J. Biomedical Science and Engineering, 2010, 3, 1182-1189
doi:10.4236/jbise.2010.312154 Published Online December 2010 (http://www.SciRP.org/journal/jbise/ JBiSE ).
Published Online December 2010 in SciRes. http://www.scirp.org/journal/JBiSE
A wavelet-approximate entropy method for epileptic activity
detection from EEG and its sub-bands
Hamed Vavadi, Ahmad Ayatollahi, Ahmad Mirzaei
School of Electrical Engineering, Iran University of Science and Technology, Tehran, Iran.
Received 11 October 2010; received 20 October 2010; accepted 26 October 2010.
ABSTRACT
Epilepsy is a common brain disorder that about 1%
of world's population suffers from this disorder. EEG
signal is summation of brain electrical activities and
has a lot of information about brain states and also
used in several epilepsy detection methods. In this
study, a wavelet-approximate entropy method is ap-
plied for epilepsy detection from EEG signal. First
wavelet analysis is applied for decomposing the EEG
signal to delta, theta, alpha, beta and gamma sub-
ands. Then approximate entropy that is a chaotic
measure and can be used in estimation complexity of
time series applied to EEG and its sub-bands. We
used this method for separating 5 group EEG signals
(healthy with opened eye, healthy with closed eye,
interictal in none focal zone, interictal in focal zone
and seizure onset signals). For evaluating separation
ability of this method we used t-student statistical
analysis. For all pair of groups we have 99.99%
separation probability in at least 2 bands of these 6
bands (EEG and its 5 sub-bands). In comparing some
groups we have over 99.98% for EEG and all its
sub-bands.
Keywords: Approximate Entropy (ApEn); W avelet
Transform; Epilepsy Detection; EEG Signal; T-Student
1. INTRODUCTION
Epilepsy is a common and important brain disorder and
about 1% of world population suffers from this disorder.
So diagnosis of epileptic activity in brain can be useful
for these patients. A s we know, abnormal neu ronal firing
in the brain is the reason of epileptic activ ities or seizure
onsets. And these activities are evident in Electroen-
cephalogram (EEG) signal. EEG is summation of neu-
ronal electrical Activities and widely used in diagnosis
epileptic disorders and seizure onsets. Three different
states (healthy, interictal and ictal) obvious in monitoring
EEG signal for diagnosis epileptic activities. Brain ac-
tivity in the ictal, interictal and healthy states are sig-
nificantly different. Since 1970s EEG signal used for
automatic diagnosis of epileptic activities in brain. Till
now several methods used for this purpose, since the
first days of automatic seizure detection, representations
based on Fourier transform and parametric methods have
been applied [1].
Through the complex and chaotic behavior of brain
activity chaos related parameters are useful to identify-
ing epilepsy. Entropies, fractal dimensions, Lyapunov
exponents are main complexity parameters. Also artifi-
cial neural network based methods and wavelet based
methods used to diagnosis epilepsy. Also time-frequency
methods used for feature extraction from EEG signal.
Alexandros T. Tzallas has been used t-f analysis to de-
termine the EEG segments, which contains epileptic
seizures and extraction feature from power spectral den-
sity (PSD) [2]. It seems that using Discrete Wavelet
Transform (DWT) is better than the Fourier and Fast
Fourier Transform since by wavelet transform we have
better time-frequency localization, multi-rate filtering,
and scale-space analysis [3].
Hiram Firpi presented a methodology to capture one
or more deterministic dynamic components of EEG sig-
nal Using Genetically Programmed Artificial Features
[4].
Because of chaotic behavior of EEG signal chaos re-
lated parameter are useful to epilepsy detection [5].
Some research used correlation dimension and lyapanov
exponent on feature extraction [6,7]. In the latter re-
search wavelet applied for preprocessing and decompo-
sition of EEG to its sub- band and it has been shown that
calculating the parameter for EEG and its sub-band is
useful in epilepsy detection and other same application
[8,9]. Among lots of parameters which have been used
as features, entropies have important role. Entropy is a
measure of system complexity and there are several
types of entropies that appropriate for our approach. Al-

