a comparative analysis of principal component and independent...
TRANSCRIPT
ORIGINAL ARTICLE
A comparative analysis of principal component and independentcomponent techniques for electrocardiograms
M. P. S. Chawla
Received: 7 February 2007 / Accepted: 1 July 2008
� Springer-Verlag London Limited 2008
Abstract Principal component analysis (PCA) is used for
ECG data compression, denoising and decorrelation of
noisy and useful ECG components or signals. In this study,
a comparative analysis of independent component analysis
(ICA) and PCA for correction of ECG signals is carried out
by removing noise and artifacts from various raw ECG data
sets. PCA and ICA scatter plots of various chest and aug-
mented ECG leads and their combinations are plotted to
examine the varying orientations of the heart signal. In
order to qualitatively illustrate the recovery of the shape of
the ECG signals with high fidelity using ICA, corrected
source signals and extracted independent components are
plotted. In this analysis, it is also investigated if difference
between the two kurtosis coefficients is positive than on
each of the respective channels and if we get a super-
Gaussian signal, or a sub-Gaussian signal. The efficacy of
the combined PCA–ICA algorithm is verified on six
channels V1, V3, V6, AF, AR and AL of 12-channel ECG
data. ICA has been utilized for identifying and for
removing noise and artifacts from the ECG signals. ECG
signals are further corrected by using statistical measures
after ICA processing. PCA scatter plots of various ECG
leads give different orientations of the same heart infor-
mation when considered for different combinations of
leads by quadrant analysis. The PCA results have been also
obtained for different combinations of ECG leads to find
correlations between them and demonstrate that there is
significant improvement in signal quality, i.e., signal-to-
noise ratio is improved. In this paper, the noise sensitivity,
specificity and accuracy of the PCA method is evaluated by
examining the effect of noise, base-line wander and their
combinations on the characteristics of ECG for classifica-
tion of true and false peaks.
Keywords Electrocardiogram � Correlated � Gaussanity �Scatter plots � Principal component analysis �Feature extraction � Variance estimator �Independent component analysis
1 Introduction
With the increasing noise and condition differences, it is
possible to assess the ability of the principal component
analysis (PCA) [1–4] to extract the appropriate ECG
components and statistically separate the conditions, under
the differing noise conditions. By this time it is strongly
felt that, emphasis is required on the choice of appropriate
standard statistical models and methods of statistical
inference for ECG. Re-sampling methods using many
randomly computer-generated ECG samples can finally be
checked for estimating characteristics of a distribution and
for statistical inference. Statistical analysis too often has
meant the manipulation of the redundant ECG data by
means of judicious methods to solve a problem that has not
yet been defined [1, 3, 5]. The foundation of all statistical
methodology is the probability theory, which progresses
from elementary to the most advanced mathematics.
Independent component analysis (ICA) is a signal pro-
cessing technique originating from the field of blind source
separation and has been widely used in many fields such as
biomedical signal processing, speech processing and
communication [2, 5, 6]. One of the most well studied and
understood fact about the physiological signals is the
measured electrical potential related to the beating of the
M. P. S. Chawla (&)
Department of Electrical Engineering,
Indian Institute of Technology, Roorkee 247667, India
e-mail: [email protected]; [email protected]
123
Neural Comput & Applic
DOI 10.1007/s00521-008-0195-1
heart [1, 2, 4, 5, 7–9]. The ECG relates the observed ionic
current on the skin to events that occur in heart. The ECG
is typically measured by placing various electrodes on the
chest as well as the arms and/or legs [10–12]. In order to
employ the ECG signal for facilitating medical diagnosis,
statistical methods like PCA and ICA can be used to cor-
rect the ECG signal by removing either all or some sources
of noise. In order to overcome the limitations of conven-
tional ECG filtering methods, investigation is oriented
toward the reconstruction of ECG signal based on higher
order statistics [1, 2, 5–7]. In the analysis and feature
extraction of electrocardiograms, PCA and ICA techniques
have been successfully applied by various researchers in
the past for the separation of artifacts and other distur-
bances to enhance the morphological ECG features for
diagnostic information [3, 11, 13–16].
Compared to PCA methods, ICA technique realizes not
only decorrelation, but also accounts for the high-order
statistical independency [1–3, 7, 17]. Much of the misun-
derstanding and lack of proper utilization of statistics of its
probabilistic foundation is felt when assumptions of the
underlying probabilistic (mathematical) model are grossly
violated and the derived inferential methods will lead to
misleading and irrational conclusions [1, 3, 5, 7, 18]. The
techniques under such situations generally used are deriv-
ative-based techniques such as, classical digital filtering,
adaptive filtering, wavelets, neural networks, mathematical
morphology, genetic algorithms, Hilbert transform, syn-
tactic methods and zero-crossing-based identification
techniques. The basic method of denoising an ECG signal
is through filtering, but filtering physiological signals is not
trivial and is highly subjective as the information is spread
over different frequency bands and different measurement
channels [1–3, 5, 6, 15, 19].
