Multifractal Analysis and Relevance Vector Machine-Based Automatic Seizure Detection in Intracranial EEG.

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International Journal of Neural Systems, Vol. 25, No. 6 (2015) 1550020 (14 pages) c World Scientific Publishing Company DOI: 10.1142/S0129065715500203

Int. J. Neur. Syst. 2015.25. Downloaded from www.worldscientific.com by CHINESE UNIVERSITY OF HONG KONG on 10/07/15. For personal use only.

Multifractal Analysis and Relevance Vector Machine-Based Automatic Seizure Detection in Intracranial EEG Yanli Zhang School of Information Science and Engineering Shandong University, Jinan 250100, P. R. China School of Information and Electronics Engineering Shandong Institute of Business and Technology Yantai 264005, P. R. China Weidong Zhou∗ and Shasha Yuan School of Information Science and Engineering Shandong University, 27 Shanda Road Jinan 250100, P. R. China Suzhou Institute of Shandong University Suzhou 215123, P. R. China ∗ [email protected] Accepted 6 April 2015 Published Online 18 May 2015 Automatic seizure detection technology is of great significance for long-term electroencephalogram (EEG) monitoring of epilepsy patients. The aim of this work is to develop a seizure detection system with high accuracy. The proposed system was mainly based on multifractal analysis, which describes the local singular behavior of fractal objects and characterizes the multifractal structure using a continuous spectrum. Compared with computing the single fractal dimension, multifractal analysis can provide a better description on the transient behavior of EEG fractal time series during the evolvement from interictal stage to seizures. Thus both interictal EEG and ictal EEG were analyzed by multifractal formalism and their differences in the multifractal features were used to distinguish the two class of EEG and detect seizures. In the proposed detection system, eight features (α0 , αmin , αmax , ∆α, f (αmin ), f (αmax ), ∆f and R) were extracted from the multifractal spectrums of the preprocessed EEG to construct feature vectors. Subsequently, relevance vector machine (RVM) was applied for EEG patterns classification, and a series of post-processing operations were used to increase the accuracy and reduce false detections. Both epoch-based and event-based evaluation methods were performed to appraise the system’s performance on the EEG recordings of 21 patients in the Freiburg database. The epoch-based sensitivity of 92.94% and specificity of 97.47% were achieved, and the proposed system obtained a sensitivity of 92.06% with a false detection rate of 0.34/h in event-based performance assessment. Keywords: EEG; seizure detection; multifractal analysis; relevance vector machine.

1. Introduction Epilepsy is a common chronic neurological disorder that affects approximately 1% of the world’s population. Epilepsy is characterized by recurrent unprovoked seizures, which are the outcomes of abnormal and excessive neuronal discharges in the brain.1–3

Electroencephalogram (EEG) is recorded from the electrodes placed on the scalp or cerebral cortex and reflects the electrical activity of the brain.4–13 EEG has been widely used to investigate brain diseases and is a well-established technique in epilepsy diagnosis and monitoring.14–24 As epilepsy monitoring

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Y. Zhang, W. Zhou & S. Yuan

takes several days, the amount of EEG data generated is huge. Therefore, automatic seizure detection technology is quite valuable to alleviate the workload of clinicians and to increase the detection accuracy.25,26 There have been various methods proposed for automatic seizure detection in the past three decades. One of the first seizure detectors was introduced by Gotman, in which EEG signals were broken into half-waves and three features including the average amplitude of half-waves relative to the background, the average duration and the coefficient of variation were extracted for seizure detection.27 Murro et al. used relative amplitude, dominant frequency and rhythmicity of EEG recordings to detect complex partial seizures.28 Ayoubian et al. designed an automatic seizure detection system using high frequency activities in wavelet domain.29 Because of the nonlinear and dynamic nature of EEG signals, nonlinear features have been receiving more attention from the researchers.30–33 Ocak employed discrete wavelet transform and approximate entropy for seizure detection.34 Acharya et al. used higher order cumulant features to detect the epilepsy EEG signals.35,36 Fractal theory is an important branch of nonlinear science and fractal measures like fractal dimension also have been used for epilepsy seizure detection.37–39 Fractal dimension is a quantitative parameter of a fractal object and describes how the fractal object occupies the metric space to which it belongs.40–44 However, a single value of the fractal dimension is not sufficient for characterizing the fractal properties of EEG, because it only gives a global description on the inhomogeneity and the complexity of EEG signals. A better description of the complexity and the dynamic behavior of EEG recordings can be obtained by applying multifractal analysis,45,46 which uses a continuous fractal dimension spectrum to characterize the local singular behavior of the fractal objects. The multifractal analysis of EEG has been shown to be useful in sleep stages classification and brain–computer interfaces.47,48 In Ref. 47, the spatio-temporal analysis of monofractal and multifractal properties of whole-night sleep EEG recordings were carried out and the range of fractal spectra was found having significant difference in different sleep stages. In Ref. 48, an evaluation of the performance of multifractal cumulants on EEG data corresponding to motor-imagery was conducted and the

