Multiple feature extraction and classification of electroencephalograph signal for Alzheimers' with spectrum and bispectrum.

Multiple feature extraction and classification of electroencephalograph signal for Alzheimers' with spectrum and bispectrum Ruofan Wang, Jiang Wang, Shunan Li, Haitao Yu, Bin Deng, and Xile Wei Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science 25, 013110 (2015); doi: 10.1063/1.4906038 View online: http://dx.doi.org/10.1063/1.4906038 View Table of Contents: http://scitation.aip.org/content/aip/journal/chaos/25/1?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Decreased coherence and functional connectivity of electroencephalograph in Alzheimer's disease Chaos 24, 033136 (2014); 10.1063/1.4896095 Brain source localization: A new method based on MUltiple SIgnal Classification algorithm and spatial sparsity of the field signal for electroencephalogram measurements Rev. Sci. Instrum. 84, 085117 (2013); 10.1063/1.4818966 Long-term variability of global statistical properties of epileptic brain networks Chaos 20, 043126 (2010); 10.1063/1.3504998 Intermittent spatio-temporal desynchronization and sequenced synchrony in ECoG signals Chaos 18, 037131 (2008); 10.1063/1.2979694 Detection of combined changes in interaural time and intensity differences: Segregated mechanisms in cue type and in operating frequency range?a) J. Acoust. Soc. Am. 123, 1602 (2008); 10.1121/1.2835226

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Multiple feature extraction and classification of electroencephalograph signal for Alzheimers’ with spectrum and bispectrum Ruofan Wang, Jiang Wang, Shunan Li, Haitao Yu, Bin Deng, and Xile Weia) School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072, China

(Received 21 November 2014; accepted 2 January 2015; published online 13 January 2015) In this paper, we have combined experimental neurophysiologic recording and statistical analysis to investigate the nonlinear characteristic and the cognitive function of the brain. Spectrum and bispectrum analyses are proposed to extract multiple effective features of electroencephalograph (EEG) signals from Alzheimer’s disease (AD) patients and further applied to distinguish AD patients from the normal controls. Spectral analysis based on autoregressive Burg method is first used to quantify the power distribution of EEG series in the frequency domain. Compared to the control group, the relative power spectral density of AD group is significantly higher in the theta frequency band, while lower in the alpha frequency bands. In addition, median frequency of spectrum is decreased, and spectral entropy ratio of these two frequency bands undergoes drastic changes at the P3 electrode in the central-parietal brain region, implying that the electrophysiological behavior in AD brain is much slower and less irregular. In order to explore the nonlinear high order information, bispectral analysis which measures the complexity of phase-coupling is further applied to P3 electrode in the whole frequency band. It is demonstrated that less bispectral peaks appear and the amplitudes of peaks fall, suggesting a decrease of non-Gaussianity and nonlinearity of EEG in ADs. Notably, the application of this method to five brain regions shows higher concentration of the weighted center of bispectrum and lower complexity reflecting phase-coupling by bispectral entropy. Based on spectrum and bispectrum analyses, six efficient features are extracted and then applied to discriminate AD from the normal in the five brain regions. The classification results indicate that all these features could differentiate AD patients from the normal controls with a maximum accuracy of 90.2%. Particularly, different brain regions are sensitive to different features. Moreover, the optimal combination of features obtained by discriminant analysis may improve the classification accuracy. These results demonstrate the great promise for scape EEG spectral and bispectral features as a potential effective method for detection of AD, which may C 2015 facilitate our understanding of the pathological mechanism of the disease. V AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4906038]

Alzheimer’s disease (AD) is a progressive, disabling neuro-degenerative disorder because of the widespread degeneration of synapses and death of neurons. Recently, electroencephalograph (EEG) is taken as a non-invasive method to track functional changes in AD brain. In this study, spectrum and bispectrum are applied to investigate the abnormalities of the five AD brain sub-regions in the frequency domain. Furthermore, multiple effective features based on spectrum and bispectrum are extracted. It is demonstrated that they could be used to classify AD from the normal effectively in the five brain regions. Particularly, each of the brain regions is sensitive to different features. Furthermore, a combination of features can greatly improve the classification accuracy. The preliminary results might provide a new imaging indicator for the detection and evaluation of the disease, which is challenged but valuable and helpful.

a)

Author to whom correspondence should be addressed. Electronic mail: [email protected]. Tel./Fax: 86-22-27402293.

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I. INTRODUCTION

AD, the most prevalent form of neuropathology leading to dementia, is a progressive, disabling neuro-degenerative disorder that affects mainly older person. It usually results in a loss in cognition, memory, judgment, even language, and functional skills.1,2 Although AD clinical diagnosis is achieved only by necropsy for the symptoms in early state are easily neglected as normal consequences of aging,3 a discriminating AD patients from the normal should be attempted. Nowadays, EEG has been widely used to track the electrical brain activity generated by cortex of AD brain, due to its high temporal resolution, non-invasion, and relatively low cost as compared with imaging tools.4,5 Abnormal field potential signals are observed in EEG when a patient is experiencing structural and functional changes in the cortex due to AD.6 Such abnormalities are reported as the slowing of the EEG,1,7 reduction of complexity in EEG,3 and perturbations in EEG synchrony.8,9 The traditional power spectral density (PSD) of EEG is a basic method to measure the activity of cortical cells arranged in parallel and space averaged over cortex physiologically,10 thus to infer information on brain activity in

