This paper proposes a new framework for epileptic seizure detection using non-invasive scalp electroencephalogram (sEEG) signals. The major innovation of the current study is using the Riemannian geometry for transforming the covariance matrices estimated from the EEG channels into a feature vector. The spatial covariance matrices are considered as features in order to extract the spatial information of the sEEG signals without applying any spatial filtering. Since these matrices are symmetric and positive definite (SPD), they belong to a special manifold called the Riemannian manifold. Furthermore, a kernel based on Riemannian geometry is proposed. This kernel maps the SPD matrices onto the Riemannian tangent space. The SPD matrices, obtained from all channels of the segmented sEEG signals, have high dimensions and extra information. For these reasons, the sequential forward feature selection method is applied to select the best features and reduce the computational burden in the classification step. The selected features are fed into a support vector machine (SVM) with an RBF kernel to classify the feature vectors into seizure and non-seizure classes. The performance of the proposed method is evaluated using two long-term scalp EEG (CHB-MIT benchmark and private) databases. Experimental results on all 23 subjects of the CHB-MIT database reveal an accuracy of 99.87%, a sensitivity of 99.91%, and a specificity of 99.82%. In addition, the introduced algorithm is tested on the private sEEG signals recorded from 20 patients, having 1380 seizures. The proposed approach achieves an accuracy, a sensitivity, and a specificity of 98.14%, 98.16%, and 98.12%, respectively. The experimental results on both sEEG databases demonstrate the effectiveness of the proposed method for automated epileptic seizure detection, especially for the private database which has noisier signals in comparison to the CHB-MIT database.

本文提出了一种使用非侵入性头皮脑电图 (sEEG) 信号进行癫痫发作检测的新框架。当前研究的主要创新是使用黎曼几何将从 EEG 通道估计的协方差矩阵转换为特征向量。空间协方差矩阵被视为特征，以便在不应用任何空间滤波的情况下提取 sEEG 信号的空间信息。由于这些矩阵是对称正定矩阵 (SPD)，因此它们属于称为黎曼流形的特殊流形。此外，提出了基于黎曼几何的核。该内核将 SPD 矩阵映射到黎曼切线空间。从分段 sEEG 信号的所有通道获得的 SPD 矩阵具有高维度和额外信息。由于这些原因，应用顺序正向特征选择方法来选择最佳特征并减少分类步骤中的计算负担。选定的特征被输入到带有 RBF 核的支持向量机 (SVM) 中，以将特征向量分类为癫痫发作和非癫痫发作类别。使用两个长期头皮脑电图（CHB-MIT 基准和私有）数据库评估所提出方法的性能。CHB-MIT 数据库所有 23 名受试者的实验结果显示准确率为 99.87%，敏感性为 99.91%，特异性为 99.82%。此外，引入的算法在 20 名患者记录的私人 sEEG 信号上进行了测试，有 1380 次癫痫发作。所提出的方法分别实现了 98.14%、98.16% 和 98.12% 的准确度、灵敏度和特异性。