obtained results showed that the multifractal cumulant features can improve the classification performance. Thus in this work, we investigated the multifractal characteristics of the EEG from epilepsy patients and employed the multifractal spectrum parameters as features of EEG patterns for seizure detection. Automatic epilepsy seizure detection is essentially a problem of pattern classification between interictal and ictal EEG. A suitable classifier can greatly improve the classification accuracy of a seizure detection system. Support vector machine (SVM) is one of the state-of-the-art machine learning methods and one of the most popular classification techniques.49 However, the SVM suffers from some important limitations, such as the absence of posterior class probability estimates in classification, the need for Mercer kernels and the parameter determination requiring time consuming cross-validation. Relevance vector machine (RVM), which was first introduced by Tipping,50 is a sparse learning algorithm based on Bayesian framework. The model function of RVM is formed as a linear combination of basis functions, which is similar to the SVM. Compared to SVM, RVM is found to be advantageous on several aspects including: (1) In classification, the model gives estimates of the posterior probability of class membership; (2) RVM has no need of a crossvalidation to tune the regularization parameter as in SVM and the parameters of RVM can be automatically obtained by an iterative procedure; (3) There is no constraint over the number or type of basis functions that may be used. Most importantly, the RVM decision function can be much sparser, that is, it utilizes dramatically fewer basis functions than the SVM classifier, which lead to significant reduction in the computational complexity and make the RVM have good generalization ability. RVM has been successfully used in various research domains, such as hyperspectral image,51 visual tracking,52 arrhythmia detection,53 etc. Thus in the seizure detection system proposed in this paper, RVM is used as the classifier for yielding the probability that an EEG segment belongs to epilepsy seizures. The paper is organized as follows. In Sec. 2, we give an overview of the EEG dataset used in the work. Then the proposed seizure detection system is described in detail in Sec. 3. Results of multifractal analysis and system performance evaluation are

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Multifractal Analysis and RVM-Based Automatic Seizure Detection

presented in Sec. 4. Section 5 is a discussion on the seizure detection system and a conclusion follows in Sec. 6.

data containing 59 seizure events of 21 patients were used as testing data to assess the performance of the proposed seizure detection system.

2. EEG Database

3.

The long-term EEG dataset used in this work contains intracranial EEG signals of 21 patients from the Epilepsy Center of the University Hospital of Freiburg, Germany. These EEG data were recorded by a Neurofile NT digital video EEG system with 128 channels, 256 Hz sampling rate and a 16-bit analogue-to-digital converter. Six channels of all implanted grid, strip and depth electrodes were selected for each patient by certified epilepsy experts.54 Three are focal channels, located near the epileptic focus, and three extra-focal. In this work, the three focal channels were used for seizure detection. For each patient, there are two to five seizure events in the EEG recordings. The onset and end time of each seizure had been previously determined by experienced experts based on the identification of epileptic patterns preceding clinical manifestation of seizures in EEG recordings.55 In addition, each patient has approximate 24 h interictal EEG recordings without seizure activity, i.e. nonseizure data. A detailed description of the database can be found in Ref. 56. In this study, mutually nonoverlapping training and testing datasets were created for each patient in the following way. Firstly, one or two seizures and a same number of interictal EEG segments were chosen randomly as training data. Then all other available EEG data, which were not included in the training dataset, can be used as testing data. However, those files, which had some EEG segments had been used as training data, were not selected into the testing dataset to maintain the continuity of each testing file. For each patient, there still were at least 20 h EEG recordings in the testing dataset, containing one to four seizure events. Thus a total of 539 h of EEG