In the first stage of analysis in this paper, an ECG data
compression procedure and detection of ECG segments
using PCA is described. In the present analysis, PCA is
used to exploit the fact that by identifying the dependencies
of higher index coefficients on the first principal compo-
nent may set a strategy for better ECG interpretation. The
extraction of independent components (ICs) is done using
ICA, and various combinational ECG lead cases among the
leads V1, V3, V6, AF, AR and AL are checked to find
correlations between them for best feature extraction and
classification. Variance is calculated for ten segments
considered for each of the IC and then total variance of
these variances is carried out to reveal all the hidden
dynamics in the ECG signals, as first discussed in [6] and
then reimplemented in [1, 5, 7, 8] as a mark of check of the
results presented in [6]. The simulation results are obtained
for CSE database ECG signals using Matlab. Based on the
combinations of the leads chosen, the position of noise and
useful ECG data in various quadrants of ICA scatter plots
are observed which could be a good basis for feature
selection as compared to PCA scatter plots obtained for the
same data base [1, 3].
2 PCA and ICA in ECG processing
One of the major concerns with high dimensional ECG
datasets is that, in some cases, all the measured segments or
intervals are not important for classification and interpre-
tation [1, 3–5, 7, 17]. Classical statistical methods break
down partly because of the increase in the number of
observations. In the present times, wavelets are also being
popularly used in ECG processing, since it is a non-
supervised method, allowing the process to be used in an
off-line automatic analysis of electrocardiograms [3, 11,
13–16, 39–42]. Moreover, the results are as accurate as
those obtained with other methods, but with much less
effort. The disadvantage of this method is the need to
calculate some approximations to find the best one,
although it is fast enough in any computer [1, 5, 7, 8, 10].
PCA is one of the most established techniques in multi-
variate statistical analysis and has been applied to ECG
compression. ICA is a statistical technique which performs
blind source separation on linear mixtures of statistically
independent ECG sources [20, 21]. The idea to use PCA
and ICA is due to the fact that, in most of the ECG data,
there is a large amount of noise and artifacts as well as
redundant information which is unnecessary for diagnostic
applications. Figure 1 gives a simple understanding of
PCA and ICA basis vectors as well of the ECG lead
configurations.
3 A comparative survey of PCA and existing methods
Principal component analysis is unsupervised, i.e., blind
and gives linear transformations of data that maximize the
variance along the new variables. A PCA classifier uses
features to discriminate between different signal classes
and may calculate the probability of a certain signal
belonging to a certain class. The classifier contains prior
knowledge about the classes and features, and is often
trained using training set, a particular set of signals where
their true class belongings are known.
Compressing ECG records using PCA involves a num-
ber of stages, as is done in the neural-network techniques; a
set of difference vectors is produced. Using PCA com-
pression, recognizable reconstruction of an ECG signal
may be achieved by summing the contributions of just the
first few basis vectors [2, 22–24]. The eigenvectors and
associated eigenvalues are derived from the particular
difference set through a linear-algebra decomposition
Neural Comput & Applic
123
process [1, 2]. They are inherently optimum in a least
mean-squares sense for representing the ECG record from
which they are derived. The sum of all such contributions
produces the complete reconstructed ECG signal. Fourier
or wavelet transform approaches may also be viewed as
transformation techniques, with the basis vectors in these
cases being sinusoids and wavelets, respectively. They are
also orthonormal, but are suboptimal, as, unlike PCA, they
are general purpose and not explicitly matched to the ECG
data set that they are used to compress [3, 4].
3.1 PCA whitening
Principal component analysis is extensively used in feature
extraction to reduce the dimensionality of the original data
by a linear transformation. PCA extracts dominant features
(principal components) from a set of multivariate data. The
dominant features retain most of the information, both in
the sense of maximum variance of the features and in the
sense of minimum reconstruction error. PCA is widely
used in face recognition, vehicle sound signature recogni-
tion, speech recognition, speaker recognition, medical
applications, signal noise reduction and active noise con-
trol. The whitening step is used to remove the correlation
between the observed ECG data. A common method to
achieve whitening is by the eigenvalue decomposition of
the covariance matrix of the mixed ECG signal [1–3, 25].
Before applying ICA to signals, it is better to preprocess
the ECG signals with a PCA-whitening method. After this
preprocessing with a linear transformation of the measured
ECG signals, the means of ECG signals are zero and the
variances are made one. This facilitates the reduction of the
correlation between several ECG signals or segments as
well as the dimension of ECG data set [9, 11, 17, 19].
Normalization of the ECG data to zero mean and unit
variance can considerably improve the results of visuali-
zation of various segments of an ECG waveform.
Visualization plots or scree plots [2, 11] obtained using
PCA can show that there is good segment separation of the
ECG waveforms.
