A reproducible two level clustering framework for profiling cognitive performance and stratifying the lowest performing group in higher education

Cognitive ability in higher education is multidimensional and varies continuously across large cohorts, making it inappropriate to interpret data-driven clusters as naturally discrete or ordinally ranked psychological categories. This study proposes a leakage-controlled framework for reproducible operational cognitive profiling using multidimensional item response theory ability estimates in logical reasoning, abstraction, and verbal reasoning. A higher education cohort was partitioned into training ( n = 29,449) and held-out test ( n = 7,364) sets, and all transformations, clustering boundaries, and profile labels were derived from the training partition and transferred unchanged to the test partition. At the first level, k-means clustering ( k = 4), selected using a composite ranking of the Silhouette, Davies–Bouldin, and Calinski–Harabasz indices, identified four profiles characterised by centroid shape rather than severity: uniformly lower, logic-dominant, verbal-abstraction dominant, and uniformly higher. The crossing of the logic-dominant and verbal-abstraction dominant profiles demonstrated that cognitive performance cannot be represented by a single ordinal severity continuum. The uniformly lower profile was further refined into four domain-specific sub-profiles. PERMANOVA indicated substantial multivariate separation (pseudo- F = 10,798, R ² = 0.524), with logical reasoning contributing most strongly to profile differentiation (η² = 0.81). Hierarchical label recovery reconstructed profile assignments on held-out data with approximately 98% accuracy, while a simple baseline achieved comparable performance, demonstrating reproducibility of the assignment rule under leakage control rather than psychological validation. The proposed framework provides an interpretable and computationally scalable approach for operational cognitive profiling to support differentiated educational interventions.