腦機介面(Brain Computer Interface, BCI)提供大腦與外部設備之間一個
有效的溝通橋樑，透過腦電圖(Electroencephalogram, EEG)解碼並轉化為指
令，從而實現與外界交流及對外部設備的控制，進而協助肢體運動功能障礙
患者表達意念，並改善現有之生活品質，而想像運動(Motor Imagery, MI)也
已被證實是操作腦機介面的一種有效方式。然而，基於想像運動操作腦機介
面的研究中，常出現無法準確辨認使用者的操作指令以及演算法複雜度高
導致計算時間過長等問題。本論文旨在開發一基於想像運動之腦機介面分
類架構，該架構分別結合以聯合近似對角化為基礎之濾波器組共同空間型
樣法以及黎曼幾何之切線空間投影法以獲取多類別想像運動腦電圖訊號之
特徵，並透過特徵選取保留與類別相關性高之特徵，以降低特徵空間維度，
後續則藉由分類器進行解碼，藉此達到腦電圖訊號分類之目的。此方法不僅
透過聯合近似對角化之方法降低演算法於多類別分類上之計算複雜度，同
時有效提升想像運動之分類性能。最後，經由BCI Competition IV dataset 2a
及自行錄製之數據集進行測試，實驗結果成功地驗證本論文所提出演算法
之有效性；其中，在BCI Competition IV dataset 2a 的數據集測試下，9 位受
試者於四類別想像運動腦電圖訊號之平均分類準確率可達75.39%，而在自
行錄製的腦波數據集測試下，5 位受試者於三類別想像運動腦電圖訊號之平
均分類準確率可達72.26%。

The brain-computer interface (BCI) establishes an effective bridge between
the human brain and external devices. BCI is a system capable of decoding
electroencephalographic (EEG) signals into device commands to communicate
with the external environment and control the devices, thereby assisting patients
with executive dysfunction to express their intent and improve the quality of life.
Nowadays, motor imagery (MI) has proved to be an effective way to operate BCI.
However, BCI based on MI often fails to correctly recognize the user’s mental
commands. Here we aim to develop a BCI classification architecture based on MI,
which combines the filter bank common spatial pattern based on joint
approximate diagonalization and Riemannian tangent space mapping to obtain
features from multiclass MI EEG. To prevent over-fitting, we retain the features
with a high correlation with the class through feature selection to reduce the
dimensionality of the feature space. Finally, use the classifier to decode EEG
signals. This architecture not only reduces the computational complexity of the
algorithm for multiclass classification through joint approximate diagonalization
but also effectively improves the classification performance of MI task. The
architecture was validated by the BCI Competition IV dataset 2a and the in-house
dataset. The results indicated that our proposed architecture had achieved 75.39%
mean accuracy on the BCI Competition IV dataset 2a with four classes of MI tasks
and had achieved 72.26% mean accuracy on the in-house dataset with three
classes of MI tasks.

摘要 ........................................................................................................................ I
Abstract ................................................................................................................ II
致謝 ..................................................................................................................... III
目錄 ..................................................................................................................... IV
圖目錄 ................................................................................................................ VII
表目錄 ................................................................................................................ XII
第一章 緒論 ......................................................................................................... 1
1-1 前言 ........................................................................................................ 1
1-2 研究動機與目的 ................................................................................... 2
1-3 文獻回顧與探討 ................................................................................... 3
1-4 內容大綱 ................................................................................................ 5
第二章 腦電訊號 ................................................................................................. 6
2-1 腦機介面 ................................................................................................ 6
2-2 想像運動 ................................................................................................ 7
2-3 腦電圖訊號量測之硬體規格 ............................................................... 9
第三章 演算法原理與分析 ............................................................................... 10
3-1 帶通濾波器之頻帶選擇 ..................................................................... 10
3-2 共同空間型樣法 ................................................................................. 11
