=Paper=
{{Paper
|id=None
|storemode=property
|title=Reliable Epileptic Seizure Detection Using an Improved Wavelet Neural Network
|pdfUrl=https://ceur-ws.org/Vol-941/aih2012_Zainuddin.pdf
|volume=Vol-941
}}
==Reliable Epileptic Seizure Detection Using an Improved Wavelet Neural Network==
https://ceur-ws.org/Vol-941/aih2012_Zainuddin.pdf
AIH 2012
Reliable Epileptic Seizure Detection Using an Improved
Wavelet Neural Network
Zarita Zainuddin1,*, Lai Kee Huong1, and Ong Pauline1
1
School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia.
zarita@cs.usm.my, laikeehuong1986@yahoo.com,
ong.pauline@hotmail.com
Abstract. Electroencephalogram (EEG) signals analysis is indispensable in epi-
lepsy diagnosis as it offers valuable insights for locating the abnormal distor-
tions in the brain wave. However, visual interpretation of the massive amount
of EEG signals is time-consuming, and there is often inconsistent judgment be-
tween the experts. Thus, a reliable seizure detection system is highly sought af-
ter. A novel approach for epileptic seizure detection is proposed in this paper,
where the statistical features extracted from the discrete wavelet transform are
used in conjunction with an improved wavelet neural network in order to identi-
fy the occurrence of seizures. Experimental simulations were carried out on a
well-known publicly available dataset, which was kindly provided by Ralph
Andrzejak from the Epilepsy center in Bonn, Germany. The obtained high pre-
diction accuracy, sensitivity and specificity demonstrated the feasibility of the
proposed seizure detection scheme.
Keywords: Epileptic seizure detection, fuzzy C-means clustering, K-means
clustering, type-2 fuzzy C-means clustering, wavelet neural networks.
1 Introduction
Since its first inception reported by German neuropsychiatrist Hans Berger in the year
1924, the electroencephalogram (EEG) signals, which record the electrical activity in
the brain, have emerged as an essential alternative in diagnosing neurological disord-
ers. By analyzing the EEG recordings, inherent information from different physiolog-
ical states of the brain can be extracted, which are extremely crucial for the epileptic
seizure detection since the occurrence of seizure exhibits clear transient abnormalities
in the EEG signals. Thus, a warning signal can be initiated in time to avoid any un-
wanted seizure related accidents and injuries, upon detecting an impending seizure
attack.
While vital as a ubiquitous tool which supports general diagnostic of epilepsy, the
clinical implementation of EEG is constrained due to the challenges of: (i) Available
therapies require long term continuous monitoring of EEG signals. The generated
massive amounts of EEG recordings have to be painstakingly scanned and analyzed
visually by neurophysiologists, which is a tedious and time-consuming task. (ii) There
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often is disagreement among different physicians during the analysis of ictal signals
[19]. Undoubtedly, an automated diagnostic system that is capable of distinguishing
the transient patterns of epileptiform activity from the EEG signals with reliable pre-
cision is of great significance.
Various efforts have been devoted in the literature in this regard. Generally speak-
ing, a typical epileptic seizure detection process consists of two stages wherein, the
inherent information that characterizes the different states of brain electrical activity
are first derived from the EEG recordings using some feature extraction techniques,
and subsequently, a chosen expert system is trained based on the obtained features.
The discrete wavelet transform (DWT) has gained practical interest in extracting the
valuable information embedded on the EEG signals due to its ability in capturing
precise frequency information at low frequency bands and time information at high
frequency bands [4], [9], [22], [25]. EEG signals are non-stationary in nature, and
they contain high frequency information with short time period and low frequency
information with long time period [18]. Therefore, by analyzing the biomedical sig-
nals at different time and frequency resolutions, DWT is able to preprocess the bio-
medical signals efficiently in the feature extraction stage.
In the second stage of the seizure detection scheme, a great deal of different artifi-
cial neural networks (ANNs) based expert systems have been utilized extensively in
the emerging field of epilepsy diagnosis. For instance, the multilayer perceptrons,
radial basis function neural networks, support vector machines, probabilistic neural
networks, and recurrent neural networks are some of the models that have been pre-
viously reported in literature [5], [12], [14], [19], [22]. ANNs are powerful mathemat-
ical models that are inspired from their biological counterparts - the biological neural
networks, which concern on how the interconnecting neurons process a massive
amount of information at any given time. The utilization of ANNs in the seizure de-
tection study is appropriate in nature, due to their capability of finding the underlying
relationship between rapid variations in the EEG recordings, in addition to having the
characteristics of fault tolerance, massive parallel processing ability, and adaptive
learning capability.
