Classification of seizure based on the time-frequency image of EEG signals using HHT and SVM

Biomedical Signal Processing and Control 13 (2014) 15–22

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Technical Note

Classification of seizure based on the time-frequency image of EEG signals using HHT and SVM Kai Fu, Jianfeng Qu ∗ , Yi Chai, Yong Dong School of Automation, Chongqing University, Chongqing 400044, China

a r t i c l e

i n f o

Article history: Received 23 January 2014 Received in revised form 4 March 2014 Accepted 17 March 2014 Keywords: Electroencephalogram (EEG) signal Hilbert–Huang transform Time-frequency image Support vector machine Seizure classification

a b s t r a c t The detection of seizure activity in electroencephalogram (EEG) signals is crucial for the classification of epileptic seizures. However, epileptic seizures occur irregularly and unpredictably, automatic seizure detection in EEG recordings is highly required. In this work, we present a new technique for seizure classification of EEG signals using Hilbert–Huang transform (HHT) and support vector machine (SVM). In our method, the HHT based time-frequency representation (TFR) has been considered as time-frequency image (TFI), the segmentation of TFI has been implemented based on the frequency-bands of the rhythms of EEG signals, the histogram of grayscale sub-images has been represented. Statistical features such as mean, variance, skewness and kurtosis of pixel intensity in the histogram have been extracted. The SVM with radial basis function (RBF) kernel has been employed for classification of seizure and nonseizure EEG signals. The classification accuracy and receiver operating characteristics (ROC) curve have been used for evaluating the performance of the classifier. Experimental results show that the best average classification accuracy of this algorithm can reach 99.125% with the theta rhythm of EEG signals. © 2014 Elsevier Ltd. All rights reserved.

1. Introduction Epilepsy is one of the most common disorders that characterized by recurrent discharge from the cerebral cortex. As the seizures are episodic in their occurrences, detection and prediction of epilepsy from electroencephalogram (EEG) signals is a tedious and timeconsuming process. It requires an expert’s effort in analyzing the entire length of the EEG recordings to detect the seizure activity. Hence, new innovations for automatic detection of seizure have been sought by many researchers for a long time. However, the EEG is a highly complex signal which is nonlinear and nonstationary, the detection of the seizure from the EEG signal using traditional spectral analysis methods based on Fourier transform has some limitations, where the Fourier transform assumes that the signal being analyzed should be stationary. Recently, many nonlinear and nonstationary methods [1–4] including short time Fourier transform (STFT) [3], wavelet analysis [2], Wigner–Ville distribution (WVD) have been proposed to extract new parameters for seizure classification in EEG signals. However, these methods also have some weaknesses, for example the major limitation of STFT is unavoidable in trade-off between time and frequency resolutions, the wavelet theory is limited by

∗ Corresponding author. Tel.: +86 23 65106464. E-mail address: [email protected] (J. Qu). http://dx.doi.org/10.1016/j.bspc.2014.03.007 1746-8094/© 2014 Elsevier Ltd. All rights reserved.

the fundamental uncertainty principle, the difficulty of the WVD is the severe cross terms as indicated by the existence of negative power for some frequency ranges [5]. More recently, a novel nonlinear and nonstationary method for analyzing signals, namely Hilbert–Huang transform (HHT), has been proposed to process high dimensional EEG signals [6,7]. A typical application of the HHT technique for seizure classification is presented in this work. As a kind of time-frequency analysis method, HHT can reveal the information of signal both in time and frequency domain. HHT is mainly applied in analyzing both nonlinear and nonstationary signal, as the core of the technique to decompose signals is posteriori and enables the extraction of the inner scales of each signal, so it has a great advantage in EEG signal processing. Compared with the above-mentioned time-frequency analysis methods, HHT is based on empirical mode decomposition (EMD) [6] which is an intuitive, direct and adaptive decomposing method using the basis of the decomposition derived from the signal. The EMD technique decomposes a dataset into a finite and often small number of intrinsic mode functions (IMFs) that admit well-behaved Hilbert transforms [8]. Recently, the applications of EMD and HHT methods are well presented by many researchers in their works [9–13]. Martis et al. used features of spectral peaks, spectral entropy and spectral energy computed from the IMFs for automated diagnosis of seizure [9]. Oweis and Abdulhay employed the weight frequency of IMF using HHT to detect seizure from EEG signal [10]. Bajaj and Pachori presented a method which used HHT