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different cortical areas. It is commonly estimated based on parametric autoregressive (AR) model, which provides a formulation for analyzing the power of shorter time series and gives a smoother spectrum when compared to classical spectrum estimation methods (e.g., FFT).10 As well known, EEG exhibits several rhythms: the delta (0:5–4 Hz), theta (4–7 Hz), alpha (8–12 Hz), and beta (13–30 Hz) frequency band. Alterations in power density of these rhythms are supposedly associated with different brain functions, e.g., sleep stage, mental task, and even severity of neuropsychiatric disorder, such as Epilepsy, Parkinson’s disease, brain death, AD, and so on.11,12 Quantitative studies have shown that the power spectrum of EEG signals slows down, particularly in the high frequency bands in AD patients, which is supposedly correlated with the severity of AD.7,12,13 PSD based on AR model could characterize the group differences between AD patients and the normal controls in frequency domain. However, it focuses on the linearity, Gaussianity, and minimum-phase within EEG signals, i.e., the amplitudes of EEG signals are normally distributed, their statistical properties do not vary over time, and their frequency components are uncorrelated.14 In fact, it is extensively reported that the EEG signals are naturally nonlinear due to the nonlinearity of the brain and at the neuronal level. Hence, non-linear analysis techniques may be a better approach than traditional linear methods to obtain a better understanding of abnormal electrophysiological behavior of AD patients in EEG signals.15 Previous studies have revealed a decrease of complexity and irregularity of AD brain by the analysis of Lempel-Ziv complexity, multiscale entropy, sample entropy, approximate entropy, synchronization likelihood, and so on.7,16–19 For instance, Abasolo et al. have found significant decrease of approximate entropy values in the parietal region for AD patients,17 and a decrease in the parietal and occipital regions with sample entropy values also be observed.18 However, these measures do not provide insight into the biological phenomena due to the inherent high order information generated by the nonlinear interaction of distinct frequency components of EEG signals.20 Bispectrum analysis, in which the signal-to noise ratio for the non-Gaussian EEG is enhanced as the Gaussian sources of noise are suppressed, becomes more attractive in the investigation of the EEG to monitor the state of brain. Nonlinearities of EEG can be identified via the information of higher order phase coupling.20 Schack et al. have examined the existence of nonlinear phase coupling between theta and gamma EEG activities during memory processing.21 By bispectral analysis, Goshvarpour et al. have observed the increase of bispectrum magnitude for each EEG channel during meditation, which could be useful for distinction between the states before and during meditation.20 Moreover, LayEkuakille et al. have indicated that the decimated signal diagonalization (DSD) bispectrum reflected the degree of brain order/disorder of the recorded EEG signal.22 Recently, bispectral entropy extracted from EEG signals has been applied to automatically monitor the epileptic activities and classified all the three classes of EEG segments, namely, normal, interictal, and ictal.23 However, whether the bispectral

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analysis could be used to discriminate AD patients from the normal controls is still unclear. In order to explore this problem, in this work, we detect and assess the abnormalities of EEG signals from ADs based on spectrum and bispectrum analyses. We further extract multiple efficient features and apply them to discriminate AD from the normal. Accordingly, the subsequent parts of this paper are organized as follows: in Sec. II, we give a description of the experimental design and the EEG recording, including information of the subjects, the EEG data recording, and preprocessing; in Sec. III, we formulate the estimation of PSD and bispectrum, extract the EEG features, and explain the statistical analysis in detail; in Sec. IV, analysis results of the two groups are presented; which is followed by discussion in Sec. V; and conclusion in Sec. VI. II. EXPERIMENT DESIGN AND EEG RECORDING A. Subjects

Experiments were performed in two groups of subjects. (a) 14 right-handed patients with a diagnosis of probable AD (age: 74–78 years old; eight females and six males) according to the international Classification of diseases (ICD-10) of the world health organization and the diagnostic criteria of dementia in the Diagnostic and Statistical Manual of Psychiatric Disorders (DSM-IV).24 In order to evaluate the cognitive function, a through clinical neuroimaging and neurological examination were executed, including computed tomography (CT), structural MRI, cerebellar testing, cranial nerve examination, and Mini-Mental-Status examination (MMSE). The MMSE scores ranged from 11.7 to 14.9, which indicated a severe cognitive impairment. Usually, there were varying levels of cognitive impairment when MMSE scores were less than 27, and vice versa. In addition, clinical history was also considered. Exclusion criteria included use of drugs of antipsychotics, antidepressants, and anxiolytics, and presence of other neurological or psychiatric illness, such as vascular dementia (VD), other cerebrovascular diseases (i.e., cerebral infarction and cerebral hemorrhage), metabolic disorder, and severe depression. (b) 14 healthy age-matched subjects served as the controls which are all right-handed (age: 70–76 years old; ten females and four males). Their MMSE scores ranged from 28.1 to 30.0. They were healthy and intellectual, with no symptoms or personal history of neurological or psychiatric disorders. Additionally, they were not abusing alcohol or illicit drugs. All of them were classified as control subjects by these clinical examinations. Our study was performed with the approval of the local Ethics Committee. All control subjects and the caregivers of the patients had signed with written informed consent for participation in the current study. In addition, their informed written consent was obtained according to the declaration of Helsinki. B. EEG recordings and preprocessing

The continuous EEG data were collected for 10 min with the subjects in a relaxed state and under the


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FIG. 1. Electrode names and positions on the head (a) and 16-channal EEG signals recorded for one AD patient (b). The measurement region is divided into five regions: frontal (F); central-parietal (CP); occipital (O); left temporal (LT); and right temporal (RT) regions, represented by blue, purple, green, yellow, and red, respectively.

