Even with the advanced imaging technologies in the scope of brain research, EEG (electroencephalograph) has been still favorable due to its superior temporal resolution of brain electrical activities. For decades, the electrical activities of human brain, recorded in the form of multi-channel waveforms, have been extensively studied in order to help clinicians diagnose and treat brain dysfunctions. More scientific evidence of EEG variations in correlation with diseases and pathologies has been disclosed, including apoplexy , epilepsy , encephalitis , aging  and epidemic diseases . In addition, EEG studies have been employed in a wide scope of studies on cognitive functions , psychology , social behavior  and even body-mind practices including Yoga, Tai Chi, Qi Gong and meditation  . Our previous study reported novel findings on EEG under Zen meditation, the ancient oriental practice of Zen sect aiming to attain the state of enlightenment   . This paper presents an innovative scheme, based on unsupervised deep learning, for analyzing spatio-spectral properties of resting and Zen-meditation EEG.
Mental exhaustion caused by overworked brain becomes common nowadays that is ascribed to the heavy information-processing demands. Zen meditation accordingly offers an effective way to relieve physiological and mental stress. In comparison with eyes-closed, relaxed rest, Zen meditation via tri-aperture concentration  effectively calms the brain and mind for bodily rejuvenation, according to the practitioners’ experiences, differing from those worldwide popular meditation practices such as transcendental meditation (TM) from India, Japanese Zen, and Tibetan Buddhism . Zen meditation follows the heart-dominating principle while other meditations are mostly mind-cultivating practices. By concentrating on unique apertures, practitioners initiate the process of cleansing all conscious states in preparation for entering the realm of true nature deeply in the heart. Such process involves the functioning alteration of major components in the brain leading to brain plasticity. Brain function under such an undisclosed realm has drawn the attention of researchers. Our study has been focused on the EEG variations.
EEG is composed of waves of different frequencies ranging from δ (0 - 4 Hz) to γ (30 - 50 Hz), associated with different physiological, pathological, psychological, mental or conscious states. For example, high alpha waves (10 - 12 Hz) emerge in the occipital region when a person is awake and relaxed with eyes closed  . Spatial distribution of various EEG rhythms provides important indications of brain functioning. It is the first attempt to employ brain mapping of centroid frequency (BMFc) to characterize the spatio-spectral properties of multi-channel EEG from which the decomposed CWT   coefficients are used to estimate the centroid frequency for each channel. To deal with the unknown complicated composition of BMFc dataset, self-organizing map (SOM) is implemented to classify and label the BMFc. SOM is a type of unsupervised learning method based on competitive learning. The output neurons of the network compete among themselves for the final decision of the one to be activated or fired. SOM (also named as Kohonennetwork) was pioneered by the Finnish researcher Teuvo Kohonen in 1980s  . Since then, SOM has been extensively used as a clustering and visualization tool in data analysis. Differing from classical neural networks, SOM does not have any hidden layer. Based on the unsupervised learning scheme, the output neurons in SOM require no designated output values. Instead, each output neuron is identified by a vector of weights. SOM maps the high-dimensional space of input dataset to a lower dimensional output space with the original topological properties well preserved. The after-trained weight matrix thus enables an easier interpretation of complex inherent structures in the data. Applications of SOM range from pattern recognition   to feature classification . Through SOM classification, the cluster properties of BMFc represent the state of brain function associated with the multi-channel EEG that assist in the long-term EEG interpretation or clinical diagnosis.
2.1. EEG Signals
EEG signals were collected in 2002-2007 from 15 Zen-meditation practitioners (experimental group) with an average of 5.8-year meditation experience and 15 ordinary, healthy volunteers (control group). The average age of experimental group was 28 years, which was 23 years in the control group. Experimental subjects practiced Zen-meditation while control subjects were at rest in normal sitting position, with eyes closed. In the experiment, we conducted overall 50-minute recording of EEG signals for both groups. EEG signals were recorded by Power Lab/16SP recording system, utilizing the 30-channel, common-reference (linked-mastoid MS1-MS2) electrode montage based on the international 10 - 20 system. Figure 1 illustrates the EEG recording montage of the 30 electrode locations. To explore local rhythmic behavior, 9 scalp regions are examined:
Frontal region (F): Fp1, Fp2.
Longitudinal Midline-frontal (LMF): Fz, FCz, Cz.
Longitudinal Midline-posterior (LMP): CPz, Pz, O2.
