A Novel Entropy Metric for Unified Analysis of Temporal, Spatial, and Spectral EEG Properties

Signal complexity analysis plays a crucial role in biomedical research, particularly in electroencephalography (EEG), for early disease diagnosis and cognitive monitoring. However, traditional entropy-basedmethods lack robustness, suffer from limitations such as sensitivity to noise, and fail to capture themulti-frequency structure of brain signals. To address these challenges, this study introduces Multivariate Multiscale Multi-Frequency Entropy (M3FrEn), a novel complexity metric that simultaneously incorporates multiscale dynamics, multichannel dependencies, and multi-frequency structure into a unified entropy-based framework. M3FrEn was evaluated using both simulated signals and real EEG data from 52 healthy subjects and 52 patients with Alzheimer's Disease (AD). Compared to existing entropy-based metrics, simulated tests demonstrated that M3FrEn reliably discriminates signals with varying complexity levels and maintains stability across embedding dimensions and data lengths. Applied to real EEG data, M3FrEn identified statistically significant differences ($p_{value} < 0.05$) between AD and control groups across multiple brain regions and frequency bands. Compared to benchmark methods, M3FrEn yielded more robust and consistent group separation. In addition, binary classification based on M3FrEn features achieved $85\%$ accuracy, with $100\%$ sensitivity and $70\%$ specificity. These results demonstrate that M3FrEn offers a powerful tool for EEG-based complexity analysis and holds promise for clinical applications in early-stage neurological disease detection.