A GCN and Autoencoder-based Framework for Fine-Grained Diagnosis of Learners' Cognitive Structures

Accurately diagnosing fine-grained differences in learners' cognitive structures, which arise from their understanding of interdependencies among knowledge concepts, remains a significant challenge in intelligent education. To address this gap, this paper introduces a novel cognitive diagnosis framework that integrates Graph Convolutional Networks (GCNs) with autoencoders. The framework explicitly models the educational prerequisite relationships within a knowledge concept map to infer the structural features of a learner's cognition. The concept map is first embedded into a structural matrix using struc2vec. A two-layer GCN then refines this matrix by integrating individual learners' performance data, obtained via the Attribute Hierarchy Method (AHM), to generate a cognitive structure representation. Subsequently, a deep autoencoder compresses this representation into a low-dimensional vector, enabling the derivation of a cognitive structure coefficient for diagnosing mastery of individual knowledge points. Empirical validation on two real-world course datasets shows that the proposed method achieves a significantly higher correlation with final exam scores (Pearson's r = .803, p < .01) than traditional methods. Crucially, it effectively discriminates distinct cognitive profiles among learners with identical test scores, providing the granularity essential for personalized learning interventions.