eyes-closed condition in order to avoid the additional artifacts caused by visual input and attention. During the experiment, all the subjects were seated upright in a dedicated semi-dark quiet room which is electromagnetic shielded. Additionally, they were told in advance to avoid any movements, such as body actions, eye movements, and blinks. To keep adequate alertness of subjects, their state and ongoing EEG was continuously monitored by experimenters during the experiment. EEG series was recorded from the 16 active shielded scalp loci of the international standard 10–20 system using Symtop recorder (model: UEA-B; sampling frequency: 1024 Hz; electrode impedances: 3 kX), which was widely used for clinical settings and research purposes. The 16 Ag–AgCl channels were located at Fp1, Fp2, F3, F4, C3, C4, P3, P4, O1, O2, F7, F8, T3, T4, T5, and T6, with all electrodes referenced to the bilateral ear (A1 and A2), as shown in Fig. 1(a). In order to reduce the dimension of the results, the 16 channels were grouped into 5 scalp regions based on their arrangement and location on the scalp to obtain a regional analysis. The regions included: (1) frontal (F); (2) centralparietal (CP); (3) occipital (O); (4) left temporal (LT); and (5) right temporal (RT). Features were extracted from each channel used in analyses. Every feature was averaged over each region for the significance analysis of group difference in follows. The raw EEG data recorded during the experiment were shown in Fig. 1(b). In order to achieve high confidence of the data, 16-channel EEG series of each subject was segmented into 5 non-overlapping epochs which last 8 s continuously by using the EEGLAB toolbox. Moreover, the artifacts caused by eye movement, muscular movement, or other visible disturbances were removed manually on the basis of a thorough visual inspection off-line. Then, each channel of intercepted EEG was decomposed into the four EEG sub-bands of interest: delta (0:5–4 Hz), theta (4–7 Hz), alpha (8–12 Hz), and beta (13–30 Hz) via the band-passed Finite Impulse Response (FIR) filter. Moreover, the digitized EEG data were processed and analyzed in a MATLAB environment (version 8.2.0.701.R2013b).

III. ANALYSIS METHODS A. Power spectral density analysis 1. Power spectral density

Due to finite size of the EEG data, one can only have an estimate of the true spectrum via a parametric approach, such as AR Burg method. There are two steps in the spectrum estimation procedure. First, estimate the parameters of the modelbased method from a given data sequence xðnÞ;0 n N 1. Second, estimate the PSD from these estimations. The AR method is based on modeling the data sequence xðnÞ as the output of a causal and discrete filter whose input is white noise, which is expressed as follows: xðnÞ ¼

p X

aðkÞ xðn kÞ þ xðnÞ;

(1)

k¼1

where aðkÞ is the AR coefficient, xðnÞ is the white noise of variance equal to r2 , and p is the order of the AR method. In this work, AR coefficients are estimated by the recursive Burg method, which is based on minimizing the forward and backward prediction errors, thus the PSD estimation is formed as25 e^p ^ BURG ð f Þ ¼ ; PSD p P j2pfk 1 þ a^p ðkÞe

(2)

k¼1

where e^p is the total least squares error. The model order p is determined by using Akaike information criterion (AIC). In our study, the model order is taken as p ¼ 10. Then, the relative PSD of each frequency point is given by PSDð f Þ ; relative PSDð f Þ ¼ f ¼f PH PSDð f Þ

(3)

f ¼fL

where ½fL ; fH is the whole range of the considered spectrum. For simplicity, relative PSD is denotedPas PSDr ðf Þ in short. H After the normalization, it follows that ff ¼f ¼fL PSDr ðf Þ ¼ 1.


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2. Power spectrum density-based features

The spectrum-based features are explained below: (i)

(ii)

Median frequency (MF) MF is accepted as one simpler way to summarize the spectral content of the PSD.23,26 The MF is defined as the frequency which contains half of the PSD power. Taking into consideration the cut-off frequencies of the band-pass filter applied to the EEG signals (0.5 and 30 Hz), the MF is computed as 2 3 MF X X 1 30Hz PSDr ð f Þ ¼ 4 PSDr ð f Þ5: (4) 2 f ¼0:5Hz f ¼0:5Hz Spectral entropy (SSE) SSE is extracted to characterize the irregularity of brain by assessing the disorder and diversity of the PSD. The values of SSE are high if the spectrum is broad and flat, (e.g., white noise), whereas the values of SSE are low if the spectrum is concentrated into narrow frequency bands (e.g., a sine wave).27 Normalized spectral entropy (SSE1) is based on Shannon’s entropy which is computed over the PSDr of a full cover of the considered spectrum ½fL ; fH Hz, and it is defined as SSE1 ¼

f ¼f 1 XH PSDr ð f Þ ln½PSDr ð f Þ; lnð N Þ f ¼fL

f ¼f 1 XH PSDr 2 ð f Þ ln PSDr 2 ð f Þ : lnð N Þ f ¼fL

SSEa ; SSEh

E½gðnÞgðn þ s1 Þgðn þ s2 Þ;

(6)

(8)

where Efg is the statistical expectation, si ði ¼ 1; 2Þ is time shift, and fgðnÞg is a Gaussian random process with the same autocorrelation function as fxðnÞg. For a random sequence, the cumulant function given above provides a measure of the distance to Gaussianity. If fxðnÞg is a Gaussian process, the third-order cumulant is zero. Moreover, when the sequence fxðnÞg is zero mean, the third-order cumulant function is changed as follows: cx3 ðs1 ; s2 Þ ¼ E½xðnÞxðn þ s1 Þxðn þ s2 Þ:

(9)

Similar to the power spectrum, bispectrum is twodimensional Fourier transform of the third-order cumulants, that is, Bx ðx1 ; x2 Þ ¼

Moreover, the SSE ratio of the alpha to theta frequency band is introduced since it is confirmed that the development of AD is accompanied with a large increase in theta activities and a progressive decline of alpha activities. Thus, SSE ratio quantifies the uncertainty of information of the two spectral frequency bands comprehensively and provides an easier and much obvious differentiation between AD patients and the control subjects than the SSE values in any separate frequency band. It is defined as follows: SSE ratio ¼

cx3 ðs1 ; s2 Þ ¼ E½xðnÞxðn þ s1 Þxðn þ s2 Þ

(5)

where N is the number of frequency points in ½fL ; fH . Moreover, the division by lnðNÞ normalizes the SSE1 to a scale from 0 to 1. Normalized spectral squared entropy (SSE2) SSE1 ¼

the phase information is ignored. In fact, the EEG signals are generated by a nonlinear system with abundant phase information except for frequency and power information. To detect the high-order information, the third order statistics is analyzed by using the bispectrum estimation. Assuming the observed data xðnÞ; 0 n N 1 is a discrete random sequence, its third-order cumulant can be defined as

