Using Petri nets with inherent fuzziness for ECG signal classification

International INTERNATIONAL Journal of Electronics and JOURNAL Communication Engineering OF ELECTRONICS & Technology (IJECET), AND
ISSN 0976 –
6464(Print), ISSN 0976 – 6472(Online), Volume 5, Issue 8, August (2014), pp. 01-09 © IAEME
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ISSN 0976 – 6464(Print)
ISSN 0976 – 6472(Online)
Volume 5, Issue 8, August (2014), pp. 01-09
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© I A E M E
USING PETRI NET WITH INHERENT FUZZY IN THE RECOGNITION OF
ECG SIGNALS
RIYADH ABDULHAMZA
Department of Electrical Engineering,
College of Engineering, University of Babylon, Babylon, Iraq
1
ABSTRACT
This paper presents an approach to electrocardiogram (ECG) beats classification using a
concept of fuzzy Petri Net. The idea of the research is organizing the Petri net structure into neural
network. The implicit fuzzy of the network give a new structure which can be named Fuzzy Petri
network. The suitable coefficients that can be used as a features for the network is found using a
proposed best basis technique. Using the proposed best basis the dimension of the input vectors are
reduced and hence reduces the complexity of the classifier. The fuzzy Petri network parameters are
learned using back propagation algorithm.
1. INTRODUCTION
Since the report of Alexander Birmick Muirhead [1], who attached wires to a feverish
patient's wrist to obtain a record of the patient's heartbeat while studying for his Doctor of science (in
electricity) in 1872, the electrocardiography became the main tool for the cardiologists to diagnose
the heart abnormalities.
The classification of biomedical signals depends, basically, on a comparison process between
certain patterns with another one, which is called the healthy control. With ECG signals there are
more than one type of healthy control. This problem complicates the classification process. In order
to classify ECG signals, it is important to detect the QRS complex within the electrocardiogram.
Since it reflects the electrical activity within the heart during the ventricular contraction, the time of
its occurrence as well as its shape provide much information about the current state of the heart. Due
to its characteristic shape it serves as the basis for the automated determination of the heart rate, and
as entry point for classification schemes of the cardiac cycle. In that sense, QRS detection provides
the fundamentals for almost all automated ECG analysis algorithms [2].
The automatic heart beat classification is important for the precise cardiac dysfunction
diagnosis, so that, many researches have been done on this field [3-10]. The automatic ECG analysis

International Journal of Electronics and Communication Engineering Technology (IJECET), ISSN 0976 –
face a difficult problem which is the variations of ECG waveforms morphology for the same patient
making the classifier performs well in the training phase and fails in the test [11].
So many factors affecting the performance of ECG analysis and classification such as the
quality of ECG signal, the estimated ECG descriptors, the applied classification rule, and the
learning dataset [12]. The mathematical and statistical tools, used for the analysis of ECG signals,
offered a good solution for many problems related to this subject.
The fuzzy logic has been used together with the neural network as a hybrid classifier enhance
the abilities of the later network and overcome the non adaptability of the former [13].
The aim of this work is to design a system for the classification of various ECG diseases by
using features extracted from the ECG signal. The system, which will incorporate wavelet and neural
fuzzy Petri network, will be compared with other systems that use neural network and fuzzy
network.
P2
P3
2
2. PETRI NET
A Petri Net is a graph-based representational system that allows simple modeling of complex
systems, especially systems that have concurrent and independent features [14,15]. They have been
used to study the performance and dependability of a variety of systems. A Petri Net is made up of
three primitive elements: places, transitions, and directed arcs. The directed arcs connect the places
to the transitions and the transitions to the places. There are no arcs connect transitions to transitions
or places to places directly. Each place contains zero or more tokens. A vector representation of the
number of tokens over all places defines the state of the Petri Net.
A Petri Net is defined by a 5-tuple (P,T,I,O,M) where:
- P is the set of places (p1, p2, …, pn).
- T is the set of transitions (t1, t2, …, tm).
- I, and O are, respectively, the set of input and output functions mapping the set of transitions T
to the bag places. Bags are sets with allowance for multiple occurrences of the same element.
They keep a count of the number of occurrences of each element.
- M defines the initial number of tokens in each place.
A Petri Net can be represented as a directed graph G = (V, E), where places and transitions
are the vertices of the graph, forming the elements of set V. The set E, consisting of input and output,
is the set of edges of the graph. Figure 1 shows a graphical representation of a Petri Net.
P1
T1
T2 P4
Figure 1: Graphical representation of a Petri Net