H. Va va di et al. / J. Biomedical Science and Engineering 3 (2010) 1182-1189 1183
though there is different definition for entropy and the
way to calculate it but all kind of entropies show system
randomness and regularity.
Some researches based on sample and spectral en-
tropy [10] have been done in application of automatic
seizure detection. Also Shannon entropy [11,12] and
Permutation entropy [13] have been used as suitable
features in the case of non-stationary time series. How-
ever all of these kinds of entropies are so useful and ap-
plicable. in the other hand, approximate entropy is the
most usable parameter in this field[14-16]. In the last
decade of century 20, STEVEN M. PINCUS introduces
approximate entropy as an efficient measure of systems
complexity [17]. Till now this parameter used in several
EEG based applications [18,19]. In some researches just
approximate entropy have been calculated for EEG [20]
and some methods have been used approximate entropy
with another parameter for increasing accuracy [21]. In
this study, a wavelet-approximate entropy method is
used for epilepsy detection. We used EEG standard
subbands that are suitable in analysis and conclusion.
2. MATERIALS AND METHODS
2.1. EEG Dataset
The dataset contains 500 single channel EEG segments
in five different sets (100 single channel EEG segments
for each O, Z, F, N, and S sets). Sets O and Z are in
healthy state with eyes open and closed, respectively.
This two sets of segments (O, Z) captured by external
surface electrodes. Sets F and N are in interictal state
obtained from epileptic zone and hippocampus zone of
brain, respectively. Set S refer to ictal state. These three
sets of segments (F, N and S) attained by intracranial
electrode.
The duration of each segment is 23.6 sec and sampled
by 173.61 Hz, so each segment contains 4096 samples.
All these EEG segments are recorded with the same
128-channel amplifier that converts by 12 A/D convertor
with bit rate of 12, and then were sampled on 173.61 Hz
[22].
Figure 1. First EEG segments of 5 groups Z, O, F, N and S.

H. Va va di et al. / J. Biomedical Science and Engineering 3 (2010) 1182-1189 1184
2.2. Wavelet Decomposition
The time-frequency representation based on Fourier
analysis suffers from a significant problem because the
spectral election is based on a sinusoidal representation
that has an infinite extent in the basis function. Wavelet
analysis idea was developed because of this defect of
time-frequency analysis. A wavelet is a “short wave”,
which has its energy concentrated in time to give a tool
for the analysis of transient, non-stationary, or time-
varying phenomena [8]. Several works applied the
Wavelet Transform to the study of EEGs. Wavelet an aly-
sis can represent EEG sub bands as a weighted sum of
shifted and scaled versions of the original wavelet,
without any loss of information and energy.
To achieve better results in feature extraction with
ApEn algorithm, with wavelet decomposition has been
used as a preprocessing level for EEG segments to ex-
tract five physiological EEG bands, delta (0-4 Hz), theta
(4-8 Hz), alpha (8-13 Hz), beta (13-30), and gamma
(30-60 Hz).
For this goal four levels discrete wavelet transform
(DWT) with third-order Daubechies (db3) wav elet func-
tion have been used. Since our dataset is in range 0-60
Hz, coefficients D1, D2, D3, D4 and A4 corresponding
to 30-60 Hz, 15-30 Hz, 8-15 Hz, 4-8 Hz and 0-4 Hz re-
spectively that are almost standard physiological
sub-bands. Now we can calculate Approximate Entropy
for each sub-band in the next level.
2.3. Appr oximate Entr opy
Approximate entrop y (ApEn) is a q u antification measure
which gives us lots of information about complexity and
regularity of time series data.
For a given N point time series data
   
 1,2,3, , 
X
xx xxN
Choose m points subsequences of EEG signal as be-
low:
  


1,2,3,,1Xixixixixi m 
For 11iNm 
Then define the distance between X(i) and X(j), d[X(i),
X(j)], as the maximum absolute difference between them
as below:




k=1,2,L,m
,max 1dXi XjxikXjk





1



And define RCO as:
RCOr std
That STD is the standard deviation of sequence, and r
can be varying between 0 and 1. Then we define

as
below:
Figure 2. Decomposition of EEG sequence with five level
discrete wavelet transform and extract five phisiological sub-
bands.