XX s1

cx3 ðs1 ; s2 Þ expðjðs1 x1 þ s2 x2 ÞÞ;

s2

(10) where jx1 j p; jx2 j p; jx1 þ x2 j p. As we known, the bispectrum is a complex-valued function of two frequencies and exhibits symmetry, thus, it is calculated only in the nonredundant region termed as X (Fig. 2). When the phasecoupling harmonics of EEG are occurred, the statistical average will lead to a sharp peak of the bispectrum in the corresponding frequency.28

(7)

where a is the alpha frequency band (½8; 12 Hz) and h is the theta frequency band (½4; 7 Hz). B. Bispectrum analysis 1. Bispectrum

Conventional spectrum methods assume linearity and Gaussianity within EEG signals. Under such assumptions,

FIG. 2. Non-redundant region used for the computation of the bispectrum for EEG signals. Bispectrum based features are calculated from this region. Frequencies are normalized by the Nyquist frequency.


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2. Bispectrum-based features

The formulae for the bispectrum-based features are given as follows: (i)

(ii)

Weighted center of bispectrum (WCOB) Similar to the median frequency, the weighted center summarizes the bispectral content.29 The WCOB is defined as follows: P P iBði; jÞ jBði; jÞ X ; f2m ¼ PX ; (11) f1m ¼ P X Bði; jÞ X Bði; jÞ where i, j are the frequency band index in the nonredundant region, f1m is WCOBx , f2m is WCOBy , and X is the region as defined in Fig. 2. Obviously, WCOB is a two-dimensional vector involving f1 and f2 , which could reflect the interaction of different frequency components. Bispectral entropy Normalized bispectral entropy (BE1) BE1 ¼

1 X pn lnðpn Þ; lnðMÞ n

(12)

where pn ¼ PjBðjBf1ð; ff2;Þjf Þj. X is the region as defined in X

1

2

Fig. 2. n ¼ 1; 2; :::; M, and M is the number of points within the region X. Moreover, the division by lnðMÞ normalizes the BE1 to a scale from 0 to 1. Normalized bispectral squared entropy (BE2) BE2 ¼

1 X qn lnðqn Þ; ð ln MÞ n

accuracy (minimal false negative and false positive results) could be obtained at the optimum threshold which was determined from the ROC curve as the closest value to the left top point (100% sensitivity and 100% specificity). Moreover, the area under the ROC curve (AUC) characterized the performance of classification, for a perfect classification the area is 1 while an AUC of 0.5 represented a worthless test. Additionally, Fig. 3 shows a block diagram with the different steps followed in this study. IV. RESULTS

We apply the spectrum and bispectrum analyses of 16channel EEG signals to discriminate AD patients from the normal controls. The results were averaged based on all the artefact-free epochs within the 5-min period of recording. In order to reduce the dimension of the results, the EEG channels were grouped in five brain regions (frontal, central-parietal, occipital, left temporal, and right temporal region). Moreover, the statistical group difference of the two groups was assessed with one-way ANOVA with Bonferroni’s correction. A. Relative PSD analysis

Spectrum analysis was first applied to every electrode and brain region. Fig. 4 showed the relative PSD of 16 EEG channels (line) and the average PSD values of five brain regions (histogram) in four frequency bands for AD group and the control group. For the two groups, the relative PSD decreased with the increase of the frequency. In the delta frequency band, the relative PSD values were ranged in

(13)

2

where qn ¼ PjBðjBf1ð; ff2;Þjf Þj2 and X is the region as defined 1 2 X in Fig. 2.23 C. Statistical analysis

One-way Analysis of Variance (ANOVA) test was used to assess significant changes in the spectrum and bispectrum based features for the two groups. A smaller P-value and a larger F-value indicate a higher group difference, and vice versa. Generally, P < 0:05 was considered as the significance level in statistics. Additionally, as the multi-comparisons were conducted, Bonferroni correction was applied to avoid spurious rejections.30 Therefore, the significance level was set at P < 0:05=4 ¼ 0:0125 with compounding F > 6:8759 for the comparison of four frequency bands and P < 0:05=5 ¼ 0:01 (F > 7:3525) as the comparison was executed in five brain regions throughout the whole frequency band. The ability of the spectrum and bispectrum-based features to discriminate AD patients from the normal controls in a certain brain region where P < 0:01 by ANOVA was evaluated using receiver operating characteristic (ROC) curves.31 Results were showed in terms of sensitivity (i.e., proportion of all AD patients who tests positive), specificity (i.e., percentage of the normal controls correctly classified), and accuracy (i.e., total fraction of AD and the normal controls well classified) for all the available thresholds. The highest

FIG. 3. Block diagram of classification between AD patients and the normal from the EEG analysis and classification.


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FIG. 4. The overall relative PSD of 16 EEG channels (line) and the average PSD values of each brain region (histogram) in the (a) delta; (b) theta; (c) alpha; and (d) beta frequency band for AD group (red) and the control group (blue). Five shading areas with different colors represent the five brain regions. The line corresponds to the top and left axis, while the histogram corresponds to the bottom and right axis. represents significant difference between the two groups with P < 0:0125 by ANOVA with statistical postcorrection.

½0:3; 0:65, while in the beta frequency band the relative PSD fluctuated in ½0:05; 0:3, indicating that most energy focused on the lower frequency when the subjects were in the resting state. Comparing the relative PSD values of AD group with that of the control group, we obtained several interesting results. There was no obvious group difference in the delta frequency band, neither for each electrode nor for brain region level (Fig. 4(a)). In the theta frequency band (Fig. 4(b)), the relative PSD values of AD group were much larger than that of the control group, especially in the centralparietal, occipital, and temporal brain regions. In the higher frequency band (Figs. 4(c) and 4(d)), the relative PSD values of AD group were much smaller than that of the control group: frontal, central-parietal, occipital, and left temporal in the alpha frequency; frontal, occipital, and right temporal in the beta frequency. Moreover, MF of the spectrum in the each brain region was shown in Fig. 5 to get insight into the overall frequency components of relative PSD. Due to the changes of relative PSD, MF in the five brain regions (Fig. 5) was significantly decreased in AD in spite of the different distribution in different brain regions, reflecting the typical slowing of AD patients’ brain recordings.

