近年來，許多科學家對於人類腦波的分析與研究越來越感興趣，他們利用一種量測腦波的方法，稱作腦電波圖(Electroencephalogram, EEG)去觀測人類的腦波變化，並且建立許多實際的應用，像是遊戲控制以及物理治療上。人腦電腦介面 (Brain computer interfaces, BCIs)可以抓取受測者的腦波訊號，並且傳到後端的系統進行一系列的訊號分析，由此可以對使用者的想法進行推論。
在本篇論文中，我們使用一種新的EEG分析方法，稱作錯誤相關電位(Error-related potential, ErrP)來提升人腦電腦介面的性能，錯誤相關電位是透過受測者對於錯誤的警覺的認知狀態所蒐集到的腦波訊號，它是屬於事件相關電位的一種(Event-related potential, ERP)。並且為了克服人腦電腦介面所擁有的資訊量不確定這項缺點，我們也使用了協同控制策略(shared-control strategy)的概念來提升我們提出的模型健全性。因此我們結合了受測者端的錯誤相關電位以及協同控制策略的概念去提出一個新的模型:繪圖模型(Drawing model)，以及利用我們提出的移動方法:減少與說服搜尋法(Reduce and convince search) (RAC搜尋法)讓系統在接受受測者的反應訊號時，繪圖模型上的物件能根據RAC 搜尋法的規則做移動。並且因為每個受測者訓練出來的分類器不是百分百正確，因此在物件移動過程中，可能會受到分類器誤判的影響導致物件偏離原有的軌道，所以加入了一個機率機制，系統在累積足夠的信心時，就會將偏離軌道的物件退回正常的軌道。我們的目的是希望提出的繪圖模型能夠讓受測者透過自己的腦波操控來順利並且快速地完成object在drawing model上的移動任務，最後我們會建立一系列的實驗，實驗結果顯示我們提出的drawing model比起不加入受測者腦波影響，完全無背景知識的try and error模型來說，整體效能提升了約16%

Many scientists are interested in the analysis of human’s brainwave using electroencephalography (EEG) and conducting several applications such as game-controlling and physical therapy based on the EEG analysis. A brain-computer interface (BCI) could capture subjects’ EEG signals and to some extent infer the subject’s intention by analyzing the signals in a back-end system.
In my thesis, we propose to use a novel kind of EEG analysis that is called error-related potential (ErrP) to enhance the performance and applicability of BCIs. ErrP is based on the fact that human’s cognitive state can be aware of error, and the unique kind of brainwave will be produced to reflect this cognitive state called ErrP which belongs to a kind of event-related potential (ERP). For conquering the low information rate of brain-computer interface, we use the shared-control strategy to enhance the robustness of our proposed model. Therefore, we combine the ErrP from human subject and shared-control strategy to propose a new kind model: Drawing model, and use the moving method : Convince and Reduce search (RAC search) we proposed to make the object move on the drawing model according to the rule of RAC search as system receive the response EEG signal of human subject.
Because the accuracy of each subject’s personal trained classifier is not 100%, therefore, the object might deviate from the normal track while the classifier make a misclassification. So we add a probability mechanism for backtracking the out-of-track object to the normal track as the system has enough confidence. Our objective is to make the object complete the drawing mission quickly by using our drawing model. In the last, we will conduct a series of analysis for our experimental results, and the results show that our proposed drawing model enhance about 16% performance by comparing to the try and error model which is without the influence of subjects’ brainwave.

摘要 I
Abstract III
1 Introduction 1
2 Related Work 5
2.1 Error-related potentials 5
2.2 Reinforcement learning task 6
2.3 Shared-control strategies for reaching task 7
3 Background 10
3.1 The human brain 10
3.2 Brain activity 14
3.2.1 Electroencephalogram (EEG) 14
3.2.2 Event-related potential (ERP) 14
3.2.3 Error-related potential (ErrP) 14
3.3 Brain-computer interfaces (BCIs) 15
3.4 Data acquisition and preprocessing 16
3.4.1 Hardware of EEG acquisition 16
3.4.2 Preprocessing of EEG data 18
3.4.3 Extract ErrP related data from EEG data 18
3.5 Feature Generation 18
3.5.1 Granger causality 19
3.5.2 Short Time Directed Transfer Function (ST-DTF) 24
3.6 Feature Selection 27
3.7 Statistical classifier 29
4. System Architecture 33
4.1 Training phase model 34
4.1.1 Model design 34
4.1.2 Experimental protocol 36
4.1.3 Training procedure of a personalized classifier 37
4.1.4 Experiment result 38
4.2 Control phase model 42
4.2.1 Model design 43
4.2.2 RAC search & Shared control strategy 44
4.2.3 Phenomenon of misclassification 49
4.2.4 Experiment results 56
5. Conclusion 62
REFERENCE 64