The block diagram of the proposed seizure detection system is illustrated in Fig. 1. The system consists of preprocessing, multifractal analysis, RVM classification and post-processing. All parts of the system are described in detail in the following sections. 3.1. Preprocessing In the preprocessing stage, a fourth-order Chebyshev band-pass digital filter was used in order to reduce the effect of artifacts. The cutoff frequency was empirically set to be 0.5 and 30 Hz for the EEG signals. Then the long-term multi-channel EEG recordings were partitioned into 4s epochs by a sliding rectangular window, without overlap between the adjacent epochs. The 4s EEG from a single channel was referred to as a segment. 3.2. Multifractal analysis and feature extraction The multifractal formalism was primarily established to account for the statistical scaling properties of singular measures arising in various fractal objects.57,58 When a fractal object is covered by nonoverlapping boxes of size ε, and µi (ε) is the concerned measure of ith box, the multifractal is described as:

Bandpass filtering & segmentation

Fig. 1.

µi (ε) ∼ εαi ,

(1)

N (α) ∼ ε−f (α) ,

(2)

where αi controls the local singularity of the measure, and is known as the singularity exponent. N (α) is the number of boxes with the same exponent α, and f (α) is interpreted as the Hausdroff fractal dimension of the subsets which have the same singularity strength α. For a multifractal, the singularity Post-processing

Preprocessing Channel 1 Channel 2 Channel 3

Methods

Multifractal analysis & feature extraction

RVM

Moving average filter

Threshold

Multichannel integration

The block diagram of the proposed seizure detection system. 1550020-3

Collar

Output

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exponent α takes on a range of values, corresponding to different fractal subsets. For each α there corresponds a single value of f (α) and the graph f (α) versus α (typically an inverted parabola) is known as the multifractal spectrum. In this work, the multifractal analysis of EEG signals was based on the moment method summarized as follows.58,59 (1) The EEG signal of length L, {x(j), j = 1, . . . , L}, was partitioned into N (ε) nonoverlapping boxes, each of size ε. Then the measurement µi (ε) in ith box was defined as follows: si si = N (ε) , µi (ε) = (3) s si i=1

where si is the sum of amplitudes of EEG sampling points in box i, N (ε) = 2k , ε = L × 2−k and k = 1, 2, . . . , log2 (L). (2) For each value of ε, we computed the moments of µi (ε) for a finite sequence of q: N (ε)

χ(q, ε) =

(µi (ε))q ∼ (ε)−τ (q) ,

(4)

i=1

where τ (q) is the mass exponent of the qth-order moment. The value of q ranges from −10 to +10, with a step size of 1. (3) For each value of q, the mass exponent τ (q)was evaluated as the slope of the log–log plot of χ(q, ε) versus ε. (4) α and f (α) were obtained via Legendre transformations: dτ (q) , α(q) = dq f (α(q)) = qα(q) − τ (q).

maximum and minimum probability measures. The parameter ∆f is expressed as ∆f = f (αmin ) − f (αmax ). In the case of ∆f > 0, the fractal is predominated by the high probability value, whereas if ∆f < 0, the fractal is predominated by the low probability value. The parameter R is defined as R = (∆αL − ∆αR )/∆α with ∆αL = α0 − αmin and ∆αR = αmax − α0 . The parameter R is used to depict the asymmetric property of the multifractal spectrum curve from the whole. 3.3. RVM classification For a two-class problem with training points X = {xi ∈ RK , i = 1, . . . , N } and corresponding class labels t = {ti ∈ {0, 1}, i = 1, . . . , N }, the RVM models binary classification using a logistic sigmoid function, which maps a linear combination of basis functions to a posterior class probability.50 Thus if x is an input vector to be classified and t ∈ {0, 1} is the corresponding target class label, then the posterior class probability that t = 1 is estimated as p(t = 1|x) = σ{y(x; w)} = 1/(1 + e−y(x;w) ), (7) N where y(x; w) = i=1 wi K(x, xi ). w = [w1 , w2 , . . . , wN ]T is a vector consisting of the linear combination weights and kernel function K(x, xi )is the basis function of RVM. Based on the Bernoulli distribution, the likelihood of the training dataset can be written as p(t|w) =

