Noise-Aware Graph-Based Cognitive Diagnostic Framework Through Low-Rank Alignment

Graph Neural Networks (GNNs) have effectively improved the performance of Cognitive Diagnosis Models (CDMs). Existing works have proposed a series of Graph-based Cognitive Diagnosis Frameworks (GCDFs) to enhance robustness to noise. However, these robust designs are often general methods for GNNs and are not designed for cognitive diagnosis, which undermines real cognitive information during the denoising process. Interestingly, a noteworthy phenomenon has been overlooked: even without robustness designs, GCDFs can still learn correct information in noisy environments. In this paper, we conduct a comprehensive empirical analysis of this issue. We found that noise primarily accumulates in lower singular components. Even in noisy environments, the principal subspaces of representations still remain stable. Based on these findings, we propose a Noise-aware Cognitive Diagnostic framework based on Low-rank Alignment, named NCDLA. The framework first performs low-rank reconstruction of the interaction matrix between students and exercises, retaining only larger singular values to achieve noise reduction. Then, the reconstructed interaction matrix and the original interaction matrix are combined with the Q matrix to form a noise-reduced heterogeneous graph and an original heterogeneous graph. In order to distinguish between the interaction patterns of correct and incorrect responses, we decompose the heterogeneous graph according to the type of response. NCDLA achieves denoising of student representations and exercises representations through a self-supervised strategy based on low-rank reconstruction and a spectral anchor regularisation method. Extensive experiments on three datasets demonstrate that NCDLA achieves optimal prediction performance and robustness.