Development of Spectral Clustering Algorithm in Cognitive Diagnosis Model: Approach for Student’s Psychological Growth

With the development of intelligent education, the diagnostic performance of the traditional cognitive diagnostic model has been unable to meet the needs of today’s education. This study uses the Gaussian mixture model (GMM) to model and optimize model parameters through maximum probability estimation. The spectral clustering (SC) algorithm iterative optimization was combined with a similarity matrix and Laplacian matrix to construct an improved spectral clustering cognitive diagnosis model. The proposed SC algorithm’s clustering accuracy was 0.95, ARI was 0.86, and FMI was 0.85, and its clustering performance was better than that of other comparison algorithms. The cognitive diagnosis model based on the SC algorithm showed 4.01 SC, and the psychological status score was 3.97. The clustering performance of the model proposed in this study showed a favorable outcome. Moreover, the cognitive diagnosis model based on SC can meet the cognitive diagnosis needs of most students and help improve their cognitive ability. The enhanced cognitive diagnostic model combining SC and the GMM proposed has significant advantages in clustering performance and educational application effects, providing technical support for promoting students’ psychological growth.