3-3 黎曼幾何與黎曼流形基礎 ................................................................. 17
3-3-1 歐氏空間與黎曼空間 .............................................................. 17
3-3-2 腦電圖訊號之黎曼幾何特性 .................................................. 17
3-3-3 黎曼距離 .................................................................................. 19
3-3-4 黎曼對數/指數投影 ................................................................. 22
3-3-5 黎曼均值 .................................................................................. 25
3-3-6 黎曼切線空間投影 .................................................................. 26
3-4 基於濾波器組共同空間型樣法之切線空間投影 ............................. 29
3-4-1 重疊頻帶之帶通濾波器組 ...................................................... 30
3-4-2 多類別共同空間型樣法 .......................................................... 32
3-4-3 特徵結合 .................................................................................. 40
3-4-4 特徵選取及分類 ...................................................................... 41
第四章 實驗結果與討論 ................................................................................... 43
4-1 實驗數據分析...................................................................................... 43
4-1-1 BCI Competition IV Dataset IIa ................................................ 43
4-1-2 自行錄製之想像運動腦電圖數據 .......................................... 45
4-2 擴展共同空間型樣法至多類別分類之方法比較 ............................. 46
4-3 FBCSP-TSM 演算法參數之選擇 ........................................................ 48
4-3-1 共同空間型樣法之空間濾波器參數比較 .............................. 48
4-3-2 帶通濾波器組之頻帶數量 ...................................................... 49
4-3-3 帶通濾波器組頻帶重疊之頻寬大小 ...................................... 51
4-4 特徵選取之實驗結果 ......................................................................... 52
4-5 多類別想像運動腦電圖訊號之實驗結果 ......................................... 60
第五章 結論與未來展望 ................................................................................... 72
參考文獻 ............................................................................................................. 73

[1] B. Xu, L. Zhang, A. Song, C. Wu, W. Li, D. Zhang, G. Xu, H. Li, and H.
Zeng, “Wavelet transform time-frequency image and convolutional
network-based motor imagery EEG classification,” IEEE Access, vol. 7, pp.
6084-6093, 2018.
[2] P. Ofner, S. Member, and G. R. Müller-Putz, “Using a noninvasive decoding
method to classify rhythmic movement imaginations of the arm in two
planes,” IEEE Transactions on Biomedical Engineering, vol. 62, no. 3, pp.
972-981, 2015.
[3] P. Gaur, R. B. Pachori, H. Wang, and G. Prasad, “An automatic subject
specific intrinsic mode function selection for enhancing two-class EEGbased
motor imagery-brain computer interface,” IEEE Sensors Journal, vol.
19, no. 16, pp. 6938-6947, 2019.
[4] Z. J. Koles, “The quantitative extraction and topographic mapping of the
abnormal components in the clinical EEG,” Electroencephalography and
Clinical Neurophysiology, vol. 79, no. 6, pp. 440-447, 1991.
[5] H. Ramoser, J. Müller-Gerking, and G. Pfurtscheller, “Optimal spatial
filtering of single trial EEG during imagined hand movement,” IEEE
Transactions on Rehabilitation Engineering, vol. 8, no. 4, pp. 441-446,
2000.
[6] W. Samek, C. Vidaurre, K. R. Müller, and M. Kawanabe, “Stationary
common spatial patterns for brain-computer interfacing,” Journal of Neural
Engineering, vol. 9, no. 2, pp. 1-14, 2012.
[7] S. H. Park, D. Lee, and S. G. Lee, “Filter bank regularized common spatial
pattern ensemble for small sample motor imagery classification,” IEEE
Transactions on Neural Systems and Rehabilitation Engineering, vol. 26,
no. 2, pp. 498-505, 2018.
[8] K. K. Ang, Z. Y. Chin, H. Zhang, and C. Guan, “Filter bank common spatial pattern (FBCSP) in brain-computer interface,” IEEE International Joint Conference on Neural Networks, pp. 2390-2397, 2008.
[9] A. Barachant, S. Bonnet, M. Congedo, and C. Jutten, “Riemannian
geometry applied to BCI classification,” International Conference on
Latent Variable Analysis and Signal Separation, Berlin, pp. 629-636, 2010.
[10] A. Singh, S. Lal, and H. W. Guesgen, “Small sample motor imagery
classification using regularized Riemannian features,” IEEE Access, vol.7,
pp. 46858-46869, 2019.