The Fuzzy Petri net is a Petri Net that has the ability to accept the fuzzy values. The tokens of
Petri Net are modified to represent the true, false or some fuzzy measure in between true and false
( 0 £ μ £ 1 ). The output of a Fuzzy Petri Net is, also, a Fuzzy value. In fact, the tokens of Petri Net
are used as a data carrier in the fuzzy Petri Nets. Another modification could be done to Petri Net by
viewing the firing mechanism as a gradual process with a continuum of possible numeric values of
the strength (intensity) of firing of a given transition. These modifications will adapt the Petri Net
with a broad class of real world phenomena including pattern classification. Up to this point, the
problem of Fuzzy Petri Net includes decision-making where input and output may be variable within
a gradient, yet the decision-making process remains relatively static.
By adding the learning abilities of neural networks to the fuzzy Petri net, the new structure will
Input Places Transitions Output Places
3
extend the decision-making problem.
3. THE NEURAL FUZZY PETRI NET
The structure of the proposed Neural Fuzzy Petri Net is shown in figure 2.
The network has the following three layers:
- an input layer composed of n input places;
- a transition layer composed of hidden transitions;
- an output layer consisting of m output places.
The input place is marked by the value of the feature. The transitions act as processing units.
The firing depends on the parameters of transitions, which are the thresholds, and the parameters of
the arcs (connections), which are the weights. Each output place corresponds to a class of pattern.
The marking of the output place reflects a level of membership of the pattern in the corresponding
class.
.
.
.
.
.
.
.
.
.
Figure 2: The structure of the Neural Fuzzy Petri Net

Wij
rij Zi Yk
Xj
Figure 3: A section of the net outlines the notations
4
The specifications of the network are as follows:
- Xj is the marking level of j-th input place produced by a triangular mapping function. The top of
the triangular function is centered on the average point of the input values. The length of
triangular base is calculated from the difference between the minimum and maximum values of
the input. The height of the triangle is unity. This process keep the input of the network within
the period [0,1]. This generalization of the Petri net will be in full agreement with the two-valued
generic version of the Petri net.
)x f (Input( j ) j = (1)
where f is a triangular mapping function.

, ( )

, if x average ( x
)
=
min( )
x x
( ) min( )
max( )
−
−

−
−
=
x x
max( ) ( )
1 , ( )
( )
if x average x
x average x
if x average x
average x x
f x
Figure 4: The triangular mapping function
- Wij is the weight between the i-th transition and the j-th input place;
- rij is a threshold level associated with the level of marking of the j-th input place and the i-th
transition;
- Zj is the activation level of i-th transition and defined as follows:
x
f(x)
average of
input j
maximum of
input j
minimum of
input j

x
j
,
r x ij j
x
= =
k ki i ( ), 1,2,...,
5
i Z =T W S r ® X
[ ( )]
ij ij j
1
n
j
=
, j= 1,2,…, n; i= 1,2,…, hidden (2)
where, “ T ” is a t-norm, “ S “ denotes an s-norm, while ® stands for an implication operation
expressed in the form
a ®b = sup{cÎ[0,1], aTc £ b} (3)
where a, b are the arguments of the implication operator confined to the unit interval. In the case
of two-valued logic, equation (4.39) returns the same truth value as the commonly known
implication operator, namely

= = =
, Î
, {0,1}
0, if a 1 and b
0
1,

a b b if a b
1,

® = a b
otherwise
otherwise
if t-norm is defined as a multiplication operator (Õ ) then