(5)

N

σ{y(xi ; w)}ti [1 − σ{y(xi ; w)}]1−ti .

i=1

(6)

(8)

To be able to quantitatively describe the differences of multifractal spectrums between the interictal and ictal EEG, we extracted eight parameters including α0 , αmin , αmax , ∆α, f (αmin ), f (αmax ), ∆f and R, to construct the feature vector of each EEG segment. Here, α0 is the singularity exponent corresponding to the maximum of the multifractal spectrum. αmax and αmin respectively denote the maximum and the minimum of singular exponent, and the difference between them is the width of the multifractal spectrum ∆α = αmax − αmin . The parameters f (αmin ) and f (αmax ) are the values of f (α) corresponding to αmin and αmax , respectively. They respectively reflect the numbers of boxes with the

Then the parameters w are given a zero-mean Gaussian prior probability distribution, N

p(w|α) = Π N (wi ; 0, α−1 i ), i=1

(9)

where α = {αi } is a vector of hyperparameters, with one hyperparameter αi assigned to each weight wi . The objective of the training is thus to estimate the weight vector by maximizing the posterior distribution of the class labels of the training data. The weights and the hyperparameters cannot be analytically obtained and therefore the approximation procedure based on Laplace’s method is utilized.50 For the current values of α, the “most probable”wMP

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are found, giving the location of the posterior distribution. Since p(w|t, α) ∝ p(t|w)p(w|α), maximizing the posterior distribution over w is equivalent to maximizing the following objective function: log{p(t|w)p(w|α)} =

N

[ti log yi + (1 − ti ) log(1 − yi )]

i=1


1 − wT Aw, 2

(10)

where yi = σ{y(xi ; w)} and A = diag(α1 , α2 , . . . , αN ) for the current α. This is a penalized logistic log-likelihood function and the iteratively reweighed least-squares algorithm can be used to find the wMP .50 wMP = ΦT Bt, (11) where B = diag(β1 , β2 , . . . , βN ) with βi = σ{y(xi ; w)}[1 − σ{y(xi ; w)}], and Φ = [φ(x1 ), φ(x2 ), . . . , φ(xN )]T is the design matrix with φ(xi ) = [K(xi , = x1 ), K(xi , x2 ), . . . , K(xi , xN )]T . The covariance T −1 (Φ BΦ + A) . Using and wMP , the hyperparameters α are updated by: γi , (12) 2 wMP i where γi = 1 − αi ii and ii is the ith diagonal element of the covariance . With the proceeding of the iteration process based on Eqs. (11) and (12), many αi will have large values, and thus, the corresponding weight values tend to be zero and are pruned out, realizing sparseness. Those training samples remaining with wi = 0 are termed relevance vectors. When the RVM classifier was obtained, it was applied to the patients’ testing data. The eightdimension feature vectors, consisting of parameters α0 , αmin , αmax , ∆α, f (αmin ), f (αmax ), ∆f and R, of the EEG segments on each channel were inputted into the RVM classifier. The classifier outputted the probabilities that the EEG segments belonged to seizure pattern. Then for each epoch, the three probability values of the three EEG segments from the three channels were processed by a series of postprocessing operations described below and finally given a decision whether the current epoch was in seizure stage or not. = αnew i

3.4. Post-processing The post-processing was designed to improve the seizure detection accuracy and reduce false detections, thus obtaining a better system performance. The post-processing included moving average filtering, threshold judgment, multichannel integration and collar technique. The operations of the postprocessing are described in detail as follows. To reduce the random noise of the outputs of RVM and to remove the possible sporadic isolated false detections caused by these noises, a moving average filter was firstly applied to the RVM output of each channel. The moving average filter is a simplest low-pass filter and defined as60 : y(m) =

