本篇論文的目的是發展一個系統化方法以提供長時段禪定腦電波信號(electroencephalograph, EEG)之總覽。此方法將長時段腦電波信號轉換為能夠快速檢視的摘要結果。
本論文提出的方法包括四個主要步驟:(1)分割;(2)特徵萃取(量化);(3)分類;與(4)結果視覺呈現。第一個步驟將腦電波依給定criteria分割。接著萃取出每個區段的特徵向量並加以分類，如此則具有類似波形的區段將分類在同一個類別。最後，分析結果包含兩部份:(1)各類別隨時間的演變，也就是腦電波紀錄的簡化總覽，和(2)對應於每一類別的代表腦電波波形。除此之外，本論文亦探討分類步驟中的參數影響，並以數種典型的禪定腦電波波形進行模擬。此系統化之方法將有助於長時段腦電波信號檢閱和禪定腦電波之深入研究。

The aim of this thesis is to develop a systematic approach to provide an overview of long-term meditation EEG (electroencephalograph). This approach translates the long-term EEG raw record into a summary report which can be evaluated at a glance.
The proposed method involves four key steps: (1) segmentation; (2) feature extraction (quantification); (3) classification; and (4) display for visualization. The first step is to break the EEG into segments of similar characteristics based on pre-specified criteria. Then the feature vector of each segment is extracted and classified. Thus, the segments with similar patterns are clustered into the same group. Finally, the results include two parts: (1) the chronological evolution of clusters, that is, the compressed temporal profile of the EEG record, and (2) the representative EEG waveform pattern of each cluster. In addition, the parameters in the clustering strategy are discussed. Some case studies using typical meditation EEG patterns are conducted in this thesis. This systematic approach could assist us in reviewing the long-term EEG of different states and further investigating the meditation process.

1 Introduction 1
1.1 Background and Motivation . . . . . . . . . . . . . . . . 1
1.2 Scope of This Research Study . . . . . . . . . . . . . . . 3
2 Theories and Methods Applied in This Thesis 4
2.1 EEG Segmentation Based on Non-linear Energy Operator . . . 4
2.1.1 Non-linear Energy Operator (NLEO) . . . . . . . . . .6
2.1.2 Segmentation Algorithm . . . . . . . . . . . . . . . 9
2.1.3 Considerations . . . . . . . . . . . . . . . .. . . 11
2.2 Quantificaton of Features of EEG Segments . . . . . . . . 12
2.2.1 Artifact Rejection . . . . . . . . . . . . . . . . 13
2.2.2 Amplitude Measurement . . . . . . . . . . . . . . . 14
2.2.3 Frequency Measurement . . . . . . . . . . . . . . . 14
2.2.4 Computation of Peak-to-peak Magnitude . . . . . . . 17
2.2.5 Construction of Multi-channel Feature Vectors . . . 17
2.2.6 Normalization of Feature Vectors . . .. . . . . . . 18
2.3 Feature Classification . . . . . . . . . . . . . . . . . 18
2.3.1 K-means Clustering Algorithm. . . . . . . . . . . . 19
2.3.2 Modified K-means Clustering Process. . . . . . . . 23
2.3.3 Outlier Identification . . . . . . . . . . . . . . 26
2.4 Formats and Meaning of the Display . . . . . . . . . . . .28
3 Considerations and Performance of the Proposed Method 29
3.1 Parameters in Clustering . . . . . . . . . . . . . . . . 29
3.1.1 Measure the Cluster Similarity . . . . . . . . . . 30
3.1.2 Determine the Number of Clusters . . . . . . . . . 33
3.2 Simulation with Typical Meditation EEGs . . . . . . . . . 34
3.2.1 Segmentation Results . . . . . . . . . . . . . . . 36
3.2.2 Feature Quantification and Classification . . . . . 36
3.2.3 Display of the Final Results of Simulation . . . . 42
4 Experiments and Results 43
4.1 The Experiment Protocol . . . . . . . . . . . . . . . . 43
4.2 Strategies for Analyzing the Meditation EEG . . . . . . . 44
4.2.1 Pre-processing . . . . . . . . . . . . . . . . . . 44
4.2.2 A Flowchart Illustrating the Strategies . . . . . 45
4.3 Experiment Results . . . . . . . . . . . . . . . . . . . 45
4.3.1 Case I . . . . . . . . . . . . . . . . . . . . . . 47
4.3.2 Case II . . . . . . . . . . . . . . . . . . . . . . 50
4.3.3 Case III . . . . . . . . . . . . . . . . . . . . . 53
5 Conclusion and Discussion 56
5.1 Summary of the Current Work . . . . . . . . . . . . . . . 56
5.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . 57

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