3.2 ECG features
Feature extraction refers to a process whereby the input
ECG data space is transformed into a feature space that
although it has the same dimensionality as the original
ECG data space, it can represent the ECG data set more
accurately within the constraints imposed by having a
reduced number of features at the representation [1, 8, 10,
12]. The most fundamental types of patient data that are
available include ECG parameters that may be measured
directly. Computerized ECG data acquisition systems are
capable of displaying and storing the measured ECG
variables as well as real-time analysis. ECG signals that are
clean and have a high signal-to-noise ratio (SNR) are rel-
atively easy to interpret, both by a computer and a human
healthcare provider. Often, however, ECG signals are
corrupted by large amounts of noise and artifacts that
makes ECG interpretation difficult [2, 3, 5–7]. Noise con-
tamination in ECG signals is typically in the form of
motion artifacts caused when the patient moves. Mostly
ECG signals are non-stationary, meaning that they do not
follow a statistical distribution around a constant mean
value over time. Therefore, it is necessary to obtain derived
features of ECG signals for use with statistical monitoring
techniques. [1, 7, 26, 27]. In PCA decomposition, the lower
Fig. 1 a Basis for PCA vectors,
b ICA basis vectors,
c components of an ECG
waveform and d representation
of ECG leads
Neural Comput & Applic
123
index basis vectors represent larger energies in the ECG
signals. For example, the first principal component looks
somewhat like part of the central QRS complex in a normal
ECG. Likewise, other lower index PC eigenvectors
resemble elements of different ECG groups, such as the T
wave and P wave [2, 28]. Higher index eigenvectors tend to
look like noise, base-line wander (BLW), etc. Indeed, the
noisy sections of the ECG record tend to have higher
values of these principal component coefficients [1–3,
7, 29]. A conclusion of this statement is that an ECG signal
reconstructed without these higher index coefficients will
tend to look like the original ECG but without the noise
[2, 3, 17].
3.3 PCA-based ECG data compression
Recently several new approaches, the neural network with
the PCA and the multi-resolution wavelet decomposition
have been introduced [23, 24, 30]. However, existing
compression strategy has not always been easily accepted
by cardiologists. Among the transformation methods, the
Karhunen-Loeve transform (KLT) shows a highest com-
pression ratio for multi-lead ECG analysis [3, 17, 22]. It is
widely accepted that an effective ECG data compression is
in acute demand in clinical data processing. Data com-
pression of ECG records is very useful to storage pails of
daily clinical data in a hospital and to support a clinical
service in a remote of the country by data transmission with
a public line [2, 11, 23, 24, 31]. The conventional methods
of data compression are divided into two categories: direct
data compression and transformation methods [2, 3, 9, 11].
The direct data compression, mainly the polygonal or
polynomial approximation and the delta coding, is superior
to the transformation methods in terms of the processing
speed and the compression ratio. However, a direct method
depends on a function employed. Accordingly, the recon-
struction distortion appears in specific parts where the
function does not represent the extent of decomposition.
On the other hand, a transformation method recovers the
original ECG signal with a certain degree of error in whole
parts.
The linear PCA can be implemented with powerful,
robust techniques as the singular value decomposition
(SVD) that guarantee numerical accuracy and stability. To
the contrary, the robustness of nonlinear PCA technique is
questionable, due to the involved local minima that gen-
erally do not allow the detection of the optimal solution.
Therefore, when the variables of interest are mostly line-
arly correlated the linear PCA becomes a highly effective
solution [2, 3, 11, 22]. A complete description of the fol-
lowing factors [2, 11, 17] is necessary for efficient data
compression without losing morphology:
1. ECG data that is compressed or stored.
2. What can be retrieved, i.e., entire ECGs or selected
cycles only after data compression.
3. How retrieved ECG data may reasonably be used.
4. The fidelity with which ECG data can be reproduced
should be specified.
5. The ECG compression ratio should be stated, with
reference to the original sampling details, that is,
sampling rate, bit resolution, and number of bits per
sample.
Using PCA compression, recognizable reconstruction of
a given ECG signal may be achieved by summing the
contributions of just the first few basis vectors as these
contain most of the energy [2, 3, 9]. The eigenvectors
themselves form part of the overhead but need to be stored
only once for the whole ECG data set, which may have
thousands of samples. The quality of the compression and
reconstruction depends on how many of the PCA coeffi-
cients are used. Good reconstruction may be achieved using
five coefficients, as depicted in the results. Due to the nature
of the process used in identifying the eigenvectors in PCA
compression, the resultant basis vectors are orthonormal,
representing independent linear variables [3, 11, 25].