1 , 1
0
j
ifdXiXjRCO forjNm
other wise







We define
m
i
C

1
1
1
1
Nm
m
ij
i
CRCO Nm




Then we can define as below

mr


1m
i
1
1logC
1
Nm
m
i
rNm 



For fixed m and r, ApEn value of sequence is:



1
ApEn m,RCOmm RCO RCO 



We used th e EE G and its sub-b and s ex tr a ct ed fro m th e
wavelet decomposition as inputs for ApEn algorithm.
We calculate ApEn value for each sub-band with r =
0.15. For calculating ApEn value for each segment we
used 0.5 second sub-segments of each segment and av-
eraged the calculated values over length of each seg-
ment.
Although it’s not necessary to average ApEn value
calculated for sub-segments over each segment but it can
be useful and reduce noise and artifacts effects on ApEn
value for each segment. We performed this procedure for
all 100 segments in each group and finally we have 100
ApEn value for each group (1 ApEn value for each seg-
ment in group). The mean and standard deviation of
ApEn value for each group has been shown in Ta bl e 1

H. Va va di et al. / J. Biomedical Science and Engineering 3 (2010) 1182-1189 1185
Figure 3. Wavelet coefficient for a segment of EEG signal decomposed by 4 levels DWT.
and Table 2.
The ApEn value has been calculated for EEG as we
see in Figure 4 although has different mean for all 5
group and we can see this difference in Figure 4. As we
see in Figure 5 without any analysis clearly it has dif-
ferent value for most segments of healthy with eyes
close and interictal in nonfocal zone and ictal segments.
But ApEn values for healthy segments and interictal in
focal zone have overlap with other groups in original
EEG segments.
2.4. T- s tudent Analytical Analysis
Statistical tests allow us to make statements with a de-
gree of precision, but cannot actually prove or disprove
anything. A significant result at the 95% probability
level tells us that our data are good enough to support a
conclusion with 95% confidence (but there is a 1 in 20
chance of being wrong). In biological work we accept
this level of significance as being reasonable. T–test is a
statistical analysis for estimate the probability of segre-
gate between two groups of data.
T –test uses the mean and variance of each group to
calculate segregation probability (p-value). For this goal
we must first calculate t-score and degree of freedom
(df).
For calculating t-score we need first to calculate that
is variance of the difference between the two means.
d
S
22
212
12
dSS
Snn 
And and are variance of group 1 and group
2 respectively and also are length of group 1
and group
1
1
S1
2
S
1
n2 n
12
d
X
X
tS


Which 1
X
and 2
X
are mean of group 1 and group
2 respectively. And degree of freedom is calculated as:
2