[11] X. Xie, Z. L. Yu, Z. Gu, J. Zhang, L. Cen, and Y. Li, “Bilinear regularized
locality preserving learning on Riemannian graph for motor imagery BCI,”
IEEE Transactions on Neural Systems and Rehabilitation Engineering, vol.
26, no. 3, pp. 698-708, 2018.
[12] J. R. Wolpaw, N. Birbaumer, D. J. McFarland, G. Pfurtscheller, and T. M.
Vaughan, “Brain-computer interfaces for communication and control,”
Clinical Neurophysiology, vol. 113, no. 6, pp. 767-791, 2002.
[13] H. S. Anupama, N. K. Cauvery, and G. M. Lingaraju, “Brain computer
interface and its types - a study,” International Journal of Advances in
Engineering & Technology, vol. 3, no. 2, pp. 739-745, 2012.
[14] L. A. Farwell and E. Donchin, “Talking off the top of your head: toward a
mental prosthesis utilizing event-related brain potentials,”
Electroencephalography and Clinical Neurophysiology, vol. 70, no. 6, pp.
510-523, 1988.
[15] M. Higger, M. Akcakaya, H. Nezamfar, G. LaMountain, U. Orhan, and D.
Erdogmus, “A Bayesian framework for intent detection and stimulation
selection in SSVEP BCIs,” IEEE Signal Processing Letters, vol. 22, no. 6,
pp. 743-747, 2015.
[16] G. Pfurtscheller and F. H. Lopes da Silva, “Event-related EEG/MEG
synchronization and desynchronizarion: basic principles,” Clinical
Neurophysiology, vol. 110, no. 11, pp. 1842-1857, 1999.
[17] Y. Wang, X. Chen, X. Gao, and S. Gao, “A benchmark dataset for SSVEPbased
brain-computer interfaces,” IEEE Transactions on Neural Systems
and Rehabilitation Engineering, vol. 25, no. 10, pp. 1746-1752, 2017.
[18] G. Pfurtscheller, C. Neuper, A. Schlögl, and K. Lugger, “Separability of
EEG signals recorded during right and left motor imagery using adaptive
autoregressive parameters,” IEEE Transactions on Rehabilitation
Engineering, vol. 6, no. 3, pp. 316-325, 1998.
[19] C. Park, D. Looney, N. ur Rehman, A. Ahrabian, and D. P. Mandic,
“Classification of motor imagery BCI using multivariate empirical mode
decomposition,” IEEE Transactions on Neural Systems and Rehabilitation
Engineering, vol. 21, no. 1, pp. 10-22, 2013.
[20] T. Mulder, “Motor imagery and action observation: cognitive tools for
rehabilitation,” Journal of Neural Transmission, vol. 110, no. 10, pp. 1265-
1278, 2007.
[21] J. Long, Y. Li, H. Wang, T. Yu, J. Pan, and F. Li, “A hybrid brain computer
interface to control the direction and speed of a simulated or real
wheelchair,” IEEE Transactions on Neural Systems and Rehabilitation
Engineering, vol. 20, no. 5, pp. 720-729, 2012.
[22] Y. Chae, J. Jeong, and S. Jo, “Toward brain-actuated humanoid robots:
asynchronous direct control using an EEG-based BCI,” IEEE Transactions
on Robotics, vol. 28, no. 5, pp. 1131-1144, 2012.
[23] E. Curran, P. Sykacek, M. Stokes, S. J. Roberts, W. Penny, I. Johnsrude, and
A. M. Owen, “Cognitive tasks for driving a brain-computer interfacing
system: a pilot study,” IEEE Transactions on Neural Systems and
Rehabilitation Engineering, vol. 12, no. 1, pp. 48-54, 2003.
[24] A. Kreilinger, H. Hiebel, and G. R. Müller-Putz, “Single versus multiple
events error potential detection in a BCI-controlled car game with
continuous and discrete feedback,” IEEE Transactions on Biomedical
Engineering, vol. 63, no. 3, pp. 519-529, 2016.
[25] D. J. McFarland, L. A. Miner, T. M. Vaughan, and J. R. Wolpaw, “Mu and
beta rhythm topographies during motor imagery and actual movements,”
Brain Topography, vol. 12, no. 3, pp. 177-186, 2000.