In this paper, PCA is used to exploit the fact that by
identifying the dependencies of higher index coefficients
on its first principal component may set a strategy for the
ECG analysis [2, 3]. In this analysis, using PCA variance
estimator [2, 11], the coefficients of the first five principal
components have been calculated for each of ECG signals
AF, AR and AL. This could be further facilitated by using
non-linear PCA compression, which enables only a single
coefficient to be required and stored for each ECG signal or
its samples. The other coefficients are inferred using the
polynomial techniques or concept. Restoring the ECG
waveform by the limited number of the orthogonal basis
corresponds to the orthogonal projection off onto the sub-
space H defined by the k eigenvectors [4, 9, 11, 17]. Let, A
be a pure rotation matrix, and is thus orthonormal, when
ATA = I = identity matrix. Any vector x can be recovered
from y by using the transformation
X ¼ ATyþ mx ð1Þ
x can be approximated by only using the k first eigenvalues
(components), which is five in this case and an Ak matrix
constructed from the k eigenvectors; this gives a possibility
to store the ECG data more efficiently. PCA is also used to
align the ECG data according to its eigen axes which
removes rotational effects. The eigenvalues can be used for
size normalization of an ECG data set. Translational effects
are also removed, since the ECG data set is centered
around its mean. The PCA based shape-space model for
ECG interpretation is
Neural Comput & Applic
123
Q ¼ wxþ Q0
or
x ¼ wþðQ� Q0Þð2aÞ
where x = shape-space vector over time. w = matrix for
an ECG data set obtained after recording from a specimen
or can be obtained from a standard CSE data base or any
other ECG data base. Assuming a projection matrix as P(k),
the orthogonal projection of f is given by
f ðkÞ ¼ PðkÞf ð2bÞ
where P(k) = H�(HT�H)-1�HT
The governing equation for PCA based ECG analysis is
Q ¼ Q0 þ Vimp
ki ð3Þ
where
Vi ith eigenvector
ki ith eigenvalue, which represents the sample variance
of x
m a scalar varying between certain limits
Q original or actual shape of ECG wave
Q0 mean shape of ECG wave
4 Standard independent component analysis (SICA)
Independent component analysis is a new technique for
ECG signals based on high-order statistics, and is used to
separate ICs from ECG measurements [1, 5, 6]. Since ICA
uses density estimation of a signal, the components with
dominant density can be easily found [23, 24]. In the
standard, noise free ECG, formulation of the ICA problem,
the observed ECG signals x are assumed to be a linear
mixture of an equal number of unknown but statistically
independent source signals [1, 5–7, 17].
If the artifacts and noise in ECG were to be removed
using ICA, the source of the artifacts and noise would be
other independent sources, and in such a situation, the
number of sources would exceed the number of recordings
[3, 7, 14]. It is thus important to determine the conditions
under which standard ICA could be used to remove artifacts
and noise from ECG recordings when the number of sources
may exceed the number of recordings [1, 7, 10, 13]. To
analyze this, consider the set of ECG recordings to be a
vector x and the pure signals (unknown) to be a vector s.
Then
X ¼ A s ð4Þ
where A is an unknown, invertible, square mixing matrix.
The output of ICA algorithm is an estimate of un-mixing
matrix w, such that
s ¼ w x ¼ w A s ð5Þ
It is evident that, wA = I, is an identity matrix. The
estimated ICs will be a mixture of those true independent
sources with element of w as the scale factor.
4.1 ECG correction using statistical measures
Independent component analysis defines a generative
model for the observed multivariate data, which is typically
given as a large database of samples. ICA cannot recover
any information from the mixtures if the ICs have Gaussian
distribution. It may be surprising that the ICs can be esti-
mated from linear mixtures with no more assumptions than
their independence. ICA is used to extract the contributions
of independent signal sources from their mixtures and aim
of applying ICA will be to separate ECG from all these [5,
13, 14, 32]. The ICA algorithm as depicted in Fig. 2 is used
to remove noise and artifacts from ECG signals and is used
as an reimplementation of [6]. The proposed method
Fig. 2 Flow chart of PCA–ICA
scheme for denoising and
correction of ECG signals
Neural Comput & Applic
123
analyses the use of PCA for the denoising of ECG signals.
ICA has some inherent limitations, due to which identify-
ing the IC of interest becomes difficult and highly
subjective at times. Band pass filtering is generally used to
attenuate the frequencies related to the above noise sources
which lie outside the frequency band occupied by the QRS
complex [15, 16, 18, 30, 33].
In the presented PCA–ICA method, the high accuracy
achieved in detecting QRS complexes is accompanied by
robustness, low computational complexity and dimen-
sionality reduction [2, 3, 11]. At the beginning of the
proposed algorithm, the enhancement of the QRS part of
the ECG is achieved by suppressing the level of the P and T
waves and disturbances in the ECG signal. These distur-
bances result mainly due to baseline drift, power line
interference and interferences from other physiological
sources. In this paper, combinations of leads V1,V3,V6,
AF, AR and AL of ECG recordings from the CSE database
is used for checking the accuracy of the combined PCA–
ICA algorithm and its reliability is evident from the results
of the scatter plots of PCA and ICA. The aim of this paper
is to justify the underlying theory of the use of ICA for
separation of the ECG signals and PCA for ECG data
compression.
5 PCA simulations
In this analysis, number of ECG samples taken in an ECG
file is 5000 and the sampling frequency of 500 Hz. In this
analysis, file-no-01 of CSE data base is used and the ECG
signals are simulated using Matlab software. Out of 12
channels, six channels viz. V1, V3, V6, AF, AR and AL
are used in the simulations. The reasons of using common
standards for electrocardiography (CSE) database is
frequently used since it is widely appreciated for the
evaluation of diagnostic ECG analyzers. The CSE Data-
base consists of about 1000 multi-lead recordings (12 or
15 leads), which obviously gives a wide range of data for
ECG analysis. In this analysis, it was investigated that
flexibility in selection of ECG segment amplitudes will be
useful to produce an acceptable ECG data compression for
a cardiologist for diagnostic applications. It is strongly felt
that PCA can be used for determining component signif-
icance to decompose a correlation matrix of an ECG
data set. A unique algorithm known as ‘‘PCA variance
estimator’’ is developed by the author, based on the
decreasing values of eigenvectors/eigenvalues [2, 3, 7].