Considering that the most obvious changes occurred in the theta and alpha frequency bands, we calculated the ratio of SSE1 on these two frequency bands and applied it to analysis of the whole brain for AD and the control group, as

FIG. 5. MF of the whole frequency for AD group (red) and the control group (blue) in the five brain regions. Standard deviations are shown with error bars.


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FIG. 6. Topographic maps of ratio of the SSE1 and SSE2 ratio of the alpha to theta frequency band for (a) AD group and (b) the control group. Meanwhile, the brain is divided into five regions by the black line. The color marked the value of SSE ratio of each corresponding electrode (blue: a low value; red: a high value).

shown in Figs. 6(a) and 6(b). As we know, SSE1 ratio mainly depended on such spectral variables as the degree of dominance of a few peaks, the number of the peaks, and their peakedness. It was found that the largest SSE1 ratio for both AD and the control group was emerged in the centralparietal, occipital, and temporal regions. However, the values were dropped in AD group (½0:4; 0:7 for AD group vs. ½0:8; 2:2 for the control group), suggesting that the irregularity of the EEG signals in AD groups decreased markedly. Moreover, the highest irregularity was located at P3 electrode in the control group while shifted to P4 in AD group. Thus, SSE1 ratio descends dramatically in P3 in AD group. In order to display the group difference much more obviously, we further calculated the ratio of SSE2 on the two frequency bands (Figs. 6(c) and 6(d)). Similarly, the largest alteration of SSE2 occurred in P3 electrode. The SSE2 ratio could amplify the influence of the peak in PSD owing to the square in the formula. However, whether it had an advantage over SSE1 ratio or not was not clear. Subsequent Sec. IV C would further compare the two types of spectral entropy ratio by one-way ANOVA and classification analysis. B. Bispectrum analysis

From the above spectrum analysis, we found that P3 electrode had significant group difference on PSD-based features. We further apply bispectrum analysis to the same electrode to explore the information of phase-coupling

harmonics, which could not be provided by spectrum analysis. Besides, the phase-coupling harmonics of EEG signals were identified by the several peaks in the three-dimensional curved surface of the bispectrum, and the corresponding bifrequency band could be accurately detected from the twodimensional contour map. Fig. 7 showed the typical three-dimensional curved surface of the bispectrum (left), the relative PSD (above, right) and the two-dimensional contour map (below, right) of P3 electrode for AD and the control groups. The difference of bispectrum for the two groups was obvious. For the control group (Fig. 7(b)), there were several peaks and slopes in the bifrequencies ranging from 0 to 15 Hz. Moreover, the value of main sharp peak reached 6 104 corresponding to the frequency ð10; 10Þ Hz (the alpha frequency band). While for AD group (Fig. 7(a), only one main peak whose value was about 3 104 located at ð7; 7Þ Hz (the theta frequency band), indicating that the P3 EEG signal of AD was tended to be Gaussian in the high bands. In summary, the frequency components where phase-coupled harmonics happened shifted to the low frequency obviously in AD, which were consistent with the previous results of spectrum. Furthermore, both the number and amplitude of the bispectral peak in AD were decreased, meaning a descent of the non-linearity and nonGaussianity for P3 EEG signal in AD brain. The application of this analysis method was further extended to the five brain region, respectively. The results of


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FIG. 7. Typical three-dimensional curved surface of the bispectrum (left), relative PSD estimated by AR-Burg method (above, right), and the two-dimensional contour map (below, right) of P3 electrode in the central-parietal brain region for (a) AD group; and (b) the control group. The 2-dimensional contour map of the bispectrum was the vertical view of the 3-dimensional curved surface, from which the frequency of bispectral peak is clearly exhibited with warmer color line.

the CP and RT regions were represented in Fig. 8. As can be seen, the group difference (peak amplitudes and number) was remarkable in brain region level, particularly in the RT region. Thus, it might be a rather sensitive analysis method for differentiating and locating the brain region of cerebral injury in AD. Other three regions (not shown here) had the similar results except the slight difference in the number and amplitude of bispectral peak. To look for some quantitative indicators, we introduced the WCOB. If each bispectral point of EEG signals was assigned a weight, then the weighted center of each brain region in the bi-frequencies plane can be calculated. Fig. 9 displayed the distribution of the weighted center of bispectrum WCOB which characterizes the relationship of different frequency components in the f1 /f2 -coordinates. The distribution of WCOB was different in the five brain regions

for two groups. For AD group, f1 and f2 showed an approximately linear correlation for each brain region, which was lost for the control group. In addition, the WCOB of AD group was smaller and much more concentrated than that of the control group, which was closely related to that the sharp peaks of bispectrum in AD group were lesser than that of the control group, which resulted from the decreased number and the left shift of the bispectral peaks in AD. From the above results, we concluded that WCOB is sensitive to the extent and the brain regions of AD may lead to a distinction of the normal region from the insulted region. This implied that the alteration of WCOB might associate with low frequency activities, less irregularity over five brain regions in AD brain. Fig. 10 showed statistical results of bispectral entropy (BE1) and bispectral square entropy (BE2) measuring the


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FIG. 8. Three-dimensional curved surface of the bispectrum and two-dimensional contour map in the CP and right temporal (LT) brain regions for AD group ((a) and (c)) and the control group ((b) and (d)), respectively.

complexity of phase-coupling in the five brain regions for AD and the control group. Both BE1 and BE2 values of AD group were smaller than that of the control group. Moreover, obvious effect of group difference was observed for BE1 than BE2. The analysis of BE1 showed that the most significant differences between AD patients and the normal controls were achieved in the frontal and the right temporal regions (p < 0.001), with similar but not so significant results in the occipital region (p < 0.05). As in the case of BE1, much higher differences between the two groups were observed in the frontal and right temporal regions (p < 0.01). On the other hand, no significant group differences were observed in the remaining three brain regions, but AD group still exhibited a slight decrease of BE2 than that of the control group.