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K. Fu et al. / Biomedical Signal Processing and Control 13 (2014) 15–22

for separation of the rhythms of the EEG signal and applied the method to classification of seizure and nonseizure EEG signals [13]. Recently, some machine learning classification techniques for seizure classification have been presented by researchers [16–18]. Among these techniques, support vector machine (SVM) has shown a good performance in classification [16]. SVM was initially developed as a binary classifier and thus it has a great advantage in binary classification problems such as seizure detection. Compared with other algorithms based on empirical risk minimization (ERM) principle, such as rule-based classifier and artificial neural network (ANN) [17,18], SVM is based on structure risk minimization (SRM) principle. It constructs an optimal separating hyper-plane in the feature space and makes the learning machine get the global optimum [15]. This paper discusses an automatic detection of epileptic seizures based on the time-frequency image using combined HHT and SVM. The statistical features including mean, variance, skewness and kurtosis of pixel intensity in the histogram of segmented grayscale time-frequency image (TFI) have been extracted. A hypothesis testing with lower p-values indicates that the four waveforms (theta, alpha, beta and gamma) with features of mean, variance and skewness are highly determinant. The optimal features of theta, alpha, beta and gamma waves are fed into the SVM with radial basis function (RBF) kernel (RBF-SVM) for classification of seizure and nonseizure EEG signals. Experiments are conducted in ten time independent trails to test the performance of the proposed method. The results show that the proposed method can achieve the best average classification accuracy of 99.125% and provide better classification accuracy than some approaches studied previously. The rest of the paper is organized as follows: the methodology of whole experiment including HHT method, time-frequency image processing method, feature extraction and SVM classifier are introduced in Section 2. The experimental results and discussion for the classification of seizure and nonseizure EEG signals are given in Section 3. Finally, Section 4 concludes the paper.

2. Methodology This work presents a novel method based on the time-frequency image using combined HHT and SVM to classify the EEG signal for seizure detection. The HHT has been employed to obtain the time-frequency representation (TFR) of the EEG signals. The TFR is considered as a TFI, which contains the information of pixel intensity. Image segmentation has been applied to the TFI which is segmented correspond to the frequency-bands of the rhythms of EEG signal. Four statistical features including mean, variance, skewness and kurtosis of pixel intensity have been extracted from the histogram of the grayscale sub-images. Finally, the SVM with RFB kernel is used to get the classification result. The block diagram of the proposed methodology is given as follows (Fig. 1).

EEG signals

Methodology

Time-frequency image

Hilbert-Huang transform

Segmentation

Frequency-bands of rhythms

Feature extraction

Histogram representation

Classification

Support vector machine

Results Fig. 1. Block diagram of the proposed methodology.

2.1.1. Empirical mode decomposition The principle of EMD is to decompose a nonlinear and nonstationary signal into a set of IMFs which is band limited. Each IMF satisfies two basic conditions [6]: 1) The number of extreme points Ne and the number of zero crossings Nz must be either equal or differ at most by one; (Nz − 1) ≤ Ne ≤ (Nz + 1)

(1)

2) At any time point ti , the local mean value of the envelope which defined by the average of the maximum fmax (t) and minimum fmin (t) envelopes is zero. [fmax (ti ) + fmin (ti )] = 0, 2

ti ∈ [ta , tb ]

(2)

The properties of IMF allow for defining the instantaneous frequency and amplitude in an unambiguous way, so Hilbert transform can then be applied to every single intrinsic mode. The EMD algorithm for the signal x(t) can be implemented by the following procedure: Step 1: Determine the local extrema (maxima, minima) of the signal x(t). Step 2: Generate the upper and lower envelopes xup (t) and xlow (t) by connecting all local maxima and minima with cubic spline interpolation. Step 3: Calculate the point-by-point mean as m(t) = (xup (t) + xlow (t))/2. Step 4: Subtract the local mean from the signal, d(t) = x(t) − m(t). Step 5: Decide whether d(t) is an IMF or not by checking the two basic conditions described above. If the criterion of the conditions is satisfied, then set imfi = d(t); else x(t) = d(t), and cycle step 1–4. Step 6: Let r(t) = r(t) − imfi , repeat step 1–5 until r(t) is a monotonic residual, then end the sifting process, or else set x(t) = r(t) and go back to step 1.