The objective of this paper is to present a novel scheme based on an improved
WNNs for the optimal classification of epileptic seizures in EEG recordings. The
normal as well as the epileptic EEG signals were first pre-processed using the DWT
wherein, the signals were decomposed into several frequency subbands. Subsequent-
ly, a set of statistical features were extracted from each frequency subband, and was
used as a feature set to train a wavelet neural networks (WNNs) based classifier. It is
worth mentioning that the feature selection of EEG signals using DWT and epileptic
seizure detection with ANNs are well-accepted methodologies by medical experts [6-
7].
The paper is organized as follows. In Section 2, the clinical data used in this study
is first presented, followed by the feature extraction method based on the DWT. The
implementation of the improved WNNs is next described in Section 3. In Section 4,
the effectiveness of the proposed WNNs in epileptic seizure detection is presented
and finally, conclusions are drawn in Section 5.
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2 Materials and Methods
The flow of the methodology used in this study is depicted in the block diagram in
Fig. 1, which will be discussed in detail in the following sections.
2.1 Clinical data selection
The EEG signals used in this study were acquired from a publicly available bench-
mark dataset [2]. The dataset is divided into five sets, labeled set A until E. Each set
of the data consists of 100 segments, with each segment being a time series with 4097
data points. Each segment was recorded for 23.6 s at a sampling rate of 173.61 Hz.
Each of the five sets was recorded under different circumstances. Both sets A and B
were recorded from healthy subjects, with set A recorded with their eyes open whe-
reas set B with their eyes closed. On the other hand, sets C until E were obtained from
epileptic patients. Set C and D were recorded during seizure free period, where set C
was recorded from the hippocampal formation of the opposite hemisphere of the
brain, whereas set D was obtained from within the epileptogenic zone. The last data
set, set E, contains ictal data that were recorded when the patients were experiencing
seizure. In other words, the first four sets of data, sets A until D, are normal EEG
signals, while set E represents epileptic EEG signals.
2.2 Discrete wavelet transform for feature extraction
DWT offers a more flexible time-frequency window function, which narrows when
observing high frequency information and widens when analyzing low frequency
resolution. It is implemented by decomposing the signal into coarse approximation
and detail information by using successive low-pass and high-pass filtering, which is
illustrated in Fig. 2.
As shown in this figure, a sample signal x(n), is passed through the low-pass filter
G0 and high-pass filter H0 simultaneously until the desired level of decomposition is
reached. The low-pass filter produces coarse approximation coefficients a(n), whereas
the high-pass filter outputs the detail coefficients d(n). The size of the approximation
coefficients and detail coefficients decreases by a factor of 2 at each successive de-
composition.
Fig. 1. Block diagram for the proposed seizure detection scheme.
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Fig. 2. A three-level wavelet decomposition tree.
Selecting the appropriate number of decomposition level is important for DWT.
For the EEG signal analysis, the number of decomposition levels can be determined
directly, based on their dominant frequency components. The number of levels is
chosen in such a way that those parts of the signals which correlate well with the fre-
quencies required for the classification of EEG signals are retained in the wavelet
coefficients [17]. Since the clinical data used were sampled at 173.61Hz, the DWT
using Daubechies wavelet of order 4 (db4), with four decomposition levels is chosen,
as suggested in [21]. The db4 is suitable to be used as wavelets of lower order are too
coarse to represent the EEG signals, while wavelets of higher order oscillate too wild-
ly [1]. The four-level wavelet decomposition process will yield a total of five groups
of wavelet coefficients, each corresponds to their respective frequency. They are
d1(43.4-86.8Hz), d2(21.7-43.4Hz), d3(10.8-21.7Hz), d4(5.4-10.8Hz), and a4(0-5.4Hz),
which correlate with the EEG spectrum that fall within four frequency bands of: delta
(1-4Hz), theta (4-8Hz), alpha (8-13Hz) and beta (13-22Hz).
