Minimum Error Entropy: A Superior Alternative to Mean Square Error for Heavy-Tailed EEG Signal Classification

The classification of EEG signals presents unique challenges, particularly when dealing with their heavy-tailed distributions (Wang et al., ۲۰۱۴), which deviate significantly from Gaussian assumptions traditionally used in signal processing. This discrepancy has profound implications for the application of traditional metrics such as Mean Square Error (MSE), which assumes Gaussianity and struggles to effectively capture the dynamics of heavy-tailed data (Heravi and Hodtani, ۲۰۱۸). Recognizing this limitation, this study explores Minimum Error Entropy (MEE) as a superior alternative to MSE, leveraging its foundation in information-theoretic learning (Principe, ۲۰۱۰) to better handle the non-Gaussian characteristics of EEG signals. By addressing this critical gap, we aim to significantly enhance the robustness and accuracy of EEG signal classification. Despite prior advancements in EEG signal processing, most studies have inadequately accounted for the statistical properties of heavy-tailed EEG signals, continuing to rely on second-order statistics like MSE. These approaches falter in accurately modeling and analyzing heavy-tailed distributions, limiting their effectiveness in real-world applications, such as brain-computer interfaces (BCIs). This gap underscores the necessity of a paradigm shift toward metrics like MEE, which inherently incorporate higher-order statistics and are robust against the challenges posed by non-Gaussian data (Kruczek et al., ۲۰۲۰). Our methodology is structured in two pivotal phases. First, we rigorously demonstrate that EEG signals exhibit heavy-tailed, non-Gaussian distributions by performing extensive statistical analyses, including kurtosis measures and distribution fitting. This statistical insight confirms the unsuitability of Gaussian-based methods for EEG signal classification (Xu et al., ۲۰۰۸). Second, we validate the efficacy of MEE over MSE in the classification of heavy-tailed EEG signals. Using the theoretical underpinnings of MEE, which prioritize the minimization of error entropy rather than squared error, we demonstrate its robustness in handling outliers and preserving critical signal features, particularly in heavy-tailed environments (Luan et al., ۲۰۱۶). The proposed approach is evaluated on the widely recognized BCI Competition IV dataset ۲a (Tangermann et al., ۲۰۱۲). This dataset includes recordings from nine subjects performing four motor imagery tasks (left hand, right hand, both feet, and tongue) captured using ۲۲ EEG and three EOG channels sampled at ۲۵۰ Hz. The dataset’s structure requires multi-label classification to map the signal data onto four target motor imagery tasks. In this study, the proposed model was trained under two different conditions using MSE and MEE as optimization metrics, and the performance was compared. Using MSE, the model achieved ۷۶% accuracy, while leveraging MEE increased accuracy to ۸۶%. This ۱۰% improvement demonstrates MEE's superior ability to handle non-Gaussian, heavy-tailed EEG signals, highlighting its effectiveness over traditional MSE-based methods for improving classification performance. In conclusion, this study bridges a critical gap in EEG signal processing by advocating for MEE as a more robust metric over MSE in heavy-tailed environments. Our findings highlight the necessity of rethinking traditional assumptions about EEG signal distributions, offering a robust and theoretically sound pathway to improve classification accuracy in BCIs and related applications (Gritskikh et al., ۲۰۲۴).

کلیدواژه ها:

EEG signal classification ، heavy-tailed distributions ، information-theoretic learning ، minimum error entropy (MEE) ، brain-computer interfaces (BCIs)