Seizure detection approach using S-transform and singular value

Epilepsy & Behavior 52 (2015) 187–193

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Epilepsy & Behavior journal homepage: www.elsevier.com/locate/yebeh

Seizure detection approach using S-transform and singular value decomposition Yudan Xia, Weidong Zhou ⁎, Chengcheng Li, Qi Yuan, Shujuan Geng School of Information Science and Engineering, Shandong University, Jinan 250100, China Suzhou Institute of Shandong University, Suzhou 215123, China

a r t i c l e

i n f o

Article history: Received 17 April 2015 Revised 27 July 2015 Accepted 27 July 2015 Available online 4 October 2015 Keywords: S-transform Singular value decomposition (SVD) Seizure detection Bayesian linear discriminant analysis (BLDA)

a b s t r a c t Automatic seizure detection plays a significant role in the diagnosis of epilepsy. This paper presents a novel method based on S-transform and singular value decomposition (SVD) for seizure detection. Primarily, S-transform is performed on EEG signals, and the obtained time–frequency matrix is divided into submatrices. Then, the singular values of each submatrix are extracted using singular value decomposition (SVD). Effective features are constructed by adding the largest singular values in the same frequency band together and fed into Bayesian linear discriminant analysis (BLDA) classifier for decision. Finally, postprocessing is applied to obtain higher sensitivity and lower false detection rate. A total of 183.07 hours of intracranial EEG recordings containing 82 seizure events from 20 patients were used to evaluate the system. The proposed method had a sensitivity of 96.40% and a specificity of 99.01%, with a false detection rate of 0.16/h. © 2015 Elsevier Inc. All rights reserved.

1. Introduction Epilepsy is a chronic neurological disorder characterized by paroxysmal and excessive neuronal discharges, which can result in loss of awareness or consciousness and disturbances of movement, sensation, mood, or mental function [1]. Approximately 1% of the world's population suffers from epilepsy [2,3]. Electroencephalography (EEG) is an important tool for the diagnosis of epilepsy, which reflects the electrical activity of the brain [4]. At present, long-term EEG recordings are usually inspected by experts visually to identify seizure activities, which is a time-consuming and tedious task. As a result, automatic seizure detection technology is very necessary to assist medical staff in analyzing EEG recordings. In recent years, there have been various kinds of automatic seizure detection methods proposed. The method presented by Gotman [5] was widely applied, this technique decomposed EEG signals into half waves and detected seizures using peak amplitude, duration, slope, and sharpness. Later, Grewal and Gotman developed a seizure warning system utilizing spectral feature extraction and Bayes's theorem [6]. Nicolaou and Georgiou proposed a seizure detection algorithm based on permutation entropy (PE) and support vector machine (SVM) [7] to classify segments of normal and epileptiform EEGs. In addition, time– frequency analysis methods have also been employed for seizure detection [8–11], such as short-time Fourier transform (STFT) and wavelet transform (WT). Short-time Fourier transform decomposes EEG signals ⁎ Corresponding author at: School of Information Science and Engineering, Shandong University, 27 Shanda Road, Jinan 250100, China. Tel.: +86 531 88361551. E-mail address: [email protected] (W. Zhou).

http://dx.doi.org/10.1016/j.yebeh.2015.07.043 1525-5050/© 2015 Elsevier Inc. All rights reserved.