[1] Ferrez, Pierre W., and José del R Millan. "Error-related EEG potentials generated during simulated brain–computer interaction." IEEE Transactions on Biomedical Engineering, 55.3 (2008): 923-929.
[2] Friedman, David, and Ray Johnson. "Event-related potential (ERP) studies of memory encoding and retrieval: a selective review." Microscopy research and technique 51.1 (2000): 6-28.
[3] Carter, C. S., Braver, T. S., Barch, D. M., Botvinick, M. M., Noll, D., & Cohen, J. D. "Anterior cingulate cortex, error detection, and the online monitoring of performance." Science 280.5364 (1998): 747-749.
[4] Ludwig, K. A., Miriani, R. M., Langhals, N. B., Joseph, M. D., Anderson, D. J., & Kipke, D. R. "Using a common average reference to improve cortical neuron recordings from microelectrode arrays." Journal of neurophysiology101.3 (2009): 1679-1689.
[5] Kamiński, M., Ding, M., Truccolo, W. A., & Bressler, S. L. "Evaluating causal relations in neural systems: Granger causality, directed transfer function and statistical assessment of significance." Biological cybernetics 85.2 (2001): 145-157.
[6] Saa, Jaime F. Delgado, and Miguel Sotaquirá Gutierrez. "EEG signal classification using power spectral features and linear Discriminant Analysis: A brain computer interface application." Eighth Latin American and Caribbean Conference for Engineering and Technology. (2010).
[7] Trieu, Hoang T., Hung T. Nguyen, and Keith Willey. "Shared control strategies for obstacle avoidance tasks in an intelligent wheelchair." IEEE 30th Annual International Conference of EMBS (2008).
[8] Nieuwenhuis, S., Ridderinkhof, K. R., Blom, J., Band, G. P., & Kok, A. "Error‐related brain potentials are differentially related to awareness of response errors: Evidence from an antisaccade task." Psychophysiology 38.5 (2001): 752-760.
[9] Pierre Ferrez., & del Millan, J. R. (2007). Error-related EEG potentials in brain-computer interfaces. Lausanne: EPFL
[10] Daly, J. J., Cheng, R., Rogers, J., Litinas, K., Hrovat, K., & Dohring, M. "Feasibility of a new application of noninvasive brain computer interface (BCI): a case study of training for recovery of volitional motor control after stroke." Journal of Neurologic Physical Therapy 33.4 (2009): 203-211.
[11] Loveleena Rajeev. (2012, March 20). Lobes of the brain and their functions. Buzzle.com. Retrieved March 5, 2014, from http://www.buzzle.com.
[12] Niedermeyer, Ernst, and FH Lopes da Silva, eds. "Electroencephalography: basic principles, clinical applications, and related fields". Lippincott Williams & Wilkins, (2005).
[13] Ekanayake, Hiran. (2010, December 25). P300 and Emotiv EPOC: Does Emotiv EPOC capture real EEG?. Visaduma.info. Retrieved October 7, 2011, from
http://neurofeedback.visaduma.info/emotivresearch.htm.
[14] Homan, Richard W., John Herman, and Phillip Purdy. "Cerebral location of international 10–20 system electrode placement." Electroencephalography and clinical neurophysiology 66.4 (1987): 376-382.
[15] Zhang, H., Chavarriaga, R., Goel, M. K., Gheorghe, L., & del Millan, J. R. "Improved recognition of error related potentials through the use of brain connectivity features." IEEE 2012 Annual International Conference of EMBC, (2012): 6740-6743.
[16] Posada, David, and Thomas R. Buckley. "Model selection and model averaging in phylogenetics: advantages of Akaike information criterion and Bayesian approaches over likelihood ratio tests." Systematic biology 53.5 (2004): 793-808.
[17] Schneider, Tapio, and Arnold Neumaier. "Algorithm 808: ARfit—A Matlab package for the estimation of parameters and eigenmodes of multivariate autoregressive models." ACM Transactions on Mathematical Software (TOMS) 27.1 (2001): 58-65.