Through the analysis of spectrum and bispectrum above, we have extracted six features (MF, SSE1 ratio, SSE2 ratio, WCOB, BE1, and BE2) in five brain regions (the frontal, central-parietal, occipital, left temporal, and right temporal regions) from AD and the normal EEG. The statistical significance of group difference using one-way ANOVA with Bonferroni correction was summarized in Table I. It was found that the statistical results of each feature in different brain regions were various. Particularly, there was a much higher effect of group difference in the frontal (F) region for the six features (P < 0:01; F > 7:3525). Moreover, the group difference was significant in the CP and LT brain regions for all three spectrum-based features, while remarkable in the RT brain region for all bispectrum-based features. As in the occipital (O) region, the remarkable differences

FIG. 9. WCOB in five brain regions for (a) AD group and (b) the control group.


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FIG. 10. Boxplots representing the distribution of mean values for bispectral entropy (BE1), and bispectral square entropy (BE2) in five brain regions (frontal; central-parietal; occipital; left temporal; right temporal) for AD (red) and the control group (blue). Significant differences between groups are marked with a symbol (* p < 0.05, ** p < 0.01, and *** p < 0.001).

between AD and the control groups were observed from spectral features of MF and SSE1 ratio, bispectral features of WCOB and BE2, respectively. Obviously, there might be multiple features which present significant group difference TABLE I. Results of one-way ANOVA for the six features including MF, SSE1 ratio, SSE2 ratio, WCOB, BE1, and BE2 in the five brain regions for AD and the control group.

in one certain brain region, however, which one could be better for discriminating AD from the normal? In order to evaluate the ability of the classification performance of the six features in five brain regions, a two-class Support Vector Machine (SVM) classifier was applied and five-folder crossvalidation classification results were shown in Fig. 10. C. Classification analysis and discriminant analysis

Brain region Method MF SSE1 ratio SSE2 ratio WCOB BE1 BE2

F P F P F P F P F P F P F

0.002 11.4 0.0028 10.22 0.0004 15.08 0.001 12.81 0.0002 16.98 0.0023 10.64

CP

O

LT

RT

0.0079 7.85 0.000006 35.53 0.0002 17.55 0.0779 3.28 0.0525 4.01 0.304 1.09

0.0077 7.92 0.0006 14.16 0.0585 3.8 0.0027 10.35 0.0127 7.02 0.3149 1.04

0.0096 7.44 0.000005 36.15 0.0056 8.62 0.0004 14.77 0.1012 2.82 0.2678 1.26

0.0004 14.78 0.0002 17.26 0.0547 3.93 0.0004 15.03 0.0002 16.9 0.0089 7.61

Fig. 11 showed the ROC curves of each feature in five brain region. We calculate the corresponding AUC whose larger value means better classification performance. In addition, the results of the sensitivity, specificity, AUC, and accuracy for the six features were shown in Table II. The classification results demonstrated that AD patients could be detected and distinguished from the normal by using the six features effectively. Notably, both highest AUC and accuracy were registered by bispectral entropy (BE1) in the right temporal region. Moreover, the highest accuracy values achieved in different brain regions were different, they were 90.0% and 90.2% with BE1 in the frontal and right temporal regions, 86.7% with SSE2 ratio in the central-parietal region, 81.6% with WCOB in the occipital region, and 89.6% with


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FIG. 11. ROC curves which evaluate the classification performance between AD patients and the normal controls with the MF, SSE1, SSE2, WCOB, BE1, and BE2 in the whole frequency band. Moreover, the green dotted line is known as the "no-discrimination line" and corresponds to a classifier which returns random guesses.

SSE1 ratio in the left temporal region, which were agreed with the statistical analyses aforementioned in Figs. 4–6. We further attempted to discriminate both groups by taking more than one extracted features to improve the classification. A discriminant analysis was applied to find the optimal combinations of the extracted features in the five brain regions. The optimal combinations of features and corresponding classification accuracy for each brain region were shown in Table III. Compared to that with only one feature, it was demonstrated the optimal combination of features could improve the classification accuracy. In the RT brain region, the classification accuracy of SSE1 ratio and BE1 was reached to 93.4% (Table III), which was higher than 84.9% only with SSE1 ratio and 90.2% with BE1 (Table II). The similar results were obtained on the other four brain regions, and the classification accuracies achieved were 92.6%, 90.0%, 86.6%, and 90.2% with different optimal combinations of features in the frontal, central-parietal, occipital, and left temporal brain regions, respectively, which was higher than that with only one feature. To investigate the influence of multiple features on the classification accuracy, a correlation analysis of the six features was carried out and the correlation matrix among the

six features for both groups was shown in Tables IV and V. From Table IV, it was found that in AD group, MF, WCOB, BE1, and BE2 were significantly correlated with each other. Thus, the combination of these four features might not improve the classification accuracy obviously. Moreover, strong correlation between SSE1 ratio and SSE2 ratio was founded, which was lost in the control group (Table V). This may explain that why only two uncorrelated combined features could greatly improve the classification accuracy in Table III. V. DISCUSSION

We have studied the ability of spectrum and bispectrum measures to characterize spontaneous EEG rhythms from 14 AD patients and 14 normal controls during resting conditions. It has been generally accepted that there are alterations of EEG rhythms in the AD brain.1,3,7,32–36 Our findings suggested that AD induced a slowing of EEG signals and a decrease in statistical irregularity. Additionally, we provided a new perspective and knowledge of phase-coupling degree in different brain regions by analyzing the bispectrum for AD and the normal controls. We further find out the best EEG feature and feature combination which to be potential