Subsequently, the statistical features of these decomposition coefficients are ex-
tracted, which are:
1. The 90th percentile of the absolute values of the wavelet coefficients
2. The 10th percentile of the absolute values of the wavelet coefficients
3. The mean of the absolute values of the wavelet coefficients
4. The standard deviation of the wavelet coefficients.
It is worth mentioning that instead of the usual extrema (maximum and minimum
of the wavelet coefficient), the percentiles are selected in this case in order to elimi-
nate the possible outliers [11]. At the end of the feature extraction stage, a feature
vector of length 20 is formed for each EEG signal.
3 Classification using an improved wavelet neural networks
WNNs are feedforward neural networks with three layers – the input layer, the hidden
layer, and the output layer [26] . As the name suggests, the input layer receives input
values and transmits them to the single hidden layer. The hidden nodes consist of
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continuous wavelet functions, such as Gaussian wavelet, Mexican Hat wavelet, or
Morlet wavelet, which perform the nonlinear mapping. The product from this hidden
layer will then be sent to the final output layer.
Mathematically, a typical WNN is modeled by the following equation:
p
x ti
y (x) wij b, (1)
i 1 d
where y is the desired output, x m is the input vector, p is the number of hidden
neurons, wij is the weight matrix whose values will be adjusted iteratively during the
training phase in order to minimize the error goal, is the wavelet activation func-
tion, t is the translation vector, d is the dilation parameter, and b is the column matrix
that contains the bias terms. The network structure is illustrated in Fig. 3.
The WNNs are distinct from those of other ANNs in the sense that [26]:
WNNs show relatively faster learning speed owing to the constitution of the fast-
decaying localized wavelet activation functions in the hidden layer.
WNNs preserve the universal approximation property, and they are guaranteed to
converge with sufficient training.
WNNs establish an explicit link between the neural network coefficients and the
wavelet transform.
WNNs achieve the same quality of approximation with a network of reduced size.
Designing a WNN requires the researchers to focus particular attention on several
areas. First, a suitable learning algorithm is vital in adjusting the weights between the
hidden and output layers so that the network does not converge to the undesirable
local minima. Second, a proper choice of activation functions in the hidden nodes is
crucial as it has been shown that some functions yield significant better result for
certain problems [23]. Third, an appropriate initialization of the translation and dila-
tion parameters is essential because this will lead to simpler network architecture and
higher accuracy [24].
Fig. 3. WNNs with d input nodes, m hidden nodes, and L output nodes.
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The selection of the translation vectors for WNNs is of paramount importance. An
appropriate initialization of the translation vectors will do a good job of reflecting the
essential attributes of the input space, in such a way that the WNNs begin its learning
from good starting points and could lead to the optimal solution. Among the notable
proposed approaches are the ones given by the pioneers of WNNs themselves, where
the translation vectors are chosen from the points located on the interval of the do-
main of the function [26]. In [10], a dyadic selection scheme realized using the K-
means clustering algorithm was employed. In [13], the translation vectors were ob-
tained from the new input data. An explicit formula was derived to compute the trans-
lation vectors to be used for the proposed composite function WNNs [3]. In [24], an
enhanced fuzzy C-means clustering algorithm, termed modified point symmetry-
distance fuzzy C-means (MPSDFCM) algorithm, was proposed to initialize the trans-
lation vectors. By incorporating the idea of symmetry similarity measure into the
computation, the MPSFCM algorithm was able to find a set of fewer yet effective
translation vectors for the WNNs, which eventually led to superb generalization abili-
ty in microarray study. In short, the utilization of different novel clustering algorithms
in WNNs aim at simpler algorithm complexity and higher classification accuracy
from the WNNs.
In this study, the type-2 fuzzy C-means (T2FCM) clustering algorithm [16] was
proposed to initialize the translation vectors of WNNs. Its clustering effectiveness as
well as its robustness to noise has motivated the investigation on the feasibility of
T2FCM in selecting the translation vectors of the WNNs. For comparison purposes,
the use of K-means (KM) and the conventional type-1 fuzzy C-means (FCM-1) algo-
rithms in initializing the WNNs translation vectors were also considered.
3.1 Type-2 Fuzzy C-Means Clustering Algorithm
Rhee and Hwang [16] proposed an extension to the conventional FCM-1 clustering
algorithm by assigning membership grades to type-1 membership values. They
pointed out that the conventional FCM-1 clustering may result in undesirable cluster-
ing when noise exists in the input data. This is because all the data, including the
noise, will be assigned to all the available clusters with a membership value. As such,
a triangular membership function is proposed, as shown in the following equation:
1 uij
aij u ij , (2)
2
where uij and aij represent the type-1 and type-2 membership values for input j and
cluster center i, respectively. The proposed membership function aims to handle the
possible noise that might present in the input data. From Eq. 2, the new membership
value, aij, is defined as the difference between the old membership value, uij and the
area of the membership function, where the length of the base of each of the triangu-
lar function is taken as 1 minus the corresponding membership value obtained from
FCM-1.