Transversal Midline (TM): T7, C3, Cz, C4, T8.
Left-frontal (LF): F7, F3, FT7, FC3.
Right-frontal (RF): F4, F8, FC4, FT8.
Left-posterior (LP): TP7, CP3, P7, P3.
Right-posterior (RP): CP4, TP8, P4, P8.
Occipital Lobe (O): O1, O2, Oz.
With the EEG electrodes circled in Figure 1.
The EEG signals were sampled at 200 Hz. To remove the slow baseline drift and high-frequency artifacts, EEG were filtered by a band-pass filter with the passband of 0.5 - 50 Hz. The segments seriously contaminated by such artifacts
Figure 1. EEG recording montage (30-channel, using linked-mastoid MS1-MS2 as the common reference). Nine groups of electrodes are circled.
as eye blinking, eyeball movement and muscle activities were removed by naked-eye screening in the pre-processing stage.
2.2. Construction of Centroid Frequency Brain Mapping (BMFc)
Continuous wavelet transform (CWT) enables the optimization of time-frequency resolution, originally proposed in the milestone studies on multi-scale, multi-resolution processing   . The capability of time-frequency localization offers a way of extracting features at various locations in time at different scales. Time-frequency representation enables the exploration of local, transient or intermittent components. Let C(a,b) denote the wavelet transform of a continuous time signal, x(t), on the basis of the scaled (by a) and shifted (by b) wavelet ψa,b(t). Wavelet transform is defined as the inner product of x(t) and the complex conjugate ,
where ψ(t) is the mother wavelet, or wavelet prototype. The child wavelet, ψa,b(t), is derived from the mother wavelet ψ(t) by,
Scale a of the child waveletcorresponding to the frequency can be converted to the so-called pseudofrequencyfa (in Hz) by,
where fs is the sampling period (second) and fcis the center frequency of a wavelet (Hz) obtained from the frequency of the maximum magnitude of the Fourier transform of the wavelet. Our previous study  revealed that mother wavelet Daubechies 6  is more feasible for EEG analysis. The family of Daubechies wavelets is known for its orthogonal property and efficient implementation.
BMFc, brain mapping of centroid frequency, is constructed by Matlab toolbox EEGLAB developed by Swartz Center for Computational Neuroscience. Centroid frequency Fc of EEG at a given time instant is computed by CWT coefficients in the frequency range of interest, (normally, fU = fs/2, half the sampling rate).
In this study, frequency range is0.05 Hz - 100 Hz, with frequency resolution of 0.05 Hz.
2.3. Self-Organizing Map
SOM applies competitive learning scheme to perform unsupervised training. Output neurons of the network compete among themselves for the final decision of the one to be activated or fired. Training of SOM network is aimed to find the No vectors of weights characterizing the output clusters. Figure 2(a) displays the schematic architecture of 12-neuron SOM network.
Input dataset consists of Ni feature vectors, for , where ndis the dimension of input vector. Hence, each vector is composed of nd centroid frequencies. Weight vector wij ( and ) connects the jth input element to the ith output neuronoi. Output
Figure 2. (a) Schematic architecture of 12-neuron SOM network. (b) Gaussian neighborhood function for determining various strengths of stimulation of the surrounding neurons.
neuronoi is quantified by weight vector for .In order to learn the input attributes without pre-labeled data, all the output neurons compete among themselves by searching for the weight vector wjthat is most similar to the current input vector. Then output neuron will be declared as the winner neuron, also called the best matching unit(BMU). To ﬁnd the BMU, distance between the current input vector xi and the weight vectors wj, for is computed by:
BMU is the output neuron with the smallest distance:
BMU, acting as a firing neuron, stimulates more on the neurons closer to itself so that it produces various strengths of stimulation of the surrounding neurons (Figure 2(b)). Such a design is based on neurobiological evidence of lateral interaction among a set of excited neurons in the human brain. Once the is determined, the weights (at the isth training step) are adjusted to approach the input vector xi by .
Input vectors are randomly fed into SOM Nt times to ensure reshuffling of learning sequences. Weight-updating formula in (7) involves learning rate function α(is) and neighborhood function hj,B(is):
where α0 is initial learning rate and is the lateral distancebetween and the jth neuron in the grid of output neurons . Learning rate function α(is) represents the rate of weight tuning and α(is) gradually decreases with the training time. Neighborhood function hj,B(is) is a two-dimensional Gaussian function (Figure 2(b)), with the purpose of producing more influence on weight update for neighboring neurons closer to . Gaussian standard deviation σ(is) controls the progressive size of the neighborhood function at the isth training step that is an exponential decay function,
where σ0 is the initial neighborhood size.