Figure 3a–f shows the ECG waveforms for six leads
considered in this analysis.
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000-1
-0.5
0
0.5
1
1.5
Number of points
Number of points
Number of points
mV
mV
mV
V6
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000-2.5
-2
-1.5
-1
-0.5
0
0.5V3
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000-2
-1.5
-1
-0.5
0
0.5V1
(a) (d)
(e)
(f)
(b)
(c)
Fig. 3 a ECG waveform of lead V6, b ECG waveform of lead V3, c ECG waveform of lead V1, d ECG waveform of lead AF, e ECG waveform
of lead AR and f ECG waveform of lead AL
Neural Comput & Applic
123
5.1 PCA scatter plots
Principal component analysis helps in dimensionality
reduction of factors, i.e., that part of the ECG data which is
contributing the least useful diagnostic information. PCA
scatter plots are used to indicate the differences in vari-
ances observed in ECG segments before and after cardiac
treatment. Good estimates of the source signals are possible
due to the ability of the subspace algorithm to track the
eigenvalues and eigenvectors in non-stationary environ-
ment. The convergence of the algorithm is illustrated by
plotting the canonical angles between the basis vectors in
the estimated and theoretical signal subspaces [34, 35].
This section of the paper deals with plotting of scatter
plots for various lead combinations. PCA scatter plots of
various ECG leads give different orientations of the same
heart information when considered for different combina-
tions of leads [2, 3, 11]. Case studies have been
investigated and results have been obtained for combina-
tions of leads or channels to find correlations between them
viz.V1, V3, V6, AF, AR and AL. In PCA implementation,
if correlation coefficient between ECG data sets reduces
then noise is better separated or reduced which results in
more diagnostic information. On the other hand if corre-
lation increases, then noise is more predominant which
results in lesser diagnostic information. Table 1 shows the
values of the correlation coefficients of various combina-
tions of correlated ECG leads before PCA whitening.
Figure 4a–f shows the scatter plots using PCA whitening
for various combinations of leads and indicates the noise
and useful data rotation in the four quadrants.
Values of correlation coefficients between various lead
combinations give different values of correlation coeffi-
cients and also indicate the noise content sustaining in the
data as well the artifacts removed before and after appli-
cation of PCA.
Correlation coefficient between ECG data sets before
and after PCA rotation indicate the capability of PCA in
identifying and separating noise and artifacts in either all
ECG leads or the specific leads. Based on the combinations
of the leads chosen, the useful ECG data and noise content
take different locations in the four quadrants of the XY or
scatter plot. Accordingly, the values of correlation coeffi-
cients become positive or negative. The orientation of
useful ECG data and noisy data indicates the trend of fil-
tering requirements further for noise reduction and feature
extraction as well the classification.
5.2 ECG segment classification using PCAVE
Figure 5 shows a new developed PCA classifier as pro-
posed by the author. The developed PCA variance
estimator (PCAVE) operates on the principle which detects
the various ECG segments in the following sequence:
1. Collect n dimensional ECG data set.
2. Mean correct all the ECG sample points, i.e., calculate
the mean and subtract it from each ECG data point.
3. Calculate the variance-covariance matrix of the ECG
data set using, R = x�xT
4. Decompose the covariance matrix using PCA.
R ¼XN
i¼1
kiPCiPCiT
where ki is the eigenvalue of each principal component
PCi.
5. Determine eigenvalues and eigenvectors of the ECG
covariance matrix.
6. Sort the eigenvalues and the corresponding eigenvec-
tors, such that, k1 C k2 C kn.
7. Rotate the principal components using varimax
rotation.
8. Varimax rotation is an orthogonal transform that
rotates the principal components such that the variance
of the factors is maximized. This rotation improves the
ECG interpretability of the principal components.
9. Select the first eigenvectors and generate the ECG data
set in the new representation.
10. Analyze each detected ECG segment or waveform.
11. Study the error signal and calculate reconstruction
error.
The performance of the PCA classifiers is evaluated by
computing the percentages of: sensitivity (SE), specificity
(SP) and correct classification (CC) or accuracy.
This section of paper deals with the PCA analysis to find
the variance and error values of each ECG segment present
in the raw ECG signal and identify the various components
present in the augmented ECG leads AF, AR and AL.
Various cases are discussed as given below.
Case 1 deals with the results of lead AF for eigenvalue
and % error estimations. Tables 2 and 3 shows the
Table 1 Correlation coefficients of ECG leads before PCA
whitening
S. no. Correlated data sets Correlation coefficient
1 V6 and AF 0.19163
2 V6 and AL 0.88174
3 V6 and AR -0.7531
4 V3 and V1 0.84569
5 V6 and V1 -0.69315
6 AF and AR -0.6966
7 AF and AL 0.13970
8 AL and AR -0.80770
Neural Comput & Applic
123
magnitude of eigenvalues, the nomenclature, % variance
and the % error of the ECG segments for the lead AF.