into time–frequency domain using a fixed and moving window function, but it has the limitation of analyzing signals at single resolution because of fixed window width. Wavelet transform solves the problem of STFT and provides multiresolution analysis via varying window width, which uses short windows at high frequencies and long windows at low frequencies. However, its accuracy depends on the chosen basis wavelet, and its computation is complicated. The S-transform first introduced by Stockwell et al. [12] is an effective time–frequency analysis technique that has been widely used for signal processing, such as detection of multiple power quality disturbances [13], electrocardiogram (ECG) beat classification [14], and heart sound segmentation [15]. Stockwell transform is a combination of continuous wavelet transform (CWT) and STFT and overcomes the disadvantages of them [16]. It presents a good time–frequency resolution characteristic by using a moving and scalable localizing Gaussian window. Singular value decomposition (SVD) is a data decomposition approach that describes the distribution of matrix data and can reduce the effect of noise. Using SVD, Kim et al. extracted illumination– invariant features for face recognition [17]. Kanjilal et al. employed SVD on the composite maternal ECG signal for fetal ECG extraction [18]. Singular value decomposition was also utilized for earthquake prediction [19]. The singular values are very stable and robust to the change of matrix elements. In this study, we used the singular values of EEG time–frequency matrix obtained with S-transform as features for seizure detection. Many of classifiers have been used for seizure detection, such as support vector machine (SVM), extreme learning machine (ELM), and artificial neural network (ANN). Bayesian linear discriminant analysis (BLDA) can be treated as an extension of Fisher's linear discriminant

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analysis (FLDA) [20], which is an efficient method for machine learning. In contrast to FLDA, BLDA employs regularization to avoid overfitting to high dimensional and noisy datasets and has shown its superior performance for motor imagery classification [21]. Bayesian linear discriminant analysis was employed to train the classifier in this study. In this paper, we first propose a novel method for seizure detection using S-transform in combination with SVD. The rest of this paper is organized as follows. Section 2 introduces the material and methods including six parts: (1) a brief introduction of the intracranial EEG (iEEG) dataset, (2) the S-transform time–frequency analysis, (3) the feature extraction method based on SVD, (4) the Bayesian linear discriminant analysis, (5) postprocessing, and (6) the performance evaluation approach. Section 3 shows the experimental results, and is followed by a discussion of the proposed method in Section 4. Finally, the conclusion is brought forward in Section 5.

training dataset, and all the remaining EEG data were utilized as testing data. In total, 156.91-h of EEG data (1.32-h of seizure data and 155.59-h of nonseizure data) containing 55 seizure events from 20 patients were selected as test data. 2.2. S-transform time–frequency analysis Stockwell transform, which is the development of CWT and STFT, is a new technique for the analysis of nonstationary signals [12]. Stockwell transform not only realizes a progressive multiresolution analysis but also has a low computation complexity. The S-transform of signal x(t) is defined by Sðτ; f Þ ¼ e j2π f τ W ðτ; f Þ

ð1Þ

þ Z∞

2. Material and methods

W ðτ; dÞ ¼

xðt Þωðt−τ; dÞdt

ð2Þ

−∞

2.1. EEG dataset The EEG data used in this study were acquired from the Epilepsy Center of the University Hospital of Freiburg, Germany [22]. The database contains intracranial EEG recordings of 21 patients suffering from medically intractable focal epilepsy. All EEGs were recorded using a Neurofile NT digital video-EEG system with 128 channels, a 256-Hz sampling rate, and a 16-bit analog-to-digital converter. Six channels of the EEG recordings were available for each patient, including three focal channels (i.e., near the epileptic focus) and three extrafocal channels. Seizure onset and offset times were notated by the experts based on EEG recordings. In this study, only three focal channels of the EEGs from 20 patients were chosen for seizure detection. The EEG data from patient 10 were discarded because of electrode box disconnection and reconnection. For each patient, there were 2- to 5-h of EEG data containing seizure events. A total of 183.07-h of intracranial EEG recordings containing 82 seizure events were used in this work. The details of the used EEG data for each patient are summarized in Table 1. The long-term EEG recordings were analyzed using a 4-s sliding window without overlap between epochs. Each epoch contained 1024 points. For each patient, one seizure event or two seizure events and the same number of nonseizure epochs were chosen randomly as Table 1 Details of the database used in this study. The acronyms used in the table are SP: simple partial seizure, CP: complex partial seizure, and GTC: generalized tonic–clonic seizure. Patient