N 1 x(n + m), 2N + 1

(13)

n=−N

where x is the input signal of the moving average filter, y denotes the output (filtered) signal, and 2N +1 is the order of the filter, that is the number of points used in the moving average. Then the filtered probability outputs of each channel were compared with a threshold to make a binary decision for each EEG segment. If the filtered output of an EEG segment was higher than the threshold, the segment was marked as “1”, otherwise it was marked as “0”. The value of threshold was different for each patient in this study and the threshold was selected by the criterion of misclassification error. That is, for each patient, the RVM outputs obtained for the training samples were collected. Then the value minimizing the number of falsely classified training samples was selected and assigned as the detection threshold of the patient. To make a decision for each epoch, the binary decisions of the EEG segments on three focal channels were then integrated by the following rules. If at least two channels had EEG segment been marked as “1” in an epoch, the epoch was marked as seizure. If only one channel had EEG segment been marked as “1”, the adjacent epochs were used to judge whether the current epoch was seizure or not. If there was at least one segment marked as “1” in adjacent epochs and in different channels, the current epoch was marked as seizure. Otherwise it was denoted as a nonseizure. Because the start and the end of a seizure are changing gradually, the feature differences of these

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seizure epochs are not significant compared with that of interictal epochs. This would cause difficulties in detecting the beginning and ending of epilepsy seizures. Hence, a collar technique was used to compensate for the difficulties. Each detected seizure event was extended n epochs on both sides. In this work, the value of n varied in different patients.

In the event-based evaluation, the adjacent decisions of the same class were considered as an event. If a seizure was detected at any time between the start and end of an expert-labeled seizure, it was considered a true detection. False detections were those that do not overlap with expert-labeled seizure events. For each patient, the event-based sensitivity was calculated by dividing the number of true detections by the total number of seizures marked by the experts, and false detection rate was defined as the average number of false detections per hour.


3.5. Performance evaluation The performance of the proposed seizure detection system was evaluated using two approaches: epochbased level and event-based level.61 For the epochbased evaluation, the seizure or nonseizure labels of the EEG epochs marked by the system were compared with those given by EEG experts. Then, three metrics of sensitivity, specificity and recognition rate were calculated for each patient.

4.

Results

In the proposed epilepsy seizure detection system, we analyzed the multifractal properties of the EEG recordings and extracted multifractal parameters from the spectrums to construct features vectors.

(a)

(b)

Fig. 2. Six 4s EEG signals (a) and their multifractal spectrums (b). The six signals come from three patients and belong to interictal and ictal EEG, respectively. 1550020-6

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As example, Fig. 2 gives six 4s EEG signals and their multifractal spectrums. The six EEG signals come from three patients and belong to two different classes (interictal and ictal), as can be seen in Fig. 2(a). In Fig. 2(b), several features can be observed. (i) The multifractal spectrums of EEG signals in different brain functional status show distinctive shapes. (ii) The maximums of f (α) drift towards lower values of α in the process of epilepsy seizures. (iii) The spectra of ictal EEG become narrower and more asymmetry compared with that of interictal EEG. To become more quantitative, the mean values and the standard deviations of eight parameters of the multifractal spectrums shown in Fig. 2(b) were summarized in Table 1. It can be noticed from Table 1 that the singular exponent α0 of ictal EEG is smaller than that of interictal EEG, which means that the EEG fractal time series loses fine structure, i.e. becomes more regular in appearance when a seizure occurs. Moreover, compared to interictal EEG, the multifractal spectra of ictal EEG signals

Table 1.

Interictal Ictal

have a greater αmin and a smaller αmax , thus with a smaller ∆α, i.e. a narrower spectrum width. The width of the spectrum ∆α is a measure of how wide the range of fractal exponents found in the EEG signal. The wider the range of possible fractal exponents, the “richer” the signal is in structure. Obviously the interictal EEG is more complex. Parameters f (αmin ) and f (αmax ) reflect the numbers of boxes with the maximum and minimum probability measures, respectively. Here both interictal and ictal EEG have f (αmin ) greater than f (αmax ) and ∆f > 0. This means the high probability measure predominate the fractal EEG series, that is, there are more points with high amplitude in the EEG signals given in Fig. 2(a). Because the mean value of ∆f of ictal EEG signals is 0.56 and greater than that of interictal EEG, the EEG in seizures is more inhomogeneous in signal amplitude and large amplitude signal predominate. Parameter R gives an estimate of asymmetry of the EEG’s multifractal spectrum. A value R < 0 means that whole spectrum is bent to left (left-skewed) and relatively dominated by low

Mean values and standard deviations of eight parameters of the multifractal spectrums shown in Fig. 2(b). α0

αmin

αmax

∆α

f (αmin )

f (αmax )

∆f

R

1.04 ± 0.01 1.02 ± 0.01

0.82 ± 0.02 0.91 ± 0.02

1.59 ± 0.06 1.32 ± 0.14

0.77 ± 0.08 0.41 ± 0.15

0.37 ± 0.04 0.67 ± 0.01

0.02 ± 0.03 0.11 ± 0.14

0.34 ± 0.07 0.56 ± 0.13

−0.47 ± 0.04 −0.48 ± 0.10

Fig. 3.