The eigenvalues of the various ECG segments for the
lead AF are arranged in the descending order as shown in
Table 2. Number of useful eigenvalues found here for the
ECG lead AF is five.
Case 2 deals with the results of lead AR for eigenvalue
and % error estimations. Tables 4 and 5 shows the mag-
nitude of eigenvalues, the nomenclature, % variance and
the % error of the ECG segments for the lead AR.
Case 3 deals with the results of lead AL for eigenvalue
and % error estimations. Tables 6 and 7 shows the mag-
nitude of eigenvalues, the nomenclature, % variance and
the % error of the ECG segments for the lead AL.
Figure 6a–c shows the bar representation of principal
components for the leads AF, AR and AL. Figure 6d shows
the peaky template of QRS complex obtained for lead AF
as first principal component using the developed PCAVE.
5.3 Effect of noise on PCA program results
A comparison of point estimates from high versus low-
noise ECG CSE recordings indicated that on the average
computer-derived wave onsets and offsets were shifted
outward by noise in the cases discussed. However, this shift
was significantly less for PCA programs than the results
which are obtained using wavelet transforms. The overhead
in PCA is increased slightly due to the requirement to store
the polynomial’s own coefficients, but this is minimal as
compared to large details obtained in wavelet transforms.
Typically a 25–30% reduction in the required bit rate for
comparable reconstruction quality is achievable using
PCA, as compared to wavelet transforms and conventional
filtering methods.
5.4 Scree plots
Scree plot is a plot of eigenvalues versus number of principal
components. The scree test uses the eigenvalues found from
principal components analysis, drawing a straight line
through the lowest eigenvalues. It is strongly felt after
obtaining the simulation results that PCA can be successfully
used for the determination of principal components of sig-
nificance to decompose a correlation matrix between various
ECG data sets or leads. Figure 7 shows the scree plots for the
combinations of the augmented ECG leads AF, AR and AL.
5.5 Limitations of PCA
Some limitations of the decomposition method as currently
employed are important and are being discussed [1–3, 9, 11,
17, 26, 36]. First is that the PCA approach in the time or
frequency domain alone, is most sensitive to various specific
cardiac events and even for certain cardiac cycles. PCA
decomposition is generally robust against minor jitters,
creating slightly larger ECG components that cover the area
of the jitter [16, 19, 32], but is not optimal if the jitter is
substantial or the event shifts widely on the time frequency
surface judiciously due to experimental corrections or
manipulations. One possible result of these shifts is the
extraction of multiple ECG components, with at least com-
ponent one for each shifted location. Another possibility is
that with strong jitter, an elongated ECG component covers
the area of the jitter. A second important difficulty in the
decomposition method is choosing the number of principal
components (PCs) to extract, which can be arbitrary chosen
or fixed as a criterion. This could be always a limitation when
using PCA, although less information is available to moti-
vate the selection in the time frequency domains together
than the time or frequency domains selected alone.
5.6 Morphological validation of PCA
In order to give more validation to the behavior of the
proposed PCA decomposition method, two additional
manipulations were conducted with the CSE based ECG
data sets [3, 4, 9, 17, 19]. First, a condition difference was
incorporated by arbitrarily reducing the amplitude of half
the ECG dataset by 50%. Second, after creating the con-
dition difference, noise was added to the ECG signals to
check the ability of PCA decomposition to detect the sig-
nals under high and low signal-to-noise conditions with
differing signal representations. Signal-to-noise levels were
adjusted using signal power measured for each simulated
ECG dataset as a whole, rather than measuring signal
power and adding noise separately for each trial performed.
This was carried out to avoid adding noise differentially to
the simulated conditions, i.e., to ECG signals with no
signal or overlapping simulated ECG signals, or to the
different simulations which had differing numbers of
simulated electrodes that had none as ECG signal, possibly
could be noise or an artifact.
6 Statistical corrections to ECG Data and ICA scatter
plots
Adaptive separation methods are generally required since
the mixing system and signal or noise statistics may be
time varying. Moreover, real-time computation is desirable
in ECG signal processing applications. The separation task
at hand is to estimate a separating matrix w or mixing
matrix H so that the original sources are recovered from the
noisy ECG mixtures. Prior to separation, the observed ECG
signals are typically spatially whitened and the signal
powers are normalized to unity [2, 5, 6, 26, 34].
Neural Comput & Applic
123
In the present paper, the three or six lead ECG data are
decomposed into statistically ICs using the Jade algorithm
after identifying noise and artifacts. The noise and artifacts
are removed using a cleaning procedure making use of
statistical measures kurtosis and variance of variance
(Varvar) as first proposed in [6] and reimplemented in
[1, 2, 5, 7, 8]. The values of statistical measures kurtosis
and variance of variance are calculated by the algorithm
and checked against predefined thresholds. Thresholds for,
Kurtosis = 4.3 and Varvar = 0.4 obtained after initial
parameterization [1, 5, 7] of CSE data base files removing
redundant features, shows improvement in the thresholds
Fig. 4 a Scatter plot of leads AL and AF before and after PCA
whitening. b Scatter plot of leads AF and AR before and after PCA
whitening. c Scatter plot of AL and AR before and after PCA whit-
ening. d Scatter plot of V6 and V1 before and after PCA whitening.