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By introducing a second layer of fuzziness, the T2FCM algorithm’s concept still
conforms to the conventional FCM-1 method in representing the membership values.
To illustrate, it can noted from Eq. 2 that a larger value of FCM-1 value (closer to 1)
will yield a larger value of T2FCM value as well.
Since the proposed T2FCM algorithm is built upon the conventional FCM-1 algo-
rithm, the formula used to find the cluster centers, cij , can now be obtained from the
following equation that has been modified accordingly, as shown below:
N
a x
j 1
m
ij j
ci N
, (3)
a
j 1
m
ij
where m is the fuzzifier, which is commonly set to a value of 2.
The algorithm for T2FCM is similar to the conventional FCM-1, which aims to
minimize the following objective function:
C N
J m (U ,V ) uijm || x j ci ||2 , (4)
i 1 j 1
but it differs in the extra introduced membership function and also the equation that
has been modified to update the cluster centers. In general, the algorithm proceeds as
follows:
1. Fix the number of cluster centers, C.
2. Initialize the location of the centers, ci, i = 1, 2, … , C, randomly.
3. Compute the membership values using the following equation:
2
1
C x c
m 1
U [uij ] (5)
k 1 x c .
j i
j k
4. Calculate the new membership value, aij from the values of uij using Eq. 2.
5. Update the cluster centers using Eq. 3.
6. Repeat steps 3-5 until the locations of the centers stabilize.
The algorithm for T2FCM is summarized in the flowchart shown in Fig. 4.
3.2 K-fold Cross Validation
In statistical analysis, k-fold cross validation is used to estimate the generalization
performance of classifiers. Excessive training will force the classifiers to memorize
the input vectors, while insufficient training will result in poor generalization when a
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new input is presented to it. In order to avoid these problems, k-fold cross validation
is performed.
To implement the k-fold cross validation, the samples are first randomly parti-
tioned into k>1 distinct groups of equal (or approximately equal) size. The first group
of samples is selected as the testing data initially, while the remaining groups serve as
training data. A performance metric, for instance, the classification accuracy, is then
measured. The process is repeated for k times, and thus, the k-fold cross validation has
the advantage of having each of the sample being used for both training and testing.
The average of the performance metric from the k iterations is then reported. In this
study, k is chosen as 10.
START
Select C
Initialize randomly
ci , i 1, 2,..., C
Compute membership, uij
Compute new membership, aij
Find new centers, ci
Centers
stabilize?
Yes No
END
Fig. 4. Algorithm for T2FCM.
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4 Results and Discussion
The binary classification task between normal subjects and epileptic patients was
realized using the WNNs models. The activation function used in the hidden nodes is
the Morlet wavelet function. During the training process, a normal EEG signal was
indicated by a single value of 0, while an epileptic EEG signal was labeled with a
value of 1. During the testing stage, a threshold value of 0.5 was used, that is, any
output from WNNs which is equals to or greater than 0.5 will be reassigned a value of
1; otherwise, it will be reassigned a value of 0. The simulation was carried out using
the mathematical software MATLAB® version 7.10 (R2010a). The performance of
the proposed WNNs was evaluated using the statistical measures of classification
accuracy, sensitivity and specificity. The corresponding classification results between
the normal and epileptic EEG signals by using the WNNs-based classifier with differ-
ent initialization approaches are listed in Table 1.
In terms of the classification accuracy, the translation vectors generated by the
conventional KM clustering algorithm gave the poorest result, where an overall accu-
racy of 94.8% was obtained. The WNNs that used the conventional FCM-1 clustering
algorithm reported an overall accuracy of 97.15%. The best performance was ob-
tained by the classifier that employed the T2FCM algorithm, which yielded an overall
classification accuracy of 98.87%.
As shown in Table 1, a steady increase in the classification accuracy was noticed
when the KM clustering algorithm was substituted with FCM algorithm, and subse-
quently T2FCM algorithm. FCM outperformed the primitive KM algorithm because
the soft clustering employed can assign one particular datum to more than one cluster.