To quantify the SOM performance, intra-cluster distance and inter-cluster distance are evaluated. Through exhaustive trials and tests, optimal parameters for SOM implementation may be determined by minimizing intra-cluster distance but maximizing inter-cluster distance, which are No = 12, Nt = 10,000, σ0 = 3 and a0 = 0.02.
2.4. Evaluation of Clustering Performance
The objective of data clustering is to identify various clusters within the dataset such that data with similar attributes are likely to be classified into the same cluster. Each cluster can be characterized by its cluster center that provides a medium for data visualization. Cluster center ci is calculated by the average of all the elements (BMFc’s) in cluster Ci,.
where Nciis the number of elements in cluster i.
A good clustering should result in a high intra-cluster similarity yet large inter-cluster deviations. Intra-cluster similarity is measured by intra-cluster distance (Din),
where denotes the Euclidean distance. Inter-cluster distance measures the degree of distinction among clusters. Inter-cluster distance Dex is the average of all the pairwise inter-cluster distance Dij between cluster Ci and Cj is the distance between cluster center ciand cj, .
Unsupervised 12-neuron SOM is applied to 60,000 BMFc’s constructed respectively from 5-minute Zen-meditation EEG and resting EEG to study the spatial property of centroid frequency.
3.1. Property of Centroid Frequency
Figure 3 displaysthe 5-minute time evolution of centroid frequency for all 30 channels using temporal resolution of one second. Different colors represent different frequencies ranging from 10 to 22 Hz (the range of Fc computed). Zen-meditation EEG (Figure 3(b)) apparently exhibits higher frequency than resting EEG (Figure 3(a)).
The 5-minute resting EEG is dominated by global high-αrhythms (10 - 12 Hz) mixed with intermediate low β(>12 - 16 Hz) activities; whereas Zen-meditation EEG contains a large amount of low-βrhythms (13 - 18 Hz) mostlyin Fz, F3, FC4, FCz, C4, Cz, CPz, CP4, P4 and Pz. Higher frequency in the βband (>20 Hz) appears in O1, O2, Oz, T7, TP7, CP3, FT8, T8 and F7.
To observe the macroscopic behavior of local rhythmic properties, Figure 4 displays the time evolution of the 30-second average centroid frequency of each of the 9 scalp regions depicted in Figure 1 (dividing 30 EEG channels into 9 groups). Region notation tagged with “-R (-Z)” indicates the result for resting (Zen-meditation) EEG. Curves of Fc-R (thin lines) group tightly in the range 13.5 - 15 Hz, yet curves of Fc-Z (thick lines) extend from 15.5 Hz (LMF region) to 19.5 Hz (O region).
Figure 3. Time evolution of 30-channel centroid frequencies for (a) resting EEG, and (b) Zen-meditation EEG.
In resting EEG, faster activities (average 14.11 Hz) appear in the TM region almost throughout the entire 5-minute duration; whereas slower EEG rhythms (average 13.71 Hz) are observed in the LMP region. In Zen-meditation EEG, slower EEG activities (15.5 Hz) appear in the LMF region almost throughout the entire 5-minute duration; whereas faster EEG rhythms are observed mostly in the occipital region (19.5 Hz).
3.2. Results of SOM Clustering
Dataset of BMFc are classified by 12-neuron SOM using 10,000 training epochs (Nts), initial learning rate (α0) 0.02 and initial neighborhood size (σ0) 3. Table 1 displays the BMFc’s of 12 cluster centers of 12 cluster centers of 5-minute resting (upper) and Zen-meditation (lower) EEG. Each cluster center is computed by averaging all the cluster members inside the cluster. Average (std), highest and lowest frequency of each cluster center are listed under each BMFc. The cluster
Figure 4. Regional average of 30-second average centroid frequency.
is indexed according to the cluster size so that C1 (C12) contains the most (fewest) elements.
Clustering result reveals more than 75% high-alpha (10 - 12 Hz) dominant BMFc’s in resting EEG (average Fc < 15 Hz in clusters C1 - C8), yet more than 80% beta dominant BMFs’s in Zen-meditation EEG (minimum Fc > 13 Hz in all clusters except C2 and C11).Cluster-center BMFc exhibits the average intra-cluster characteristics of all the elements (BMFc’s). To explore the detailed spatio-spectral activities, Table 2 displays the representative BMFc’s randomly selected from top four clusters of resting and Zen-meditation EEG.
