This study investigates the Zen-meditation brain dynamics by recurrence analysis and correlates the nonlinear dynamical properties with the spatio-spectral properties of 30-channel Zen-meditation EEG (electroencephalograph). First of all, continuous wavelet transform (CWT) is implemented to decompose EEG into six rhythmic bands. The final dataset is composed of brain potential mappings at the peaks of Cz in each rhythmic band. To classify the behavior of spatio-spectral properties, the unsupervised learning method, self-organizing map (SOM) is employed. The second part of this thesis is the characterization of nonlinear brain dynamics based on embedding theories and reconstructed EEG phase trajectory. To analyze the phase trajectory of nonlinear system characterizing the brain dynamics, we construct the recurrence plot from a 5-second segment of each EEG channel The recurrence plot is further quantified by recurrent parameters to observe the behavior of recurrence of particular system states. SOM clustering result of the brain potential mapping at Cz peaks (BPP) in each EEG rhythmic band will be correlated with the brain mapping of recurrence (BMR) to observe the spatio-spectral characteristics of nonlinear dynamical recurrence.
摘要 i Abstract ii 誌謝 iv Content v List of abbreviation vii List of Figures viii List of tables xi Chapter 1 Introduction 1 1-1 Background and Motivation 1 1-2 Scope of this Thesis 4 Chapter 2 Theories and Methods 5 2-1 Continuous Wavelet Transform (CWT) 5 2-1-1 Continuous wavelet transform 5 2-1-2 Six EEG rhythmic bands 8 2-2 Self-Organizing Map (SOM) 10 2-3 Nonlinear Recurrence Analysis 18 2-3-1 Construction of recurrence plot 18 2-3-2 Quantification of the recurrence plot 19 2-3-3 Brain mappings of recurrence parameters (BMR) 23 2-4 Evaluation SOM clustering performance 23 2-4-1 Cluster center 23 2-4-2 Fault cluster rate (FCR) 24 Chapter 3 Strategy and Implementation 25 3-1 Outline of Complete Scheme 25 3-2 Classification of Brain Mappings of Six EEG Rhythmic Bands 27 3-2-1 Brain Mapping Construction 27 3-2-2 SOM implementation 29 3-2-3 SOM parameter analysis 31 3-3 Issues of Recurrence Plot Analysis 40 3-3-1 Parameters for constructing recurrence plot 40 3-3-2 Effect of window size on estimate of recurrent parameters 43 Chapter 4 Results 62 4-1 Correlation between Clustering Results and Recurrent Parameters 63 4-1-1 Outline of complete scheme for section 4-1 64 4-1-2 Major cluster for different EEG rhythmic bands 65 4-1-3 Results of brain mapping of recurrence (BMR) 68 4-2 Extremal Recurrence Rate (%γ) Correlating with Clustering of Six EEG Rhythmic Bands 91 4-2-1 Outline of complete scheme for section 4-2 91 4-2-2 Extremal recurrence rate (%????) correlating with BPP clustered by SOM. 93 Chapter 5 Conclusions and Future work 102 5-1 Conclusions 102 5-2 Future work 103 Appendix A Orthodox Zen Meditation 104 Appendix B Raw EEG for Figure 4-13 106 Reference 109