2.1. Hilbert–Huang transform Hilbert–Huang transform is an empirical-based data analysis method. Compared with the traditional time-frequency analysis method such as STFT and wavelet analysis, HHT thoroughly get rid of the linear and stationary bound. The HHT technique for analyzing data consists of two components: EMD and Hilbert spectral analysis (HSA). It will be shown that HHT provides a good local description of the oscillating components of the nonstationary or nonlinear signal [10].

At the end of this process, the signal x(t) can be expressed as follows: x(t) =

N 

ci (t) + rN (t)

(3)

i=1

where N is the number of intrinsic modes, ci (t) is the ith IMF, and rN (t) is the final residual which can be interpreted as the DC component of the signal.

K. Fu et al. / Biomedical Signal Processing and Control 13 (2014) 15–22

2.1.2. Hilbert spectral analysis In order to compute instantaneous frequencies and amplitudes and describe the signal more locally, the Hilbert transform is applied to every IMF obtained by above EMD method. For any signal x(t) of Lp class [19], its Hilbert transform y(t) is 1 P 

y(t) =



+∞

−∞

x() d t−

(4)

where P is the Cauchy principal value of the singular integral. We can construct analytic function z(t) bellow: z(t) = x(t) + jy(t) = a(t)ej(t)

(5)

The amplitude of pre-envelope a(t) and instantaneous phase (t) are defined as, a(t) =



x(t)2 + y(t)2

(6)

y(t) x(t)

(7)

(t) = arctan

The instantaneous frequency can then be written as the time derivative of the phase, as shown bellow: w(t) =

d(t) dt

(8)

or f (t) =

1 d(t) 2 dt

(9)

It should be noted that the TFI is converted into an 8-bit grayscale image to get the grayscale histogram in our method. 2.2.3. Histogram representation of grayscale sub-images The histogram is a graphical representation of the distribution of data. The histogram of an image represents the distribution of the pixels in the image over the scale. It has been show that histogram of image can give us an intuitive view and detailed information to classify EEG signals [20]. Considering an image I, in which the intensity at pixel with coordinates (x, y) can be represented as I(x, y). For the histogram h, the hi indicating that intensity i appears hi times in the image. So the hi can be defined as: hi =

i  i  x





ai (t) exp(j

The shape in the histogram of the sub-image provides us detailed information for detecting the seizure from the EEG signals. Four statistical features including mean (), variance ( 2 ), skewness (˛) and kurtosis (ˇ) have been derived from the histogram of 8-bit grayscale sub-images of EEG signals. The use of these features is motivated by the fact that distribution of histogram is often characterized by its level of dispersion, asymmetry, and concentration around the mean. These features are defined as follows:

fi (t)dt)

(10)

where the ai and fi is instantaneous amplitude and instantaneous frequency of the ith IMF, respectively. The time-frequency distribution of EEG signal can be considered as a TFI [20], and so the method of image processing can be used to handle the problem of seizure classification. 2.2.2. Segmentation of time-frequency image Image segmentation method can be applied to TFR to localize significant structures in them and extract time-frequency signatures of different components of the signal. The aim of TFI segmentation of EEG signals is to obtain regions that correspond to the frequency-bands of rhythms. The TFI can be divided into five sub-images corresponding to the frequency-bands of the rhythms. The classification of the main EEG rhythms based on their frequency ranges is as follows [20]: Delta: 0–4 Hz. Theta: 4–8 Hz. Alpha: 8–12 Hz. Beta: 12–30 Hz. Gamma: 30–50 Hz.