® =
if r x
otherwise
r
ij
ij j
1,
n
Õ=

= Ú
j
if r x
ij j
j
ij
i ij
,
otherwise
r
Z W
1 1,
- Yk is the marking level of the k-th output place produced by the transition layer and performs a
nonlinear mapping of the weighted sum of the activation levels of these transitions (Zi) and the
associated connections Vjk
No ofTransitions
Y f V Z j m
i
.
=
1
(4)
where “ f ” is a nonlinear monotonically increasing function from R to [0,1].
THE LEARNING PROCEDURE
The learning process depends on minimizing certain performance index in order to optimize
the network parameters (weights and thresholds). The performance index used is the standard sum of
squared errors. The errors are the differences between the marking levels of the output places and the
target values. The training set (x, t), which is the marking levels of the input places (denoted by x)
and the required marking of the output places (target “ t ”), are presented to the network in order to
optimize the parameters. The performance index is as follows:


=
1
= −
k k E t y
+ −
k Z V
μ (8)
6
m
k
1
2 ( )
2
(5)
where
tk is the k-th target;
yk is the k-th output.
The updates of the parameters are performed according to the gradient method
param iter param iter E param ( +1) = ( ) −aÑ (6)
where E param Ñ is a gradient of the performance index E with respect to the network parameters, a
is the learning rate coefficient, and iter is the iteration counter.
The nonlinear function associated with the output place is a standard sigmoid described as
1
1 exp( )
=
i ki
y
THE RECOGNITION SYSTEM
After recording the ECG signal, the R-Peak measurement is found by looking for the zero
crossing points, as well as the local maximum.
Feature extraction is affected by the peak-to-peak magnitudes, the offset of the signal, and R-peak
position in the windowed ECG. These effects are due to the physiology, sex and age of the
patient, and the parameters of the measurement system. The dependence of the feature extraction
method to the offset and the peak-to-peak magnitude of the signal are decreased by the
normalization. The signal is then processed using wavelet transform.
SELECTION OF BEST FEATURES
When using the DWT in order to obtain a compact representation of the signal data we need
to choose how many the best wavelet coefficients to retain that will still adequately describe the
signal. The statistical parameters may be a good tool for describing the signal. As a starting point, all
the training data needs to be represented by matrices. If we have two classes, could be then
generalized for more than two classes, which can be referred to as C1 and C2 (class 1 and class 2).
The next step is to calculate the mean of each data set and the mean of the entire data set. The overall
mean can be calculated by merging the means of the individual data sets as shown in the following
equation
( ) ( ) 1 1 2 2 μ = p ×μ ÷ p ×μ all (7)
Where

=
=
n
i
i x
1
N 1

In which all μ is the overall mean and p refers to the apriori probability of that class and j μ
is the mean of class j. In a problem with two classes of equal representation the probability factor can
be assumed to be 0.5, and N is the number of data points.
TP
( ) = (9)
TP FN
Pr ( ) = (10)
7
NORMALIZATION OF ECG SIGNAL
Feature extraction is affected by the peak-to-peak magnitudes, the offset of the signal, and R-peak
position in the windowed ECG. These effects are due to the physiology, sex and age of the
patient, and the parameters of the measurement system. The dependence of the feature extraction
method to the offset and the peak-to-peak magnitude of the signal are decreased by the
normalization. The ECG signals are normalized as follows:
1- A rectangular window is formed so that a single ECG beat is contained in this window. By
adjusting the ECG signal, the position of the R-peak in the QRS complex is centered in the
window.
2- Peak-to-peak magnitudes of the ECG signal are normalized to 1mV. Thus, it is provided that
classification decision does not depend on the maximum amplitude of the ECG records.
3- Mean value of the ECG signal in the window is fixed to zero value. Thus, offset is removed
from the signal.
4. RESULTS
To examine the classification of the networks, eight different classes of ECG beats are used.
The ECG beats are: normal beat (N), left bundle branch block (LBB), right bundle branch block
(RBB), paced beat (P), premature ventricular contraction (V), atrial premature beat (A), ischemic
heart beat (I), and myocardial infarction (MI). The training and test sets are formed by data obtained
from different patients. Three statistics are used to compare the results: Sensitivity (SE), positive
predictivity (PP), and Total Classification Accuracy (TCA). These definitions are as follows:
i
i i
Sensitivity Se
+
TP
i
TP FP
i i
Positive edictivity PP
+

=
=
8
j 1
TP
i
Tr
TCA (11)
where (TPi) is the number of correctly classified episodes of the ith class; (FPi) is the number
of correctly classified as another class episodes; (FNi) is the number of miss classified episodes; and
(Tr) is the number of all beats in the training set. The obtained results are shown in figures 5-10.