Seizure type

Seizure origin

EEG length (h)

Number of used seizures

Total number of EEG epochs for training

1 2 3 4 5 6 7 8 9 11 12 13 14 15 16 17 18 19 20 21 Total

SP SP, CP, GTC SP, CP SP, CP, GTC SP, CP, GTC CP, GTC SP, CP, GTC SP, CP CP, GTC SP, CP, GTC SP, CP, GTC SP, CP, GTC CP, GTC SP, CP, GTC SP, CP, GTC SP, CP, GTC SP, CP SP, CP, GTC SP, CP, GTC SP, CP –

Frontal Temporal Frontal Temporal Frontal Temporal/occipital Temporal Frontal Temporal/occipital Parietal Temporal Temporal/occipital Frontal/temporal Temporal Temporal Temporal Frontal Frontal Temporal/parietal Temporal –

9 5.62 8.19 10 9.90 6.42 6 3.57 10 8 8 4 7 10 11.69 14.80 12.97 13 12.91 12 183.07

4 3 5 5 5 3 3 2 5 4 4 2 4 4 5 5 5 4 5 5 82

8 52 14 18 56 40 18 54 44 68 16 38 58 74 64 28 26 14 36 94 820

where W(τ, f ) is the CWT of x(t), ω(t, f) is mother wavelet function that is defined by t2 f 2 jf j ωðt; f Þ ¼ pffiffiffiffiffiffi e− 2 e− j2π f t 2π

ð3Þ

and the frequency f decides the width of wavelet basis. In addition, the mother wavelet function has to satisfy the condition of zero mean. The S-transform of signal x(t) is finally given as follows: þ∞ Z

Sðτ; f Þ ¼ −∞

ðτ−t Þ2 f 2 jf j xðt Þ pffiffiffiffiffiffi e− 2 e−i2π f t dt: 2π

ð4Þ

The application of S-transform decomposes a given dataset into a complex time–frequency matrix whose rows correspond to frequency and columns to time. The matrix contains much important information such as amplitude, phase, and frequency. In this study, we make use of the amplitude matrix for feature extraction. Seizures in recorded EEG usually occur below 30 Hz [23]; thus, the frequency range of S-transform is selected from 1 to 30 Hz. With S-transform, each epoch of data yields a 30 × 1024 amplitude matrix, in which 30 represents frequency sampling points from 1 Hz to 30 Hz and 1024 represents time sampling points. In order to analyze the local characteristic and to reduce the dimension of the matrix, we divide the matrix into 12 blocks. The time axis is divided into 3 segments averagely, while the frequency axis is divided into 4 segments according to different frequency band distributions, including delta (1–4 Hz), theta (4–8 Hz), alpha (8–12 Hz), and beta (12–30 Hz). As a result, 12 submatrices are generated for subsequent processing. 2.3. SVD-based feature extraction Singular value decomposition could decompose a matrix into three matrices. According to the SVD theory, for a given matrix Am × n ∈ Rm × n, there exist two orthogonal matrices Um × m ∈ Rm × m and Vn × n ∈ Rn × n which satisfy the following equation: A ¼ UΛ VT

ð5Þ

where Λ is an m × n diagonal matrix, whose diagonal elements are the singular values of matrix Am × n that are sorted in a decreasing way such that σ1 ≥ σ2 … ≥ σn ≥ 0. The columns of the orthogonal matrices Um × m and Vn × n are called the left and right singular vectors of matrix Am × n, respectively.