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TABLE II. Results of the ROC analysis for the six features: MF, SSE1 ratio, SSE2 ratio, WCOB, BE1, and BE2 which include sensitivity, specificity, accuracy, and AUC. Parameters of ROC curve Brain region Frontal

Centro-parietal

Occipital

Left temporal

Right temporal

Feature

Sensitivity (%)

Specificity (%)

Accuracy (%)

AUC

MF SSE1 ratio SSE2 ratio WCOB BE1 BE2 MF SSE1 ratio SSE2 ratio WCOB BE1 BE2 MF SSE1 ratio SSE2 ratio WCOB BE1 BE2 MF SSE1 ratio SSE2 ratio WCOB BE1 BE2 MF SSE1 ratio SSE2 ratio WCOB BE1 BE2

93.3 86.7 79.3 93.4 93.6 94.2 80.2 83.5 91.2 78.5 83.4 67.2 81.3 79.3 78.6 85.4 83.4 70.3 87.2 92.5 91.4 88.4 82.1 79.3 89.2 87.6 80.2 88.4 91.3 90.6

80.0 79.7 67.2 82.6 86.1 81.7 73.3 86.8 83.7 73.6 71.3 74.3 78.6 72.9 73.3 78.2 75.6 61.5 78.4 82.8 86.6 83.7 73.8 73.5 82.8 83.4 72.7 85.1 88.7 88.9

86.6 83.3 74.2 88.4 90.0 88.6 76.5 85.0 86.7 76.4 78.2 71.3 80.0 76.7 75.0 81.6 78.3 67.3 82.5 89.6 88.3 85.3 78.4 75.2 85.2 84.9 76.8 86.7 90.2 89.7

0.9133 0.9822 0.9422 0.9244 0.9500 0.9411 0.9400 0.9267 0.9011 0.9632 0.8746 0.8735 0.8842 0.9267 0.9011 0.9478 0.9050 0.8244 0.9036 0.9367 0.9025 0.9478 0.8673 0.8133 0.9289 0.9767 0.9144 0.9789 0.9846 0.9647

indicators for cognitive degeneration in AD in a certain brain region by examining the discriminating power of different features proposed. Three spectral-based features (median frequency, spectral entropy ratio, and spectral square entropy ratio) and three bispectral features (the weighted center, bispectral entropy, and bispectral square entropy) were extracted to evaluate the changes of frequency components, statistical irregularity, and nonlinear complexity of phasecoupling in ADs. Compared to the normal controls, the relative PSD values of AD patients were significantly increased in the theta frequency band while markedly decreased in the alpha frequency band, particularly in central-parietal, occipital, and temporal brain regions. Moreover, the decreased median frequency also indicated a loss of frequency components in the high frequency bands, suggesting that brains affected by AD show a much slower physiological behavior.1,3,7,12,37,38

These abnormalities could reflect two different pathophysiological changes: the relative PSD decrease for higher frequencies could be related to alterations in cortico-cortical connections, whereas the increase for lower frequencies could be related to the lack of influence of subcortical cholinergic structures on cortical electrical activity.12,39,40 Furthermore, less irregularity was observed by spectrum entropy and spectrum square entropy analysis in this work, which was intrinsically related to the reduced number of signal components.41,42 These results were consistent with the other widely held view that the complexity of AD EEG, obtained by applying non-linear methods to study the brain activity in AD, was reduced.3,7 For instance, Escudero et al. (2006) have revealed that AD patients usually have lower sample entropy values than the normal by multi-scale entropy analysis.16 Abasolo et al. (2006) have found an increase of EEG regularity in AD patients with the

TABLE III. Optimal combination of extracted features obtained by discriminant analysis in the five brain regions. Brain region Optimal combination Accuracy (%)

F

CP

O

LT

RT

BE1 þ SSE2 ratio 92.6

SSE1 ratio þ MF 90.0

SSE1 ratio þ WCOB 86.6

SSE1 ratio þ WCOB 90.2

SSE1 ratio þ BE1 93.4


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TABLE IV. Correlations among the six extracted features: MF, SSE1 ratio, SSE2 ratio, WCOB, BE1, and BE2 in the five brain regions for AD group.

MF SSE1 ratio SSE2 ratio WCOB BE1 BE2

MF

SSE1 ratio

SSE2 ratio

WCOB

BE1

BE2

1 0.04 0.2 0.72 0.73 0.8

0.04 1 0.97 0.22 0.29 0.3

0.2 0.97 1 0.4 0.46 0.45

0.72 0.22 0.4 1 0.68 0.86

0.73 0.29 0.46 0.68 1 0.92

0.8 0.3 0.45 0.86 0.92 1

significantly decreased sample entropy values.18 The reduction of complexity or irregularity was associated with a decreased dynamic complexity of part of the brain,43 and the neurotransmitter deficiency, neuronal death, and even the alteration of network structure.12,34–36 Although the analysis results of PSD characterize the changes of EEG in the frequency domain, they could not provide the high order phase-coupling information which was critically important to investigate the non-linearity interaction among its frequency components.44 Bispectral analysis offered a way of gaining phase information by identifying the phase couplings harmonics of signals. It was demonstrated that bispectral analysis was effective to assess the brain function and state, in medical contexts such as the automatic identification of epilepsy,23,45 the monitor of depth of anaesthesia,46 and even meditation.20 Additionally, much attention had been given to research the electrophysiological signals by applying the bispectrum based features. Huang et al. have extracted WCOB and bicoherence index from scalp EEG of rats to diagnose ischemic cerebral injury with the average classification accuracy of 91.67%.47 Moreover, the features of weighted center of bispectrum and bispectral entropies were adopted to identify the epileptic EEG signals automately by Acharya et al.23,45 In other works, bispectral entropies have also been derived to find the rhythmic nature of heart rate variability (HRV) from bispectrum plots.48 However, bispectrum analysis was seldom used to differentiate AD patients from the normal. In this work, bispectral analysis showed that phase couplings harmonics were occurred in the lower frequency band in AD group than the control group. Furthermore, it was observed that the numbers and amplitudes of bispectral peaks dropped, suggesting a decrease of non-Gaussianity and nonlinearity of EEG in ADs, particularly in high frequency band. In addition, the application of this method to five brain regions achieved TABLE V. Correlations among the six extracted features: MF, SSE1, SSE2, WCOB, BE1, and BE2 in the five brain regions for the control group.