e Scatter plot of V6 and AF before and after PCA whitening. f Scatter
plot of V6 and AL before and after PCA whitening. h Scatter plot of
V6 and AR before and after PCA whitening. i Scatter plot of V3 and
V1 before and after PCA whitening
Neural Comput & Applic
123
Table 3 Eigenvalues and % variances of components of lead AF
S. no. Eigenvalue number Magnitude of eigen value Nomenclature of ECG segment Total variance of ECG segments (%)
1 Eigenvalue 1 0.0211 QRS Complex 87.8932
2 Eigenvalue 2 0.0019 T wave 7.8456
3 Eigenvalue 3 0.0005 P wave 1.9292
4 Eigenvalue 4 0.0003 BLW 1.0586
5 Eigenvalue 5 0.0002 Noise 0.6448
Table 4 Eigenvalues and % variances of various ECG components for the lead AR
S. no. Eigenvalue number Magnitude of eigen value Nomenclature of ECG segment Total variance of ECG segments (%)
1 Eigenvalue 1 0.0089 QRS Complex 88.11
2 Eigenvalue 2 0.0005 T wave 4.95
3 Eigenvalue 3 0.0004 P wave 3.96
4 Eigenvalue 4 0.0002 Noise 1.98
Table 5 Eigenvalues and % error of various ECG components for the lead AR
S. no. Eigenvalue number Magnitude of eigen value Nomenclature of ECG segment Error of various ECG segments (%)
1 Eigenvalue 1 0.0089 QRS complex 0.0178
2 Eigenvalue 2 0.0005 T wave 0.001
3 Eigenvalue 3 0.0004 P wave 0.0008
4 Eigenvalue 4 0.0002 Noise 0.0004
5 Eigenvalue 5 0.0001 BLW 0.0002
Table 2 Eigenvalues and % error of various ECG components for the lead AF
S. no. Eigenvalue number Magnitude of eigen value Nomenclature of ECG segment Error of ECG segments (%)
1 Eigenvalue 1 0.0211 QRS complex 0.0400
2 Eigenvalue 2 0.0019 T wave 0.0038
3 Eigenvalue 3 0.0005 P wave 0.0010
4 Eigenvalue 4 0.0003 Base-line wander (BLW) 0.0006
5 Eigenvalue 5 0.0002 Noise 0.0002
Fig. 5 Proposed PCA classifier
Neural Comput & Applic
123
obtained as in [6]. The initial source signals are two
positive kurtotic signals representing ECG signals and
artifacts having frequencies slightly below 0.5 Hz, i.e., the
frequency of BLW [1, 2, 5, 7, 34].
6.1 Selecting appropriate nonlinearity
Blind source separation has many important applications
in communications and array signal processing. Many
widely used methods require prior knowledge on the sign
of the kurtosis of the sources and may fail if the mixtures
contain both sub- and super-Gaussian signals. Typically
prior information on the sign of the kurtosis is assumed to
be available and the nonlinearities are selected accordingly
[34, 37]. This assumption is often unreasonable. The zero-
memory nonlinearities needed for finding independent
sources are selected online by monitoring the statistics of
each estimated source signal. Consequently, separation
may be achieved even if a change in the sign of the
kurtosis occurs. Simulation examples illustrating the
ability to adapt to time-varying mixing systems and source
distributions of unknown kurtosis are presented using
ECG signals. In order to affect a truly blind algorithm, the
statistics of each output of the separation system are
recursively tracked [34] and an appropriate nonlinearity
for each channel is selected from two alternatives
depending on whether the source is deemed to have neg-
ative or positive kurtosis [35, 38].
Since the signal statistics may be time varying, the
algorithm which is discussed here does not make
restrictive assumptions on the form of the power density
Fig. 6 a Bar representation of principal components of lead AF.
b Bar representation of principal components of lead AR. c Bar
representation of principal components of lead AL. d Peaky template
of QRS complex obtained for lead AF as first principal component
Table 6 Eigenvalues and % error of components of an ECG data set
AL
S. no. Eigenvalue
number
Magnitude
of eigen
value
Nomenclature
of ECG
segment
Total variance
of ECG
segments (%)
1 Eigenvalue 1 0.0088 QRS complex 87.6345
2 Eigenvalue 2 0.0004 T wave 4.6449
3 Eigenvalue 3 0.0003 P wave 3.5277
4 Eigenvalue 4 0.0002 BLW 2.2125
5 Eigenvalue 5 0.0001 Noise 0.9794
Table 7 Eigenvalues and % error of various ECG components for
the lead AL
S. no. Eigenvalue
number
Magnitude
of eigen
value
Nomenclature
of ECG
segment
Error of
various ECG
segments (%)
1 Eigenvalue 1 0.0088 QRS complex 0.0176
2 Eigenvalue 2 0.0004 T wave 0.0008
3 Eigenvalue 3 0.0003 P wave 0.0006
4 Eigenvalue 4 0.0002 BLW 0.0004
5 Eigenvalue 5 0.0001 Noise 0.0002
Neural Comput & Applic
123
function (pdf), can adapt to changes in the mixing system
and signal statistics, and lends itself to real-time compu-
tation. In many BSS problems, prior information on the
type of pdf and the sign of the kurtosis is not available
[34, 35].