Y. Xia et al. / Epilepsy & Behavior 52 (2015) 187–193

After singular value decomposition, Am × n can be expressed as a set of basis matrices Ai each multiplied by a weight σi σ i Ai ¼

R X

i¼1

σ i ui vTi

ð6Þ

i¼1

where R is the rank of A. Singular values show the natural characteristic of the matrix and reflect the energy information contained in each subspace, which means that the larger singular values contain more energy of the matrix. On the other hand, singular values have a good stability and are not affected by the matrix element variations. Sudden changes in the data will lead to the change of singular values and to the redistribution of the energy in each subspace. So, the singular values can be regarded as the features of EEG signals for seizure detection. In this study, we employed the largest singular values as the features of EEG data because of the fact that the singular values of each submatrix decay rapidly. For each of those 12 submatrices obtained by S-transform mentioned above, the largest singular value was extracted by SVD, as shown in Fig. 1. Then, the largest singular values in the same frequency band were added together, and a 4-dimensional feature vector was constructed for classification. Fig. 2 describes the difference of singular values between 100 seizure epochs and 100 nonseizure epochs that were selected randomly from different patients. It can be seen that the singular values of seizure epochs were generally greater than those of nonseizure epochs. 2.4. Bayesian linear discriminant analysis Bayesian linear discriminant analysis can be regarded as an extension of FLDA with Bayesian strategy [20]. Assume that the target x and the feature vector s with addictive white Gaussian noise in Bayesian regression satisfy x ¼ wT s þ n:

5

Singular values Seizures Nonseizures

1 0.5 0

0

10

20

30

40 50 60 EEG epochs

70

80

90

100

Fig. 2. The comparison of the singular values between the seizure and nonseizure EEG epochs.

The prior distribution of w is defined as pðwjα Þ ¼

   α D2  ε 12 1 exp − wT I0 ðα Þw 2π 2π 2

ð9Þ

where α is the prior distribution parameter, D is the vector number, and I0 (α) is a D + 1 dimensional, diagonal, square matrix 2

α 60 0 6 I ðα Þ ¼ 4 ⋮ 0

0 α ⋮ 0

3 ⋯ 0 ⋯ 07 7 ⋱ ⋮5 ⋯ ε

ð10Þ

where ε is a very small value. The posterior distribution of w obeys a Gaussian distribution as well and can be calculated based on Bayes' rule pðwjβ; α Þ ¼ Z

pðYsx jβ; wÞpðwjα Þ pðYsx jβ; wÞpðwjα Þdw

:

ð11Þ

ð7Þ The mean m and the covariance C of the posterior can be obtained by Eqs. (12) and (13), respectively:

Then the likelihood function of the weight w is  pðYsx jβ; wÞ ¼

x 10

1.5 Amplitude

A¼

R X

2

189

β 2π

N2

  2 β  exp − ST w−x 2

ð8Þ

where Ysx represents the pair {S, x}, S denotes the matrix obtained from the horizontal stacking of the training feature vectors, x denotes a vector containing the regression targets, β is the inverse variance of the noise, and N is the number of samples in the training set.

 −1 ^ ^T þ I0 ðα Þ SX m ¼ β βS S

ð12Þ

 −1 ^T þ I0 ðα Þ : C ¼ βS S

ð13Þ

For a new input vector ^s waiting for being classified, the linear discriminant function is given as y ¼ mT ^s

ð14Þ

where y is the output of the BLDA classifier. 2.5. Postprocessing In order to reduce false detections, the postprocessing is performed after the BLDA classifier. The postprocessing stage includes smoothing, threshold judgment, multichannel decision, and collar technique. Firstly, a moving average filter (MAF) is used to smooth the BLDA outputs in each channel and to eliminate some occasional interference. The MAF is a low-pass filter which can reduce random noise [24]. It is defined as yðiÞ ¼

Fig. 1. The division of the S-transform time–frequency matrix.

0 1 X xði þ jÞ N þ 1 j¼−N

ð15Þ

where x denotes the input signal, y denotes the output signal, and N + 1 denotes the smoothing length of MAF that is specific for each patient in this study.

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• Specificity: true negatives/the total number of nonseizures marked by the EEG experts. True negatives (TNs) represent the number of nonseizures identified by both the algorithm and the EEG experts. • Recognition accuracy: the number of correctly identified epochs/the total number of epochs.