Mean values and standard deviations of the multifractal parameters of interictal and ictal EEG. 1550020-7

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fractal exponents. The singularity spectra of ictal EEG signals are more asymmetric, implying that the EEG in epilepsy seizure is more regular or smooth looking. On the whole, the fact that ictal EEG signals have lower values of α0 , narrower range ∆α of possible fractal exponents and more asymmetric left-skewed shape indicates that EEG decreases in the degree of multifractality and complexity when epilepsy seizures occur. While the mean value of ∆f of ictal EEG is greater than that of interictal EEG, implying that large amplitude signal predominate in ictal EEG and the degree of amplitude undulation increases along with the epilepsy seizures. To make the difference of the multifractal parameters more apparent, Fig. 3 presents a comparison on the mean values and standard deviations of the multifractality parameters between intericatal and ictal

Table 2.

p

EEG. In addition, the p-values produced by oneway analysis of variance (ANOVA) are presented in Table 2. Statistically significant difference was found in all the eight parameters between interictal and ictal EEG (p-value < 0.05). In this study, the multifractal parameters were used to build features vector for distinguishing ictal EEG patterns from interictal EEG by RVM and post-processing operations. The performance of the proposed seizure detection system was assessed on all the testing data of 21 patients in Freiburg database. The results of the epoch-based and event-based performance assessment for the detection system are listed in Table 3. It can be noticed from Table 3 that the average sensitivity for all the 21 patients was 92.94% in the epoch-based evaluation and the average values of specificity and recognition rate were

The p-values of eight multifractal parameters.

α0

αmin

αmax

∆α

f (αmin )

f (αmax )

∆f

R

4.4370 × 10−20

2.6080 × 10−7

1.0262 × 10−10

3.6110 × 10−23

0.0035

0.0338

0.0013

1.7415 × 10−4

Table 3. Patient

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Average

Results of the epoch- and event-based performance assessment for the presented seizure detection system. Number of seizures in testing dataset

Epoch-based performance Sensitivity (%)

Specificity (%)

Recognition rate (%)

Sensitivity (%)

False detection rate (/h)

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

54.55 95.89 91.46 96.67 92.86 100.00 91.89 94.74 97.08 100.00 84.29 100.00 100.00 91.96 100.00 100.00 100.00 81.82 78.57 100.00 100.00

98.58 99.59 99.35 90.73 96.46 97.31 99.99 90.79 94.18 97.94 98.31 99.98 97.56 98.50 93.40 97.30 99.55 99.08 99.67 99.05 99.64

98.56 99.58 99.31 90.75 96.45 99.31 99.98 90.80 94.19 97.95 98.27 99.98 97.57 98.47 93.44 97.32 99.55 99.07 99.66 99.06 99.64

33.33 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 66.67 100.00 100.00 100.00 100.00 100.00 100.00 66.67 66.67 100.00 100.00

0.30 0.09 0.13 0.79 0.48 0.69 0.00 1.15 0.90 0.19 0.26 0.00 0.62 0.19 0.46 0.53 0.12 0.18 0.04 0.04 0.07

92.94

97.47

97.57

92.06

0.34

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Event-based performance

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97.47 and 97.57, respectively. Nine patients had the sensitivity of 100% and only two patients (patients 1 and 19) had unsatisfactory sensitivities (less than 80.00%). Furthermore, all the patients had specificity and recognition rate more than 90.00%.

At the event-based evaluation level, 54 out of 59 seizures were detected correctly by the proposed detection system. This gives an average sensitivity of 92.06%. The system missed five seizures, which came from patients 1, 11, 18 and 19, respectively.

Fig. 4. (Color online) An example of missed seizures because of unobvious epileptic activity. The top left panel gives 1-h raw EEG data from patient 11, where the expert-labeled seizure is between the two red vertical lines. The EEG of the seizure part is also presented in the top right panel individually. All the other panels present the curves of eight multifractal parameters of the 1-h EEG, respectively.