[26] F. Yger, M. Berar, and F. Lotte, “Riemannian approaches in brain-computer
interfaces: a review,” IEEE Transactions on Neural Systems and
Rehabilitation Engineering, vol. 25, no. 10, pp. 1753-1762, 2017.
[27] M. Moakher, “A differential geometric approach to the geometric mean of
symmetric positive-definite matrices,” SIAM Journal on Matrix Analysis
and Applications, vol. 26, no. 3, pp. 735-747, 2005.
[28] P. T. Fletcher and S. Joshi, “Principal geodesic analysis on symmetric
spaces: statistics of diffusion tensors,” Computer Vision and Mathematical
Methods in Medical and Biomedical Image Analysis, Berlin, pp. 87-98,
2004.
[29] A. Barachant, S. Bonnet, M. Congedo, and C. Jutten, “Multiclass braincomputer
interface classification by Riemannian geometry,” IEEE
Transactions on Biomedical Engineering, vol. 59, no. 4, pp. 920-928, 2012.
[30] Q. Novi, C. Guan, T. H. Dat, and P. Xue, “Sub-band common spatial pattern
(SBCSP) for brain-computer interface,” 2007 3rd International
IEEE/EMBS Conference on Neural Engineering, pp. 204-207, 2007.
[31] Q. Wei and Z. Wei, “Binary particle swarm optimization for frequency band
selection in motor imagery based brain-computer interfaces,” Bio-Medical
Materials and Engineering, vol. 26, no. 1, pp. 1523-1532, 2015.
[32] D. T. Pham, “Joint approximate diagonalization of positive definite
Hermitian matrices,” SIAM Journal on Matrix Analysis and Applications,
vol. 22, no. 4, pp. 1136-1152, 2001.
[33] G. Dornhege, B. Blankertz, G. Curio, and K. R. Müller, “Boosting bit rates
in noninvasive EEG single-trial classifications by feature combination and
multiclass paradigms,” IEEE Transactions on Biomedical Engineering, vol.
51, no. 6, pp. 993-1002, 2004.
[34] M. G. Wentrup and M. Buss, “Multiclass common spatial patterns and
information theoretic feature extraction,” IEEE Transactions on Biomedical
Engineering, vol. 55, no. 8, pp. 1991-2000, 2008.
[35] A. Ziehe, P. Laskov, G. Nolte, and K. R. Müller, “A fast algorithm for joint
diagonalization with non-orthogonal transformations and its application to
blind source separation,” Journal of Machine Learning Research, vol. 5, pp.
777-800, 2004.
[36] W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery,
“Numerical recipes in C,” 1988.
[37] B. D. Mensh, J. Werfel, and H. S. Seung, “BCI competition 2003-data set
Ia: combining gamma-band power with slow cortical potentials to improve
single-trial classification of electroencephalographic signals,” IEEE
Transactions on Biomedical Engineering, vol. 51, no. 6, pp. 1052-1056,
2004.
[38] W. Quigguo, M. Fei, W. Yijun, G. Xiaorong, and G. Shangkai, “Feature
combination for classifying single-trial ECoG during motor imagery of
different sessions,” Progress in Natural Science, vol. 17, no. 7, pp. 851-858,
2007.
[39] C. Brunner, R. Leeb, G. Muller-Putz, A. Schlogl, and G. Pfurtscheller, “BCI
competition 2008-Graz data set A,” Institute for Knowledge Discovery
(Laboratory of Brain-Computer Interfaces), Graz University of Technology,
pp. 136-142, 2008.
[40] X. Xie, Z. L. Yu, H. Lu, Z. Gu, and Y. Li, “Motor imagery classification
based on bilinear sub-manifold learning of symmetric positive-definite
matrices,” IEEE Transactions on Neural Systems and Rehabilitation
Engineering, vol. 25, no. 6, pp. 504-516, 2017.
[41] A. Gallace and C. Spence, “Touch and the body: the role of the
somatosensory cortex in tactile awareness,” Psyche: An Interdisciplinary
Journal of Research on Consciousness, vol. 16, no. 1, pp. 30-67, 2010.