Secondly, the smoothed value is compared with an appropriate threshold, which is also specific for each patient. After comparison, binary decisions are achieved, where 1 represents nonseizure epoch and −1 represents seizure epoch. Thirdly, multichannel decision is employed to reduce false detections further. The multichannel decision rule is defined as follows: for each epoch in three channels, if seizures are detected at least in two channels at the same time, the whole epoch is marked as a seizure; if the seizure is detected only in one channel, the epoch is also marked as a seizure when there is a seizure in its adjacent epoch. Otherwise, the epoch is declared as a nonseizure. Lastly, the collar technique is applied to compensate for the missing part of a seizure. Since the start and the end of a seizure are gradual processes, the change of the extracted features will not be very clear. In addition, the smoothing used in the first step also makes the start of a seizure obscure. So every seizure is extended from the left side to reduce boundary misjudgment in this work.

Moreover, in order to verify the performance of the proposed method roundly, the event-based approach was also employed to evaluate our algorithm. At this level, two statistical measures were applied: the number of true detected seizures and the false detection rate. All the detected events by the algorithm overlapping with a single seizure event marked by the EEG experts were considered as true detections. A sequence of consecutive false positives, which were not overlapped with the seizures, was defined as a false detection. False positive (FP) represents the number of seizure segments identified only by our algorithm but not by experts [26].

2.6. Performance evaluation approach

3. Results

The performance of the proposed method was assessed at two levels: the segment-based level and the event-based level. The segment-based assessment approach regards every segment as an independent testing sample, while the event-based assessment approach tends to establish an event to reflect the performance of a system for a specific application [25]. For the segment-based level, the EEG segments labeled by our algorithm were compared with those marked by the experts. Three statistical measures of sensitivity, specificity, and recognition accuracy were employed for the evaluation of this method:

In this study, all experiments were carried out in MATLAB 7.0 environment running in an AMD Sampson processor with 2.70 GHz. Stockwell transform was first performed on EEG epochs, and the obtained time–frequency matrix was divided into submatrices for feature extraction. Then the singular values were calculated from each submatrix using the method described in Section 2.3. After that, the sums of the largest singular values in the same frequency band were used as features. Finally, the features were fed into the BLDA classifier for a binary classification, and the postprocessing was utilized to improve the detection accuracy further. Fig. 3 shows an example of the detection process of one-hour of EEG data from patient 17. The experimental results of segment-based assessment approach for each patient are presented in Table 2. On average, the proposed method achieved a sensitivity of 96.40%, a specificity of 99.01%, and a

• Sensitivity: true positives/the total number of seizures marked by the EEG experts. True positives (TPs) represent the number of seizures identified by both the algorithm and the EEG experts. x 10

a)

b)

c)

d)

e)

f)

2 0 -2

3 2 1 0

5 0 -5

2 0 -2

2 0 -2

2 0 -2

4

0

100

200

300

400

500

600

700

800

900

0

100

200

300

400

500

600

700

800

900

0

100

200

300

400

500

600

700

800

900

0

100

200

300

400

500

600

700

800

900

0

100

200

300

400

500

600

700

800

900

0

100

200

300

400 500 EEG epochs

600

700

800

900

x 10

5

Fig. 3. An example of the detection process of one-hour EEG data from patient 17. (a) One-hour raw EEG data with channel 1. (b) The singular value features extracted from the EEG data. (c) The output of the BLDA classifier with channel 1. (d) The binary decisions with channel 1 after smoothing and threshold judgment. (e) The binary decisions after three channels are fused. (f) The final classification results after applying the collar technique. The seizure event marked by the EEG experts is between the two vertical lines. 1 represents nonseizure epoch, while −1 represents seizure epoch.