On the contrary, KM algorithm, which used hard or crisp clustering, assigns one da-
tum to one center only, and this degrades greatly the classification accuracy. While
FCM relies on one fuzzifier, T2FCM adds a second layer of fuzziness by assigning a
membership function to the membership value obtained from the type-1 FCM mem-
bership values.
In the field of medical diagnosis, the unwanted noise and outliers produced from
the signals or images need to be handled carefully, as they will affect and skew the
results and analysis obtained afterwards. In this regard, the concept of fuzziness can
be incorporated to deal with these uncertainties. Outliers or noise can be handled
more efficiently and higher classification accuracy can be obtained via the introduc-
tion of the membership function. The noise in the biomedical signals used in this
work has thus been handled via two different approaches. The first treatment is in the
Table 1. The performance metrics for the binary classification problem.
Performance metric
Initialization methods
Sensitivity Specificity Accuracy
KM 85.00 97.30 94.80
FCM 93.82 97.92 97.15
T2FCM 94.96 99.43 98.87
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Table 2. Performance comparison of classification accuracy obtained by the proposed WNNs
and other approaches reported in the literature
Feature Selection Method Classifier Accuracy References
Time Frequency Analysis ANNs 97.73 [20]
DWT with KM MLPs 99.60 [15]
DWT MLPs 97.77 [8]
Approximate Entropy ANNs 98.27 [8]
This Work 98.87
feature selection stage, where the 10th and 90th percentiles of the absolute values of the
wavelet coefficients were used instead of the minima and maxima values. The second
way is via the T2FCM clustering algorithm used when initializing the translation
parameters for the hidden nodes of WNNs. The clustering achieved by T2FCM
proves to result in more desirable locations compared to the conventional KM and
FCM-1 methods, as reflected in the higher overall classification accuracy.
Numerous epileptic detection approaches have been implemented in the literature
using the same benchmark dataset as in this study. For the sake of performance as-
sessment, comparison of the results with other state-of-the-art methods reported in the
literature was included, as presented in Table 2. As depicted in this table, the pro-
posed WNNs with T2FCM initialization approach outperformed the others generally.
However, the achieved classification accuracy of 98.87% by the proposed model was
inferior to the multilayer perceptrons (MLPs)-based classifier as described in [15],
which might be attributed to their feature extraction method. Instead of using basic
statistical features, the authors used the KM clustering algorithm to find the similari-
ties among the wavelet coefficient, where the obtained probability distribution from
the KM was used as the input of the MLPs-based classifier. A better set of determinis-
tic features might be obtained from this approach, which will be an interesting topic to
pursue in future. However, it is pertinent to note that the MLPs-based classifiers are
subject to slow learning deficiency and getting trapped in local minima easily.
In order to evaluate the statistical significance of the obtained results, statistical test
on the difference of the population mean of the overall classification accuracy was
performed using the t distribution. The experiment was run 10 times to obtain the
values of the summary statistics, namely, the mean and the standard deviation of the
samples. The 1% significance level, or α=0.01 was utilized to check whether there is
significant difference between the two population means. Two comparisons were
done, namely, between KM and T2FCM, and between FCM and T2FCM. The formu-
la for the test statistics is given by:
x1 x2 1 2
t , (6)
sx1 x2
where x1 and x2 are the sample means; 1 and 2 are the population means; and
sx1 x2 is the estimate of the two standard deviations.
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For both cases, the values of the test statistic obtained fall in the rejection region.
So the null hypothesis is rejected and it is concluded that there is significant differ-
ence between the classification accuracy obtained using the different initialization
methods, that is, the performance of T2FCM is superior to those of KM and FCM.
5 Conclusions
In this paper, a novel seizure detection scheme using the improved WNNs with
T2FCM initialization approach was proposed. Based on the overall classification
accuracy obtained from the real world problem of epileptic seizure detection, it was
found that the proposed model outperformed the other conventional clustering algo-
rithms, where an overall accuracy of 98.87%, sensitivity of 94.96% and specificity of
99.43% were achieved. The initialization accomplished via T2FCM has proven that
the algorithm can handle the uncertainty and noise in the EEG signals better than the
conventional KM and FCM-1 algorithms. This again suggested the prospective im-
plementation of the proposed method in developing a real time automated epileptic
diagnostic system with fast and accurate response that could assist the neurologists in
their decision making process.
Acknowledgements. The authors gratefully acknowledge the generous financial sup-
port provided by Universiti Sains Malaysia under the USM Fellowship Scheme.
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