2
22
22
1
22
1 2
12
11
d
S S
n
n
df Snn
 





H. Va va di et al. / J. Biomedical Science and Engineering 3 (2010) 1182-1189 1186
Table 1. Mean of ApEn value for each group of EEG segments and their sub-bands.
EEG (0-60 Hz) gamma (30-60 Hz) alpha (15-30 Hz) beta (8-15 Hz) delta (4-8 Hz) theta (0-4 Hz)
Z 0.19405 0.10457 0.11704 0.17796 0.17155 0.17670
O 0.23011 0.10396 0.11104 0.18613 0.17508 0.17457
F 0.30957 0.16150 0.15622 0.20147 0.16922 0.15888
N 0.34250 0.12386 0.15622 0.18628 0.16964 0.16554
S 0.19994 0.22115 0.15962 0.18498 0.16751 0.15719
Table 2. Standard deviation of ApEn value for each group of EEG segments and their sub-bands.
EEG (0-60 Hz) gamma (30-60 Hz) alpha (15-30 Hz) beta (8-15 Hz) delta (4-8 Hz) theta (0-4 Hz)
Z 0.02819 0.01611 0.00909 0.01052 0.01237 0.00924
O 0.04149 0.00977 0.00764 0.00836 0.00722 0.01071
F 0.05089 0.08510 0.06089 0.03029 0.01114 0.02158
N 0.04585 0.04233 0.06089 0.01093 0.00725 0.00907
S 0.03344 0.07088 0.04150 0.02473 0.01890 0.02141
Figure 4. ApEn value for all 100 segments of EEG data for
each group (O-healthy with eyes open, Z-healthy with eyes
close, F- interictal in focal zone, N- interictal in nonfocal zone
and S- ictal).
After calculating score and we can extract
p-value from p-value table of t-test analysis.
tdf
In this work ApEn value computed for each segment
and its sub-bands used to compare same sub-band of
each group with other group.
2.5. Summary of method
 Step 1: wavelet decomposition of EEG signal to
achieve standard physiological sub-bands
 Step 2: calculating Approximate Entropy (ApEn)
value for EEG and its sub-bands
 Step 3: statistical analysis with t test for investigate
Figure 5. ApEn value for all 100 segments of EEG data for 3
different states (O-healthy with eyes open, N- interictal in
nonfocal zone and S- ictal).
the potential of separation between groups with
extracted features with Approximate Entropy
(ApEn) for EEG and its sub-bands.
3. RESULTS
Means and variances of ApEn values have been calcu-
lated for these 5 groups are shown in Table 1 and 2.
With these parameters we calculate t-score and degree of
freedom for all EEG data and their sub-bands. With
these values we tabulate P-values of two sided t-test and
the results shown as Table 3.
The confidence interval for most groups are so good
and as we see in Tab le 3 most of parameters extracted

H. Va va di et al. / J. Biomedical Science and Engineering 3 (2010) 1182-1189 1187
Table 3. Assuming the null hypothesis for each pair of groups and their sub-bands.
EEG gamma alpha beta delta theta
Z&O <0.0001 0.9759 0.0005 0.0002 <0.0001 0.0026
Z&F 0.002 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001
Z&N <0.0001 <.0001 <0.0001 <0.0001 <0.0001 <0.0001
Z&S <0.0001 <0.0001 <0.0001 <0.0001 0.0011 <0.0001
O&F <0.0001 <0.0001 <0.0001 0.0066 0.0041 0.0061
O&N 0.0949 <0.0001 <0.0001 0.4511 <0.0001 0.1092
O&S <0.0001 <0.0001 0.0002 <0.0001 <0.0001 0.0001
F&N <0.0001 0.0002 NaN 0.5883 0.0043 0.9731
F&S <0.0001 0.0353 <0.0001 <0.0001 0.1371 <0.0001
N&S <0.0001 0.9816 <0.0001 <0.0001 0.0087 <0.0001
Table 4. Comparison significance of ApEn and CD and LLE.
ApEn CD [3] LLE [3]
EEG <0.0001 for 8 pai r <0.0001 for 2pa i r <0.0001 for 3pa i r
gamma <0.0001 for 6 pair --- <0.0001 for 2pa i r
alpha <0.0001 for 7 pai r --- <0.0001 for 2pair
beta <0.0001 for 6 pai r <0.0001 for 2pa i r <0.0001 for 3pa i r
delta <0.0001 for 5 pair <0.0001 for 2pair ---
theta <0.0001 for 8 pair <0.0001 fo r 2pair ---
Figure 6. Block diagram of overall method.
for these 5 groups show considerable difference between
these grou p s.
We compared all pairs of groups but distinguishment
between states shows that different epileptic state (healthy,
interictal and ictal) was more important in our approach.
But the parameters extracted by this method can separate
even groups in same state (such Z and O or F and S) as
well as other groups. For example we can find out our
signal is interictal and it is from focal or nonfocal zone.
For Z and O except the gamma sub-bands we have
very noticeable separation (all of the sub-bands over
99.95% except gamma).
For Z and F all of the sub-bands can separate these
groups with over 99.99% and the EEG signal also has a
good separation rate (99.8%). All of the sub-bands and
the EEG signal have 99.99% separation rate for Z and F.
for Z and S we have the same results and separation rate
for EEG gamma, alpha, beta and theta sub-bands are
over 99.99% and for delta sub-band separation rate is
99.89%. We have excellent separation between O and F
in EEG, gamma and alpha sub-bands over 99.99% and
for other sub-bands the separation probability are re-
spectively 99.34% for beta, 99.59% for delta and
99.39% for beta sub-band. With comparing the value for
groups O and N EEG signal hasn’t good result in separa-
tion these groups (90.51%) but gamma, alpha and theta