1 hi L

=

(12)

i=0

1  2 (hi − ) L−1 L−1

2 =

(13)

i=0

1  3 (hi − ) 3

(14)

1  4 (hi − ) 4

(15)

L−1

˛=

i=0

L−1

ˇ=

i=0

i=1

• • • • •

(11)

L−1

2.2.1. Time-frequency representation using HHT A time-frequency representation (TFR) is a view of a signal represented over both time and frequency and it is very useful for analyzing nonstationary signals. TFRs are often represented by either amplitude or energy density over time and frequency. The energy density distribution called Hilbert–Huang spectrum of the original signal can be obtained by HHT. Previous subsection has fully described the HHT, and the amplitude and frequency functions are also expressed as functions of time which can be constructed as H(f, t) [6,7]. It displays the relative energy contributions for a certain frequency at a specific time. The Hilbert–Huang spectrum is defined as: H(f, t) = Re

I(x, y)

y

2.3. Features extracting based on the histogram

2.2. Time-frequency image processing methodology

n

17

where  is the standard deviation, hi is intensity of the ith pixel in the histogram, and L is the number of intensity levels in the grayscale sub-image. The mean of the histogram can reflect the average values of grayscale images, while variance measures how far the values are spread out. Skewness can reflect the degree of asymmetry of the histogram. If the histogram is symmetrical, then the skewness is zero. If the left hand tail is longer, skewness will be negative and if the right hand tail is longer, then skewness will be positive. Kurtosis is a measure for the degree of flatness or peakedness in the variable distribution. High kurtosis tends to have a distinct peak near the mean, decline rather rapidly, and have heavy tails, while low kurtosis tends to have a flat top near the mean rather than a sharp peak. The standard normal curve of histogram has a kurtosis of zero. 2.4. Support vector machine SVM is a machine learning method which is based on statistical learning theory of Vapnik–Chervonenkis dimension theory [14], mainly solves the small sample problem. The SVM maximizes the margin by determining a separating hyper-plane to identify different classes of data [15,16]. For two-class problem, consider a with input data xk ∈ Rn and output given training set {xk , yk }N k=1

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K. Fu et al. / Biomedical Signal Processing and Control 13 (2014) 15–22

subject to inequality constrain (17), where c is a positive real constant which controls the punishment for misclassified samples. The problem in the primal weight space is a constrained optimization problem, next formulate the Lagrangian, then take the conditions for optimality and finally solve the problem in the dual space [15]. The nonlinear SVM classifier can take the form:



y(x) = sign

N 



˛k yk K(x, xk ) + b

(19)

k=1

where ˛k are Lagrange multipliers, K(x, xk ) is a kernel function, it enables us to work in huge dimensional feature spaces without actually having to do explicit computations in this space. In this work, the RBF kernel is used, it can be formula as Fig. 2. Samples of EEG signals of set A and set E.

K(x, xi ) = exp

data yk ∈ R with class labels yk ∈ {−1, 1}. We consider the following linear classifier:





y(x) = sign wT x + b

(16)

In order to tolerate misclassifications, the optical separating hyper-plane should satisfy the following condition: T

yK [w xk + b] ≥ 1 − k ,

k = 1, . . ., N

(17)

where  k are slack variables, and  k > 0. SVM formulations are done within a context of convex optimization theory. In order to obtain the optical plane, we need to solve the following primal problem in w and  k :

 1 T k w w+c 2 N

min Jp (w, ) =

k=1

(18)



2  − x − xi

2 2

(20)

where  controls the width of RFB kernel. In previous subsections we have got features of the EEG signals, and then we can send them into the SVM to get the classification result. 3. Results and discussion The EEG dataset is obtained from Bonn University open source database. The dataset consists of five sets denoted as A–E. Each one of this dataset contains 100 single-channel EEG signals, and each one having 23.6 s duration and sampling frequency of 173.61 Hz. Set A and B were taken from surface EEG recordings of five healthy volunteers with eyes open and closed, respectively. The signals in sets C and D were measured intracranially in seizure-free intervals from five patients in the epileptogenic zone (D) and from the hippocampal formation of the opposite hemisphere of the brain (C).

Fig. 3. The components of seizure (A) and nonseizure (B) EEG signals decomposed by EMD.

K. Fu et al. / Biomedical Signal Processing and Control 13 (2014) 15–22

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Fig. 4. The Hilbert–Huang spectrums of seizure (A) and nonseizure (B) EEG signal.