8
0 10 20 30 40 50 60 70
100
90
80
70
60
50
40
30
20
10
0
Number of Features
Total Classification Accuracy (%)
Neural
Neural Fuzzy
Neural Fuzzy Petri
0 10 20 30 40 50 60 70
100
90
80
70
60
50
40
30
20
10
0
Number of Features
Neural
Neural Fuzzy
Neural Fuzzy Petri
Figure 5: Classification Accuracy versus Figure 6: Classification Accuracy versus
Number of Coefficients with DWT (db1) features Number of Coefficients with DWT (db2) features
0 10 20 30 40 50 60 70
100
90
80
70
60
50
40
30
20
10
0
Number of Features
Neural
Neural Fuzzy
Neural Fuzzy Petri
0 10 20 30 40 50 60 70
100
90
80
70
60
50
40
30
20
10
0
Number of Features
Neural
Neural Fuzzy
Neural Fuzzy Petri
0 10 20 30 40 50 60 70
100
90
80
70
60
50
40
30
20
10
0
Number of Features
Neural
Neural Fuzzy
Neural Fuzzy Petri
0 10 20 30 40 50 60 70
100
90
80
70
60
50
40
30
20
10
0
Number of Features
Neural
Neural Fuzzy
Neural Fuzzy Petri

9
5. CONCLUSIONS
In this study, a hybrid fuzzy network and Petri net with wavelet feature extraction method are
used to classify eight classes of normal and abnormal ECG beats.
The ECG beats are taken from MIT-BIH Arrhythmia data base and European ST-T data base.
Decision making is obtained by three stages: normalization process, feature extraction, and neural, neural
fuzzy or fuzzy Petri network.
In order to generalize the classification process, two different sets of ECG beats are taken from
two different patients, used for the training and testing processes of the ECG classifier.
The results show that networks, the Fuzzy Petri and neural fuzzy network, give better results with
wavelet transform than neural network. The interpretation of decision making is an advantage of fuzzy
network over the neural network.
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[1] Julian D. G., “Cardiology “, W. B. Saunders Company, 1998.
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[3] Costas Papaloukas et. al., An ischemia detection method based on artificial neural networks,
Artificial intelligence in medicine, Elsevier Science B.V., 24,167-178, 2002.
[4] Silipo R., Bortolan G., Marchesi C., ”Design of hybrid architectures based on neural classifier
and RBF pre-processing for ECG analysis”, International Journal of Approximate Reasoning,
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[5] Bousseljoit R. and Kreiseler D., “ECG Signal Pattern Comparison via Internet”, IEEE,
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[10] Rashed U., Mirza M. J., “Identification of Sudden Cardiac Death Using Spectral Domain
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[11] Gabrys B. and Bargiela A., “General Fuzzy Min-Max Neural Network for Clustering and
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[12] Banerjee S. and Mitra M., Application of Cross Wavelet Transform for ECG Pattern Analysis
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[13] Sung-Kwun and Pedry C. W., ”Fuzzy Polynomial Neuron-Based Self-Organizing Neural
Networks”, International Journal of General Systems, 2003 Vol. 32, No. 3, pp. 237–250,2003.
[14] Zhon Y., and Murata T., “Modeling and Analysis of distributed Multimedia synchronization by
extended-timing Petri Nets”, Society for Design and Process Science, Vol. 5, No. 4, pp. 23-37,
2001.
[15] Bhat A.A., “Stochastic Petri Net Models of Service Availability in a PBNM System for Mobile
Ad Hoc Networks”, Thesis, Virginia State University, 2004.
[16] Kavita L.Awade, “ECG Signal Processing for Detection and Classification of Cardiac Diseases”,
International Journal of Electronics and Communication Engineering Technology (IJECET),
Volume 1, Issue 1, 2010, pp. 33 - 43, ISSN Print: 0976- 6464, ISSN Online: 0976 –6472.

Using Petri nets with inherent fuzziness for ECG signal classification

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