H. Va va di et al. / J. Biomedical Science and Engineering 3 (2010) 1182-1189 1188
sub-bands have separation rate over 99.99%. distin-
guishment for this pair of group in beta sub-band is 54.
99% and for delta sub-band is 89.08%.
Comparing O with S shows up to 99.99% separation
probability for EEG, gamma, beta, delta and theta sub-
bands and 99.98% for alpha subband.
For groups F and N the EEG signal has separation
with over 99.99% probability and 99.98% for gamma
sub-band. For alpha sub-band we can’t tabulate P-value
since both of the t-score and degree of freedom were
zero. Beta and theta sub-bands don’t show good separa-
tion rate (41.17% and 0.269%) but delta sub-band has
99.57% probability for separation rate.
For comparing interictal and ictal states (F and S, and
N and S) EEG signal and alpha, beta and theta sub- band s
have separation probability ov er 99.99 % for both pa irs F,
S and N, S. As we see in table 3 separation probability
between F and S for gamma sub-band is 96.47% and
86.29% for delta sub-band.
Separation rate for pair N, S in gamma sub-band isn’t
good not at all (1.84%) but for alpha sub-band is suitable
(99.13%).
4. DISCUSSION
Some other studies have been done in feature extraction
for epilepsy detection. But most of them just have used
for separate 3 groups of these 5 groups and have ignored
the other ones [3,23]. The extracted parameters in this
study can separate all of these 5 groups. Considering just
3 groups of these 5 groups shows significant difference
(see Figure 5). In comparison ApEn with CD and LLE
[3] we can see two major improvements.
1) We calculate separation rates for all 10 pairs with
all of 5 groups but in [3] and some other studies just 3
groups have been considered.
2) ApEn values can separate most sub-bands of each
pair but as we see in Tab l e 4 . In some sub-bands corre-
lation dimension or largest lyapanov exponent don't
show significant difference. And in other sub-bands
these values just can separate 2 or 3 pair of groups.
5. Conclusion
In this study, the Approximate Entropy combined with
wavelet analysis used to extract the features for epilepsy
detection. In order to automatic detection of epileptic
activity in EEG signals we have 3 different states
(healthy, interictal and ictal) and significant results are
obtained. The value of ApEn can be used to distinguish
the different EEG state. According to ApEn analysis
features of EEG and their sub-bands show acceptable
performances in our approach. Our extracted feature can
be useful and applicable for automatic detection of brain
diseases such as epilepsy. The approaches of using ApEn
combined with wavelet analysis suggest new idea and
method for detecting the features of epileptic activities in
EEG signal.
This method also can be used for other non-stationary
signals and other approach. Because the speed of this
method is high enough, we can use this method for
real-time non-stationary signals.
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