Computational Intelligence - February 2014 - 55

identification while referring to the least
number of ECG signal features.
This paper proposes a new non-fiducial method that applies chaos theory to
capture the major indices of chaotic
ECG signals, i.e. Lyapunov exponents
spectrum and correlation dimension.
The features of chaotic characteristics
have recently been tried to classify heart
diseases in the literature [13-17]. Lai et
al. [13] developed a QRS detection
algorithm based on an one-pole filter,
and investigated the automatic ECG
classification using fractal and cross correlation analyses. Raab et al. [14] used
the concept of large-scale dimension
densities to analyze heart rate variability
data. This method uses a normalized
Grassberger-Procaccia algorithm and
estimates the dimension in the rather
large-scales of the system. Anuradha et
al. [15] studied the nonlinear dynamics
of electrocardiogram (ECG) signals for
arrhythmia characterization. The statistical analysis of the calculated features
indicate that they differ significantly
between normal heart rhythm and the
different arrhythmia types and hence,
can be useful in ECG arrhythmia detection. Roopaei et al. [16, 17] extracted
discriminative information from the trajectories of VT and VF signals in the
state space. In this way, first, signals are
sketched in the state space by the delay
time method. Then, the state space is
considered as an image and trajectories
of VT and VF signals are considered as
two different images. However, utilization of them in biometric identification
is very rare because of extremely high
uncertainty of human's ECG data making it difficult to be applied in industrial
practice. That means that it is not easy to
acquire and identify specific features of
the signals. In this paper, we make an
attempt to further utilize the chaotic
characteristics of the ECG signals to fulfill biometric identification by incorporating new indices extracted from ECG
data, which include Lyapunov exponents spectrum, correlation dimension,
root mean square (RMS) level.
Some published papers took available
ECG data from the public databases [22,
23, 26, 27, 30, 31], i.e., the MIT-BIH

Normal Sinus Rhythm, the MIT-BIH
Arrhythmis database and the PTB database, as the tested objectives which were
mostly collected from the 12-lead ECG
system. Some research interests were
actually conducted in the labs [24, 25, 28,
29, 32, 33]. The data of MIT-BIH were
not conscientious and precisely prepared
because the lead configuration utilized
may not be the same. Furthermore,
while the simplest configuration of standard lead I were applied in the published
papers such as those depicted previously
[23, 25, 31-33], they need a contact electrode attached at the ankle as virtual
ground (this means that three contact
electrodes are required, see related figures
illustrated in [34]) which render these
approaches hard to be used practically. In
the presented experiments, the ECG
data were collected using Lead-I configuration of Einthoven limb leads [35, 36]
from a self-developed portable instrument ET-600 [37] without the need of
virtual ground (that is, only two contact
electrodes are needed [28, 29]) and processed via a digital signal processing unit.
The ECG signals can be obtained from
ET-600 without connecting to the right
ankle (reference ground). The subject
only needs to hold the two grips for a
few seconds to allow ECG signals collected by the ET-600. The digital processing unit is then used to extract and
calculate the parameters of Lyapunov
exponents and correlation dimension
after signal filtering. The values of the
Lyapunov exponents, correlation dimension and RMS level are used as the feature parameters which the characteristic
distributions appear the proposed features would be appropriate for biometric
identification. Finally, a neural network is
applied as a classifier for the features classification. Preliminary experiments have
shown the possibility of applying the
ECG signals in individual identification.
II. Chaotic Analysis
A. Phase-Space Reconstruction

It is difficult to discover the dynamic
characteristics and behavior in time
series. If there is not enough degree-offreedom for phase space to observe the

dynamics of the high dimensional system, one cannot extract the specific features. Let the time series under consideration be given by
X (t j) = {x (t j), x (t j + x), x (t j + 2x), ...,
(1)
x (t j + (m - 1) x)},
where j = 1, 2, f, x is the delay of
time series, m is the embedded dimension. The information of the time series
can be shown in the high-degree phase
space via the time-delay space reconstruction. It is necessary to select the
proper time delay x and embedded
dimension m for representing the chaotic phenomenon.
Takens et al. [38] proved that the
time-lagged variables constitute an adequate embedding provided the measured variable is smooth and couples to
all the other variables, and the number
of time lags is at least 2d + 1 (d is the
system dimension), then the reconstructed time series show the same characteristics as the original time series. The
proof of Takens' embedding theorem
can see in [39].
It wasn't explained in [38] how to
choose the delay-time x when the
embedded dimension is m . Therefore,
one can observe the phase plot to
choose a proper delay-time x . The
observation of the state for the phase
space indicates whether the time-delay
x chosen is appropriate for the system
or not. If the delay-time x is too little,
the reconstructed attractor is very close
to the diagonal line. If the delay-time x
is too large, the reconstructed attractor is
spread in the phase space. After the
appropriate delay-time x is chosen, we
next discuss how to choose the embedded dimension m.
B. Embedded Dimension

The attractor extended on the chosen
dimension does not have the probability
of overlapping. The chosen dimension is
called the embedded dimension m. It is
necessary to choose an appropriate
embedded dimension m, if the embedded dimension m is too little, the attractor is overlapping in the phase space; if
the embedded dimension m is too large,

February 2014 | Ieee ComputatIonal IntellIgenCe magazIne

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