Fig. 5. 1-h interictal EEG on three focal channels of patient 5. False detection shown by arrows was caused by large amplitude artifacts. 1550020-9

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For patient 11, the missed seizures resulted from the unobvious epileptic activity in the EEG recordings as illustrated in Fig. 4. As can be seen in this figure, there is no significant difference in the multifractal parameters between the seizure and nonseizure EEG parts, causing the seizure not to be detected by the system. For patients 1, 18 and 19, the missed seizures were because of the short duration (less than 10s). The false detection rates of all the 21 patients are presented in Table 3, with the average value of 0.34/h. Five patients (patients 4, 6, 8, 9 and 13) had high false detection rates (above 0.60). The majority of the false detections were caused by large amplitude rhythmic bursts and artifacts as illustrated in Fig. 5. The proposed epileptic seizure detection algorithm was implemented in MATLAB R2012b environment running on a desktop PC with an Intel dualcore 2.8 GHz CPU and 2GB of RAM. The time of the algorithm running on a 1-h three-channel EEG was about 1.2 min, which is much shorter than the duration of the EEG data. In addition, the average detection delay between seizure onsets marked by the expert and the system was 1.2 s. Thus the fast running speed and the high accuracy of detecting the early stage of seizures makes the proposed seizure detection system feasible for online real-time implementation. 5.

Discussion

In this work, we analyzed the multifractal characteristics of the EEG recorded from epileptic patients and proposed a seizure detection system by combining with RVM classifier. In general, the dynamics analysis of EEG is complicated due to its irregular nature and high heterogeneity. To characterize the underlying neuronal dynamics of the brain associated with different physiological states, nonlinear analysis methods have been widely used to EEG signals. It has been proved that a number of nonlinear analysis methods and measures have the ability to capture the sudden changes in the EEG signals.62 As one kind of nonlinear method, the multifractal formalism can describe the local singular behavior of the EEG fractal time series and reveals more “hidden” information of EEG by using singularity spectrum to characterize its nonlinear dynamics. In this work, the multifractal spectrums of EEG signals in different

brain functional status showed different shapes and statistically significant difference was also found in all the eight multifractal features between interictal and ictal EEG. Compared with that of interictal EEG, the multifractal spectrums of ictal EEG had smaller singular exponent α0 , narrower width ∆α and more asymmetric shapes. These all meant that the EEG fractal time series lost fine structure, i.e. becomes more regular in appearance when a seizure occurs. Meanwhile the greater value of ∆f of ictal EEG implied that large amplitude signals predominate and the EEG in seizures was more inhomogeneous in signal amplitude. Therefore, the multifractal features could capture the sudden changes in the interictal stage and gave a high accuracy when the seizure detection system based on these features was tested on Freiburg EEG dataset. In addition, a series of post-processing operations were carried out in the proposed detection system, which also further improved the seizure detection accuracy and reduced false detections. More specifically, the operation of moving average filtering was used to reduce the possible false detections from sporadic fluctuations. Multichannel integration fused spatio-temporal information from multichannel EEG and further increased the detection accuracy. In addition, collar technique located the onset of seizures more accurately and improved the sensitivity as well. Thus the proposed detection system achieved an epoch-based sensitivity of 92.94% and an event-based sensitivity of 92.06% when it was tested on 539 h of EEG recordings containing 59 seizures. In the proposed seizure detection system, we employed RVM as the classifier to output the seizure probability of an EEG segment. Compared with other kernel-based learning machines such as SVM, RVM avoids some limitations of SVM, such as the need for Mercer kernels and the set of the regularizing parameter which usually requires crossvalidation-based optimization. Most importantly, compared with SVM, RVM yields superior results both in terms of model sparseness and generalization ability. RVM utilizes dramatically fewer basis functions, which lead to significant reduction in the computational complexity of the decision function, thereby making the seizure detection system suitable for real-time applications. Actually, we only need to calculate Eq. (7) at the testing stage of the RVM classifier. As mentioned above, the running

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Table 4. Authors


Aarabi et al.55 Raghunathan et al.63 Chua et al.64 Yuan et al.65 This work

Related works and the results of performance assessment. Number of patients

Epoch-based sensitivity (%)

