标题： BTTDA：用于脑机接口的块项张量判别分析 显示英文标题

标题： BTTDA: Block-Term Tensor Discriminant Analysis for Brain-Computer Interfacing

摘要： 脑机接口（BCIs）允许大脑与外部设备直接通信，通常使用脑电图（EEG）来记录神经活动。 降维和结构正则化对于有效分类任务相关的脑信号至关重要，包括事件相关电位（ERPs）和运动想象（MI）节律。 当前基于张量的方法，如Tucker和PARAFAC分解，往往缺乏充分捕捉EEG数据复杂性的灵活性。 本研究引入了块项张量判别分析（BTTDA）：一种新颖的基于张量的监督特征提取方法，旨在通过提供灵活的多线性降维来提高分类准确性。 扩展高阶判别分析（HODA），BTTDA使用一种新颖且可解释的HODA前向模型，并结合一个消去方案以迭代提取判别块项，从而改进分类的特征表示。 BTTDA及其秩-1项之和变体PARAFACDA在MOABB基准框架提供的公开ERP（二阶张量）和MI（三阶张量）EEG数据集上进行了评估。 基准测试显示，BTTDA和PARAFACDA在ERP解码中显著优于传统HODA方法，达到了最先进的性能（ROC-AUC = 91.25%）。 对于MI，HODA、BTTDA和PARAFACDA的解码结果表现不佳，但BTTDA仍然显著优于HODA（64.52% > 61.00%）。 BTTDA的块项结构实现了可解释且更高效的降维，而不会牺牲判别能力。 这为BCI以及更广泛的神经影像应用中的特征提取提供了一种有前景且适应性强的方法。 显示英文摘要

摘要： Brain-computer interfaces (BCIs) allow direct communication between the brain and external devices, frequently using electroencephalography (EEG) to record neural activity. Dimensionality reduction and structured regularization are essential for effectively classifying task-related brain signals, including event-related potentials (ERPs) and motor imagery (MI) rhythms. Current tensor-based approaches, such as Tucker and PARAFAC decompositions, often lack the flexibility needed to fully capture the complexity of EEG data. This study introduces Block-Term Tensor Discriminant Analysis (BTTDA): a novel tensor-based and supervised feature extraction method designed to enhance classification accuracy by providing flexible multilinear dimensionality reduction. Extending Higher Order Discriminant Analysis (HODA), BTTDA uses a novel and interpretable forward model for HODA combined with a deflation scheme to iteratively extract discriminant block terms, improving feature representation for classification. BTTDA and a sum-of-rank-1-terms variant PARAFACDA were evaluated on publicly available ERP (second-order tensors) and MI (third-order tensors) EEG datasets from the MOABB benchmarking framework. Benchmarking revealed that BTTDA and PARAFACDA significantly outperform the traditional HODA method in ERP decoding, resulting in state-of-the art performance (ROC-AUC = 91.25%). For MI, decoding results of HODA, BTTDA and PARAFACDA were subpar, but BTTDA still significantly outperformed HODA (64.52% > 61.00%). The block-term structure of BTTDA enables interpretable and more efficient dimensionality reduction without compromising discriminative power. This offers a promising and adaptable approach for feature extraction in BCI and broader neuroimaging applications.