The top four clusters of BMFc of resting EEG are characterized by the following spatio-spectral properties:
C1: global high-αrhythms (~12 Hz);
C2: mainly high αaround 13 Hz, with intermittent left-frontal low β(13 - 14 Hz);
C3: global high α(~13 Hz) mixed withright-temporal low β(15 - 16 Hz);
C4: background high α(12 - 13 Hz) with occipital localized low β(15 - 16 Hz).
The top four clusters of BMFc of Zen-meditation EEG exhibit quite different spatio-spectral scenarios:
C1: 14 - 17 Hz background mixed with intermittent high β(20 - 25 Hz), slower activities in posterior regions;
C2: similar to C1, yet slower rhythms in frontal regions and intermittent high βactivity (~22 Hz) recurring in occipital area;
C3: 15 - 19 Hz βband, right-temporal higher β(20 - 25 Hz) extending to right occipital regions;
C4: similar to C3, yet high βmigrating towards left temporal regions.
Different clusters accordingly portray different spatio-spectral properties in the entire resting (Zen-meditation) course. Long-term multi-channel EEG
Table 1. BMFc’s of 12 cluster centers of 5-minute resting (upper) and Zen-meditation (lower) EEG. Average (std), highest and lowest frequency of each cluster center are listed under each BMFc.
Table 2. Representative BMFc’s randomly selected from top four clusters of resting and Zen-meditation EEG.
record may be interpreted by the cluster id that provides an alternative illustration of the temporal scenario of spatio-spectral characteristics. Figure 5 demonstrates the BMFc scenarios of (a) resting and (b) Zen-meditation EEG using a
Figure 5. BMFc scenarios of (a) resting and (b) Zen-meditation EEG (moving step of 0.05 second), labeled by the cluster id at the bottom of each BMFc.
step size of 0.05 second, with the cluster id shown at the bottom of each BMFc.
Higher Fc of resting EEG mostly focalizes in the left inferior temporal regions. On the other hand, Zen meditation EEG exhibits faster rhythms in a larger scalp area, including left inferior temporal, occipital and frontal regions. Figure 6 displays the distribution of the 5-minute average centroid frequency at each electrode site for (left) resting and (right) Zen-meditation EEG, that well corroborates the spatial property mentioned.
4. Conclusions and Discussions
The main contribution of this study includes the finding of global rapid rhythms (beta band) in Zen-meditation EEG and the introduction of unsupervised, self-learning scheme to the analysis of abundant complicated biomedical data involving spatio-spectral variations. BMFc quantifying the EEG spatial-spectral properties exhibits prominent difference between resting and Zen-meditation EEG. Zen-meditation EEG oscillates at the rhythms 3 - 5 Hz higher than resting EEG all over the entire scalp. The maximum of average centroid frequency is 20.77 Hz and the minimum of average centroid frequency is 15.12 Hz for Zen-meditation EEG, which is respectively 14.75 Hz and 13.57 Hz for resting EEG. Beta rhythms in the mid-beta band (16.5 - 20 Hz) distribute almost all over the scalp except a small mid-central region (Fz, FCz, Cz). Evidently, Zen-meditation EEG exhibits higher centroid frequency with a larger frequency range. Moreover, local spectral properties as shown by the centroid frequency of each individual channel reflect consistently faster rhythmic activities in Zen-meditation EEG than which in resting EEG. Beta rhythms have been associated with mind-body intervention, attention, emotion and cognition during
Figure 6. Distribution of 5-minute average centroid frequency for (left) resting and (right) Zen-meditation EEG.
the past decade . Previous study reports the increase of occipital beta power in the attentional task with correct responses but lack of beta activity change before erroneous responses . Global high beta rhythms, particularly at channels Oz, O1 and O2, of Zen-meditation EEG imply the state of exceptional mindfulness concentration evoked by Zen meditation.
This research was supported by the grants from the Ministry of Science and Technology of Taiwan (Grant No.: MOST 108-2221-E-009-079). We are thankful to Master student Shao-Hong Wang for his support of computer programming and data analysis.
List of Abbreviation
ANN: artificial neural network;
BMFc: brain mapping of centroid frequencies;
CWT: continuous wavelet transforms;
SOM: self-organizing map.
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