Enhanced Functional Connectivity for EEG Classification with a Modified Maximum Entropy Model: A Case Study of Alzheimer's Disease

Accurate characterization of functional connectivity (FC) in neural signals is critical for investigating a wide range of brain disorders and cognitive processes. Conventional approaches typically rely on correlation-based metrics to capture pairwise interactions; however, such measures may fail to capture more global patterns of connectivity. Pairwise Maximum Entropy Models (pMEM) a complementary global perspective by jointly modeling all pairwise interactions, but they can diverge significantly from traditional linear FC measures and are often prone to numerical instability. In this study, we propose a penalized pMEM framework that incorporates correlation-based FC into pMEM as a prior constraint, aiming to balance the global coupling captured by pMEM with the interpretability and simplicity of correlation-based approaches. By regulating the adherence of pMEM parameters to traditional FC, our method achieves more stable learning and better preserves key linear relationships. We evaluate the proposed framework using a public available EEG dataset comprising individuals with Alzheimer's disease and healthy controls. The proposed hybrid modelling of FC achieves a classification accuracy of 83.13%, outperforming both standalone pMEM and correlation-based classifiers. Furthermore, the penalized pMEM reveals more pronounced group difference in network small-worldness, offering improved interpretability alongside enhanced classification performance.