Set E only contains seizure activity. For a more detailed description of the data please refer to the manuscript [21]. Typical EEG signals (one from set A and E) are shown in Fig. 2. In this work, the dataset A and E are used to form the nonseizure and seizure class, respectively. The EMD method decomposes a dataset into a set of IMFs. Fig. 3(A) and (B) illustrates the result of decomposition performed by EMD of seizure and nonseizure EEG signals, respectively. It can be observed that the modes are a set of amplitude modulation and frequency modulation signals and ordered from the highest frequency to the lowest. Further analysis using Hilbert transform in time-frequency domain may lead a better discrimination of seizure and nonseizure EEG signals. In previous subsections we have demonstrated that the Hilbert–Huang transform is suitable for analyzing nonlinear and

nonstationary EEG signals. The Hilbert–Huang spectrum is an energy density distribution spectrum which can represent the signals in time-frequency domain. Fig. 4(A) and (B) shows the Hilbert–Huang spectrums of seizure and nonseizure EEG, respectively. A visual comparison between the two figures can give us a qualitative discrimination of seizure and nonseizure EEG signals. From the perspective of the Hilbert–Huang spectrum distribution, it is clearly observed that the difference between the seizure and nonseizure EEG signal, this gives us a certain direction in further analyzing with the Hilbert–Huang spectrums. The Hilbert–Huang spectrum of EEG signal has been represented as a TFI. Next, we try to obtain our results from the perspective of image processing. For better histogram representation, the TFI is converted into an 8-bit grayscale image. The 8-bit grayscale subimages representation of TFI of seizure and nonseizure EEG signal

Fig. 5. The 8-bit grayscale sub-images representation of TFI of seizure (A) and nonseizure (B) EEG signal corresponding to frequency-bands of: (a) delta rhythm, (b) theta rhythm, (c) alpha rhythm, (d) beta rhythm, (e) gamma rhythm.

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K. Fu et al. / Biomedical Signal Processing and Control 13 (2014) 15–22

Fig. 6. The histogram of grayscale sub-images representation of seizure (A) and nonseizure (B) EEG signal corresponding to frequency-bands of: (a) delta rhythm, (b) theta rhythm, (c) alpha rhythm, (d) beta rhythm, (e) gamma rhythm.

corresponding to frequency-bands of the rhythms are presented in Fig. 5(A) and (B), respectively. The histograms of grayscale sub-images of seizure and nonseizure EEG signal are computed and presented in Fig. 6(A) and (B), respectively. The class discrimination ability of four statistical features (mean, variance, skewness and kurtosis) is quantified using t-test. The t-test assesses whether the distribution means of two groups are statistically different from each other. The p-values of the four features of five waveforms of seizure and nonseizure EEG signal class using t-test are presented in Table 1. It can be clearly observed that the last four waves (theta, alpha, beta and gamma) with the features of mean, variance and skewness provide a significantly difference (p < 0.001). Hence, the three feature vectors of the four waves are fed into a RBF-SVM classifier for training to get the classification model. Before implementing the classification test, the best optimal parameters of c and g which belong to the RBF-SVM should be determined. There are many parameter optimization methods for SVM, such as grid search method, genetic algorithm (GA) [22,23] and particle swarm optimization (PSO) algorithm [24]. In this work, the GA is used to find the best parameter of c and g. 60% features of the dataset are randomly selected for training and the remaining data for testing the performance of the classification. The parameters of the GA are determined by setting the maximum evolution algebras to 200 and the maximum populations to 20, using 5-fold cross validation (CV). The process of parameter optimization using GA for the theta wave is shown in Fig. 7. When the features of theta wave are used, the best CV accuracy can reach 100%. The parameter optimization results and CV accuracy of RBF-SVM using GA for theta, alpha and beta wave in one test are presented in Table 2. The classification performance of the SVM classifier can be determined by computing the sensitivity, specificity and accuracy which are defined as shown in Eqs. (21)–(23).

Sensitivity =

TP TP + FN

(21)

Fig. 7. The process of parameter optimization for the theta wave using RBF-SVM.

Table 2 The parameter optimization results and CV accuracy of RBF-SVM with features of mean, variance and skewness using GA. Waveform

Parameter c

Parameter g

CV accuracy (%)

Theta Alpha Beta Gamma

0.9631 59.6180 15.4420 11.0079

2.9920 6.3511 16.3492 2.1794

100 96.67 96.25 90

Specificity = Accuracy =

TN TN + FP

(22)

TP + TN TP + TN + FP + FN

(23)

where TP and TN represent the total number of correctly detected true positive patterns and true negative patterns. The FP and FN represent the total number of false positive patterns and false negative patterns. For each waveform, we randomly do ten time independent trails and the average classification accuracy for seizure and