Y. Xia et al. / Epilepsy & Behavior 52 (2015) 187–193 Table 2 Detection performance of our proposed method on the segment-based level. Patient

Sensitivity (%)

Specificity (%)

Recognition accuracy (%)

1 2 3 4 5 6 7 8 9 11 12 13 14 15 16 17 18 19 20 21 Mean

88.89 100.00 98.17 100.00 93.33 100.00 100.00 100.00 98.11 100.00 100.00 100.00 96.65 97.06 97.25 100.00 90.91 100.00 72.94 94.74 96.40

99.73 98.20 99.31 95.86 97.00 99.75 99.89 98.33 99.61 99.91 99.46 99.73 99.41 99.89 99.06 99.38 98.94 99.83 97.09 99.78 99.01

99.71 98.22 99.29 95.90 96.99 99.75 99.89 99.36 99.60 99.91 99.46 99.74 99.31 99.86 99.04 99.39 98.93 99.83 96.90 99.74 99.04

recognition accuracy of 99.04%. In addition, it can be seen from Table 2 that the best sensitivity of 100%, specificity of 99.91%, and recognition accuracy of 99.91% were obtained from seizures of patient 11. For fifteen patients, the sensitivity was above 96%. The sensitivity was low for patient 1 because of the fact that the duration of seizure activities was very short. The sensitivity was lower than 75% for patient 20 because the difference in the used features between seizure and nonseizure data was not very obvious. The specificity was above 95% for all patients, and among them, the specificity was greater than 99% for fourteen patients. The results of the event-based assessment approach are presented in Table 3. In the event-based level, 55 seizures were used to test our algorithm, and 53 seizures were detected correctly. Except for two patients, 100% of seizure events were detected for all the other patients. Most of the detected seizure events had obvious changes of the used features. Only 2 seizures were missed using our method, which came from patients 18 and 20. For patient 18, the duration of missed seizures was

191

shorter than 8 s. The missed seizure of patient 20 was due to there being no obvious change between seizure and nonseizure EEG data. In addition, the average false detection rate was 0.16/h for all the 20 patients, and among them, ten patients had a zero false detection rate. Overall, the average sensitivity was lower than the average specificity; This was because the seizure events of each patient were rare and because the durations of seizure events were very short compared with nonseizure data. The threshold is adjustable for each patient, which allows for a balance of the sensitivity and false detection rate.

4. Discussion Automatic seizure detection is significant in the diagnosis of epilepsy, which can help relieve the heavy working load of the medical staff. It is well known that preprocessing and feature extraction play an important role in developing an effective detection system. Stockwell transform and singular values used in this study showed their excellent ability to discriminate between seizure and nonseizure signals. As a new time–frequency analysis approach, S-transform appears to have a better time–frequency resolution compared with WT and STFT and is more suitable for EEG signal analysis. The selection of features for EEG signals is of great significance as well, and suitable features can improve the classification accuracy. The single feature used in our algorithm is singular value, which makes it a less complex method compared with other methods using different types of features. Moreover, SVD has advantages of low computation complexity and storage, and singular values are robust to noise. Fig. 4 shows the mean value and standard deviation of the singular value, which is obtained by SPSS software. One hundred epochs of seizure and nonseizure data are randomly selected from different patients. We can see in Fig. 4 that the mean value of seizure data is much greater than that of nonseizure data. The two-sample t-test shows that there is no overlap between seizure and nonseizure data, so the singular values have high separability for seizure and nonseizure signals. The EEG database used in this work has been employed in other seizure detection systems. Chua et al. developed an improved patientspecific seizure detection system in which four features, including relative half-wave amplitude, rectified zero crossings, coefficient of variation of half-wave duration, and line length, were used with a quadratic discriminant analysis (QDA) classifier to distinguish between seizure and nonseizure data [27]. The algorithm was tested on 63 seizures

Table 3 Detection performance of our proposed method on the event-based level. Patient

Number of seizures marked by experts

Number of true seizures marked by our system

False detection rate (/h)

1 2 3 4 5 6 7 8 9 11 12 13 14 15 16 17 18 19 20 21 Total

2 2 4 4 3 2 2 1 3 2 3 1 3 3 4 4 3 2 4 3 55

2 2 4 4 3 2 2 1 3 2 3 1 3 3 4 4 2 2 3 3 53

0.71 0.2 0 0.22 0.5 0 0 0 0.125 0 0 0 0 0 0.27 0.07 0.55 0.18 0.42 0 0.16

Fig. 4. The mean value and standard deviation of the singular value feature between seizure and nonseizure EEG signals.