MF SSE1 ratio SSE2 ratio WCOB BE1 BE2

MF

SSE1 ratio

SSE2 ratio

WCOB

BE1

BE2

1 0.28 0.02 0.67 0.55 0.65

0.28 1 0.26 0.11 0.3 0.11

0.02 0.26 1 0.05 0.01 0.17

0.67 0.11 0.05 1 0.95 0.91

0.55 0.3 0.01 0.95 1 0.89

0.65 0.11 0.17 0.91 0.89 1

higher concentration of the weighted center of bispectrum and lower complexity reflecting phase-coupling by bispectral entropy, which was also related to a slowing of the brain activity in AD. Notably, we aimed to examine the group difference of spectral and bispectral features on a basis of topographical sub-region, which do not necessarily correspond to the cortical location of the source of the brain activity. This differed from the previous researches which employed most of the features on either a global or an individual channel basis. Finally, the multiple efficient features based on spectrum and bispectrum were applied to classify AD patients from the normal controls. The results in Fig. 11 and Table II evaluated the ability of the classification performance of all features in five brain regions, respectively. It revealed that the classification of each brain region could perform better with different features, and the highest accuracy values achieved were 90.0% and 90.2% with BE1 in the frontal and right temporal regions, 86.7% with SSE2 ratio in the centralparietal region, 81.6% with WCOB in the occipital region, and 89.6% with SSE1 ratio in the left temporal region, which were agreed with the statistical analyses aforementioned. Remarkably, the highest two values of accuracy 90.0% and 90.2% were obtained in the frontal and right temporal brain regions, suggesting that the BE1 was superior to other features in the two regions. Meanwhile, specificity of 86.1% and 88.7% (ratio of the normal control properly classified) and sensitivity of 93.6% and 91.3% (percentage of AD patients correctly identified) were achieved. In addition, the spectrum based features performed spectacularly well in the central-parietal and left temporal regions, with the accuracy of 86.7% and 89.6%, respectively. Interestingly, via a discriminant analysis, the optimal combination of the six extracted features in every brain region was determined. The classification with the combined features could achieve 92.6%, 90.0%, 86.6%, 90.2%, and 93.4% in the frontal, central-parietal, occipital, left temporal, and right temporal brain regions, respectively, which was higher than that with only one feature, as shown in Table III. In the previous studies, much research has been done to discriminate the two groups from the view of non-linear dynamics. However, the accuracies achieved are lower in most papers: 69.5% using D2,49 77.3% with sample entropy,18 81.8% with Lempel-Ziv complexity,50 and 90.1% with multi-scale entropy.16 More recently, Wang et al. have obtained the classification accuracy of 91.4% with the combination of the relative PSD and the normalized degree of functional network, which was higher than that of any one feature (88.5% for PSD value and 82.9% for degree of network).51 Compared with these researches, it was founded that the application of spectral and bispectral-based features proposed in this paper could improve the classification accuracy, which might be attributed to the following two points: (i) the methodological extracted features could characterize the underlying physiological changes much more obviously, especially the optimal combination of features; (ii) the differences of the various results might be associated with the composition of AD patient samples, including the difference of gender, age, and degree of the disease’s severity (reflected


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by the MMSE scored). In addition, the investigation on the functional brain connectivity could be extended in our further study as a biomarker for cognitive impairment in AD. VI. CONCLUSIONS

In this paper, we have detected the abnormalities of corticocortical EEG signals of AD patients by spectrum and bispectrum analyses and extracted six efficient features to perform classification of AD from the normal. By the analysis of relative PSD estimated by AR Burg method, it is found that compared with the control group, the relative PSD of AD group is significantly increased in the theta frequency band while markedly decreased in the alpha frequency band, particularly in central-parietal, occipital, and temporal brain regions. In order to explore the nonlinear high order information, we introduce bispectral analysis. It is shown that the frequency components where phase-coupled harmonics happened shifted to the low frequency. Moreover, less bispectral peaks appear and the amplitudes of peaks fall, suggesting a decrease of non-Gaussianity and nonlinearity of EEG in ADs. Further, six features are extracted to assess the abnormalities quantitatively from frequency perspective. The frequency features of the median frequency and the weighted center of bispectrum imply a loss of frequency components in ADs. Additionally, spectral entropy ratio 1 and 2 and bispectral entropy 1 and 2 are decreased, suggesting a less irregularity and phase-coupling complexity of electrophysiological behavior. Finally, all efficient features are applied to the classification of the two groups for five brain regions. It is indicated that all these features could differentiate ADs from the normal, and the classification of each brain region could perform better with a specific feature. Besides, the optimal combination of features determined by discriminant analysis can improve the classification accuracy. In sum, the spectral and bispectral analyses could detect and identify the abnormalities of AD brain effectively. Although the sample size of the subjects is small, the results obtained in this paper may facilitate our understanding of the functional alteration in AD brain. ACKNOWLEDGMENTS

This work was supported by Tianjin Municipal Natural Science Foundation under Grant Nos. 12JCZDJC21100 and 13JCZDJC27900, National Natural Science Foundation of China (NSFC) under Grant Nos. 61302002 and 61372010, and Jilin Provincial Natural Science Foundation under Grant No. 20130101170JC. 1

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