Table 1 p-Values of features (mean, variance, skewness and kurtosis) for all waveforms (delta, theta, alpha, beta and gamma) using t-test. waveforms

p-Values for mean

p-Values for variance

p-Values for skewness

p-Values for kurtosis

Delta Theta Alpha Beta Gamma

8.9559E−10 0 3.4685E−08 2.8493E−11 0

0.0346 0 0 0 2.4324E−09

0.0237 0 0 0 1.5458E−09

0.0612 0.0518 0.1642 0.1497 0.4326

K. Fu et al. / Biomedical Signal Processing and Control 13 (2014) 15–22

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Table 4 A comparison of performances of the various methods for detection of seizures using dataset A and E. Researchers

Methods

Accuracy (%)

Nigam et al. [25]

Nonlinear preprocessing filter, diagnostic artificial neural network (LAMSTAR) Entropy measures, adaptive neurofuzzy inference system (ANFIS) Chaotic measures, surrogate data analysis Fast Fourier transform (FFT), decision tree (DT) Discrete wavelet transform (DWT), mixture of expert model. Discrete wavelet transform-relative wavelet energy, MLPNN Wavelet transform and Shannon entropy, k-nearest neighbor Hilbert–Huang transform, support vector machine

97.2

Kannathal et al. [26]

Kannathal et al. [27] Polat et al. [28]

Fig. 8. The classification result of the RBF-SVM for theta wave. Table 3 The results for seizure and nonseizure EEG signals with features of mean, variance and skewness for theta, alpha, beta and gamma wave. Waveform Theta Alpha Beta Gamma

Sensitivity (%) 95–100 97.5–100 97.5–100 75–92.5

Specificity (%) 95–100 92.5–95 87.5–90 87.5–95

Subasi [29]

Guo et al. [30]

Accuracy (%) 97.5–100 95–97.5 92.5–95 85–88.75

nonseizure EEG signals can reach 99.125% (97.5–100%) for the theta wave. Fig. 8 shows the plot of classification result of theta wave using RBF-SVM. Table 3 shows the minimum and maximum classification accuracies for ten random trails for three waveforms of EEG signals. The receiver operating characteristics (ROC) curve is used in medicine to determine a cutoff value for a clinical test, which gives us intuitive view of entire spectrum of sensitivities and specificities. The ROC plot is a graph of sensitivity (y-axis) vs. 1 − specificity (xaxis). The area under ROC curve provides a measure of performance for classification and diagnostic rules, the larger of the ROC area, the better of the classification accuracy. The performance of RBF-SVM for different waves has been evaluated by ROC plot which is shown in Fig. 9. It is clear that the ROC for theta wave is 1.0, which indicates that theta wave is the best waveform for EEG signal classification. Table 4 presents a comparison on the results between the method developed in this work and other methods proposed in the literature handling the classification problem using the same dataset A and E. In our method, we randomly select 60% features for training and the remaining data for testing, the average accuracy obtained from our method is 99.125% for ten time trails (97.5–100%)

Wang et al. [31]

This paper

92.22

∼90 98.72

95

95.2

99–100

99.125

which is higher than several existing methods and similar to Wang et al. [31]. It is worth to mention here that a novel method proposed in this paper for seizure classification of EEG signals also can be applied for analysis and classification of other nonlinear and nonstationary signals. 4. Conclusions In this paper, a new seizure detection method based on the TFI of EEG signals using combined HHT and SVM has been proposed. The HHT based TFR has been applied to the seizure and nonseizure EEG signals. The segmentation of the TFI has been employed based on the frequency-bands of the rhythms. The features are obtained by computing the histogram of each grayscale sub-images of EEG signals. Three features (mean, variance and skewness) which are highly determinant have been used as input to a RBF-SVM classifier for training to get the optimal parameters with GA. The classification accuracy and ROC curve of the classifier have been used for evaluating the classification performance of RBF-SVM classifier. The experiment results indicate that the features of the theta, alpha, beta and gamma waves with RBF-SVM provide higher classification accuracy in classification of seizure and nonseizure EEG signals. Future directions of the research may include application of proposed technique for classification of other disorders (i.e. sleep and heart related diseases). References

Fig. 9. The ROC plots of theta, alpha, beta and gamma wave.

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