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Table 4 Comparison of performance for different methods. Method

Sensitivity (%)

Number of seizure events used False detection rate (/h) Number of channels used

Improved patient-specific seizure detection [27] Differential windowed variance [28] Multistage seizure detection [29] A fuzzy logic system [30] Seizure detection using Stockwell transform and boosting algorithm [31] Our proposed algorithm

78 91.525 87.5 95.8 94.26

63 59 24 56 82

0.18 – – 0.26 0.66

– 3 3 6 3

96.40

55 (test) + 27 (train)

0.16

3

from 15 patients and yielded a sensitivity of 78%, with a false detection rate of 0.18/h. Majumdar and Vardhan presented a seizure detection method using differential operator combined with windowed variance to automatically detect seizure onset in continuous ECoG signals [28]. The algorithm achieved a sensitivity of 91.525% from 15 patients with 59 seizures. Raghunathan et al. proposed a multistage seizure detection method which utilized wavelet filtering and a combination of variance and coastline features to detect morphologies of electrographic seizures [29]. The method was assessed on 24 seizures of 5 patients, and the sensitivity was 87.5%. In the study of both Majumdar and Raghunathan, three channels of EEG data were selected for experiments. Rabbi and Fazel-Rezai developed a fuzzy logic seizure detection system where amplitude, frequency, and entropy were extracted as features and considered as the inputs for a fuzzy system [30]. Electroencephalography recordings from 20 patients having 56 seizures were used to evaluate the system, and a sensitivity of 95.8%, with a false detection rate of 0.26/h, was obtained. In that study, six channels of EEG data were used. Compared with other seizure detection systems, the algorithm proposed in our study achieves a higher sensitivity of 96.40%, with a lower false detection rate of 0.16/h. On the other hand, we use only three channels of EEG data, giving the algorithm a low complexity. Recently, Yan et al. presented a seizure detection method using Stockwell transform and boosting algorithm [31]. This method was tested on 82 seizures of 20 patients and achieved a sensitivity of 94.26%, with a false detection rate of 0.66/h. In comparison with the study of Yan, we proposed a novel feature, singular value, which has shown its good ability for classification. In addition, Yan employed gradient boosting algorithm to train the classifier. For the gradient boosting algorithm, an appropriate iteration number has to be chosen to avoid overfitting. However, the BLDA classifier employs regularization to avoid overfitting without considering the iteration number. Moreover, our proposed method has achieved more satisfactory results. The comparison on the results between our proposed method and the other methods is presented in Table 4. Although our proposed method has achieved satisfactory results, we only evaluated the algorithm on the Freiburg intracranial EEG dataset, and in order to better verify the performance of the proposed method, we will apply the algorithm to long-term intracranial EEG recordings in real clinical application [32]. In addition, scalp EEG recordings [33] will also be investigated in future work.

5. Conclusion In this study, we proposed a novel method for automatic seizure detection using S-transform and singular value decomposition. The EEG recordings were divided into 4-s epochs, and each epoch were converted into a time–frequency matrix using S-transform. Then the time– frequency matrix was divided into submatrices, and the singular values were extracted from each submatrix based on SVD. After that, the sums of the largest singular values in the same frequency band were calculated as features, and Bayesian linear discriminant analysis was applied to classify seizure and nonseizure epochs. The algorithm has been implemented on the Freiburg EEG database. Experimental results show that

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