrast poles (reading-focused, video-heavy, revision-heavy, and problem-first) plus a large near-mean residual ($\sim$64.9%). Reclustering that residual adds four finer styles, giving a bootstrap-stable hierarchy of 8 named strategies. We split each learner's timeline by respond count so clusters use only the early half and outcomes only the late half. Early clusters predict later engagement (continuing to practice and finishing late sessions, especially persistence, $η^{2}\approx 0.106$; completion $η^{2}\approx 0.021$) but not later unassisted accuracy (correctness on late first-attempts without help; $p_{\mathrm{adj}}\approx 0.093$). Volume rises with some styles, yet volume-only clustering barely matches strategy labels (ARI$=0.064$). A knowledge-tracing model (SAKT) on the seven TOEIC exam sections predicts next correctness only modestly better than a baseline that knows only how hard each section usually is (AUC lift $+0.051$; CI $[+0.045,+0.058]$), and that mastery signal is nearly independent of behavior styles (ARI$=0.007$). Behavioral clustering here describes study styles and engagement, not knowledge gains.