Specificity (%)

Event-based sensitivity (%)

False detection rate (/h)

21 5 15 21 21

68.9 87.5 — 91.72 92.94

97.8 99.82 — 94.89 97.47

98.7 — 78 93.85 92.06

0.27 — 0.18 0.35 0.34

time of the proposed seizure detection system on a 1-h three-channel EEG was about 1.2 min, among which the time consumed in RVM classification is only about 12 s. Taken together, the proposed detection system has advantages of high accuracy, low computational complexity and low time cost. Beyond its advantages, there also is a limitation in the proposed detection system. We extracted eight features from the multifractal spectrum of EEG signals and they were all used to construct a feature vector without carrying out a feature selection procedure. Feature selection and finding an optimal feature set should be considered in our future work to further improve the detection accuracy and reduce the training time of RVM classifier. The EEG database used in this study has been applied in many other seizure detection systems. Aarabi et al. extracted temporal, spectral and complexity features from intracranial EEG and presented a fuzzy rule-based system for seizure detection.55 The system was evaluated on 302.7 h EEG from 21 patients with 78 seizures. A segment-based sensitivity of 68.9% and a specificity of 97.8% were achieved, with the average false detection rate of 0.27/h. Compared to this system, our seizure detection system yielded a much higher segment-based sensitivity, albeit with a little higher false detection rate. Raghunathan et al. proposed a cascaded two-stage seizure detection algorithm, consisting of a discrete wavelet transform on EEG data and extraction of two linear features (coastline and variance energy).63 The algorithm performed only on five patients with 24 seizures and yielded a sensitivity of 87.5%. Chua et al. developed a subject-specific seizure detection method based on quadratic discriminant classifier.64 The detection method was tested on 63 seizures of 15 subjects and achieved a sensitivity of 78%. In the seizure detection system proposed by Yuan et al.,

fractal intercept and the relative fluctuation index were extracted as EEG features, and the extreme learning machine was adopted as classifier.65 The system was assessed only on about 170 h EEG data, and yielded a segment-based sensitivity of 91.72% and a specificity of 94.89%, with a false detection rate of 0.35/h. Compared with this system, the total duration of testing data in our method was much longer and our seizure detection method yielded a comparable performance and had a lower computational complexity in feature extraction and classifier testing. Although detailed comparison with these works is difficult due to the difference in the methodology of performance assessment, the seizure detection system presented in this paper yielded comparable results. Table 4 lists the results of the related works in detail.

6.

Conclusion

In this work, we investigated the multifractal characteristics of the EEG from epileptic patients and extracted eight parameters (α0 , αmin , αmax , ∆α, f (αmin ), f (αmax ), ∆f and R) from multifractal spectrums. Unlike the single fractal dimension which describes the overall complexity of an EEG signal, the multifractal formalism uses a continuous fractal dimension spectrum to characterize the local singular behavior of the EEG fractal time series and reveals more “hidden” information in EEG. Our study found that the multifractal spectrums of EEG signals in different brain functional status showed different shapes and all the eight multifractal features had statistically significant difference between interictal and ictal EEG. Compared with that of interictal EEG, the multifractal spectrums of ictal EEG had smaller singular exponent α0 , narrower width ∆α, more asymmetric shapes and greater value of ∆f . These all meant that the degree of multifractality decreased

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and the EEG fractal time series became more regular when a seizure occurred. Meanwhile the greater value of ∆f of ictal EEG implied that it was predominated by large amplitude signals. Based on these multifractal features, we proposed a seizure detection system by combining with RVM classifier. The system achieved a promising result with a high epochbased sensitivity of 92.94% when it was tested on the Freiburg EEG dataset. The high accuracy and the low time cost (processing 1-h three-channel EEG only needs about 1.2 min) of the system make it has potential to be used for real-time seizure detection in clinical applications.

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Acknowledgments The support of the Key Program of Natural Science Foundation of Shandong Province (No. ZR2013 FZ002), the Program of Science and Technology of Suzhou (No. ZXY2013030), the Development Program of Science and Technology of Shandong (No. 2014GSF118171), and the Fundamental Research Funds of Shandong University (No. 2014QY008), China is gratefully acknowledged.

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