本論文主要研製一基於黎曼幾何空間之想像運動的特徵提取演算法，在想像運動的腦電訊號分類中，共同空間型樣法是一個常被用來提取腦電訊號特徵的演算法，透過共同空間濾波器進行資料重組，去除事件不相關雜訊的影響，強化事件相關的腦波特徵，藉以極大化不同訊號群組之間的差異性。相較於腦電訊號的協方差矩陣位在傳統歐式空間；黎曼幾何空間更能夠表達腦電訊號在空間中距離分布。因此本論文以黎曼幾何空間作為基礎，改良現有共同空間型樣法的演算法架構，並利用黎曼幾何空間和切線空間的轉換，提升腦電訊號特徵提取的效果，最後透過BCI競賽和自錄的腦電訊號驗證其分類的準確度有明顯的提升。

This thesis, based on Riemannian geometric space, focuses on the design and implementation of a classification algorithm for motor imagery Electroencephalography(EEG). When classifing imaginary brain electrical signals, the common spatial pattern method is often used to extract the feature of EEG signals. The common spatial filter performs data reorganization to remove the effects of event-unrelated noise and enhance the EEG feature associated with the event. Thereby it maximizes the difference between different signal groups. Note that the distance distribution of the covariance matrix of the EEG signal located in Riemannian geometry space, that is more distinguishable than that in the traditional Euclidean space. Therefore, based on Riemannian geometric space, this thesis uses the transformation of Riemannian geometric space and tangent space combined with the existing common spatial pattern method to improve the EEG feature extraction effect. Finally, BCI competition and the self-recorded EEG signals are used to verify that the classified accuracy of the proposed method is significantly effective.

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