6.2 Interpretation of kurtosis coefficients
Simulated cases illustrating the capability to adapt to
time-varying mixing systems and source distributions of
unknown kurtosis are presented using CSE data base
ECG signals. The track of the sign of difference of
kurtosis coefficients, i.e., (k1 - k2) for the two ECG
channels is presented in the respective graphs for
physiological interpretation of electrocardiograms and
gaussanity.
If (k1 - k2) is positive it means that on the respective
channel, we have a super-Gaussian signal, otherwise we
have a sub-Gaussian signal. The typical number of samples
needed to achieve separation is around 300–400 [1, 5, 6,
34, 37]. Here, k1 and k2 are the kurtosis coefficients of the
ICs ICA1 and ICA2.
Tables 8, 9, 10, give the values of kurtosis and variance
of variance coefficients for the combination of the leads
AF, AR and AL.
In this case, k1 = 23.6985 and k2 = 3.1324, hence
(k1 - k2) = (23.6985 - 3.1324) = 20.5661. Since (k1 -
k2) is positive it means that on each of the respective
channels, we have a super-Gaussian signal.
From Fig. 8b, it is apparent that BLW as well as noise is
removed using statistical measures kurtosis and variance of
variance along with ICA, the concept as proposed first in
Fig. 7 a Scree plot for
combination of leads AR
and AF. b Scree plot for
combination of leads AL
and AF. c Scree plot for
combination of leads AL
and AR
Neural Comput & Applic
123
[6]. Table 8 indicates that, ICA-2 is a noise component
having |Kurt| \ 4.3 and has been successfully removed
using ICA followed by statistical corrections.
In this case, k1 = 23.6674 and k2 = 3.1332, hence
(k1 - k2) = (23.6674 - 3.1332) = 20.5342. Since (k1 -
k2) is positive it means that on each of the respective
channels, we have a super-Gaussian signal.
In this case, k1 = 23.6834 and k2 = 3.1353, hence
(k1 - k2) = (23.6834 - 3.1353) = 20.5481.
Since (k1 - k2) is positive it means that on each of the
channels, we have a super-Gaussian signal.
In this analysis, ICs are extracted, but as apparent from
the results obtained, they contained sufficient amount of
noise which was removed further using statistical mea-
sures, modulus of kurtosis and variance of variance
(Varvar) as proposed in [6] and reimplemented on a dif-
ferent data base at a sampling frequency of 500 Hz as
compared to [6], where the sampling frequency used was
256 Hz. After obtaining corrected ECG signals, further
investigations can be done for ECG segment analysis and
various interval classifications under different conditions.
Figure 9a shows source signals AL and AF before and after
ICA mixing, whereas Fig. 9b depicts the extracted inde-
pendent components and reconstructed ECGs for leads AL
and AF after statistical corrections. Figure 10a shows the
source signals for leads AL and AR before and after ICA
mixing, whereas Fig. 10b indicates the extracted indepen-
dent components and reconstructed clean ECG signals of
the leads AL and AR.
6.3 ICA scatter plots
For various lead combinations, ICA scatter plots have been
obtained using Matlab software. Based on the combina-
tions of the leads chosen, the position of noise and useful
ECG data can be better oriented in various quadrants of
ICA scatter plots for better feature selection as compared to
PCA scatter plots. PCA scatter plot analysis helps in
deciding which combination of leads gives most useful
diagnostic features, whereas ICA scatter plots can actually
give the features more prominently after correction pro-
cedure in either specific or all leads. Figure 11a–c give the
scatter plots for various combinations of the leads AF, AR
and AL.
7 Discussions
Principal component analysis preprocessing is used for data
compression, feature extraction and the decision-making
stage for R-peak detection. On the other hand, ICA pro-
cessing is for extraction of ICs and cleaning of ECG signals
together with statistical measures kurtosis and variance of
variance. ICA decomposition gives constant correlation
coefficient, whereas PCA decomposition exhibits varying
correlation coefficient.
In the present scheme of analysis, various segments of
an ECG data set are detected by considering PCA for data
reduction followed by ICA plus statistical measures for
cleaning the ECG as discussed and originated in [6]. A
threshold criterion is set in PCA analysis for ECG segment
classification based on variance concept. The efficacy of
the algorithm lies in the fact that PCA promotes data
compression whereas ICA helps in the identification of
noise and artifacts. The statistical measures, viz. kurtosis
and variance of variance decides the cleaning of the ECG
signals and identification of useful ECG components. The
correction of ECG data after removal of noise and artifacts
indicate that the extent of filter requirement reduces after
using ICA and statistical measures modulus of kurtosis and
variance of variance (Varvar). PCA based scatter plot
analysis, helps in deciding which combination of leads
gives most useful diagnostic features, whereas ICA scatter
plots can actually give the features more prominently after
the cleaning procedure in any of the leads. Thus, methods
like PCA and ICA would help the physicians to examine
and analyze the ECG signals more accurately, to further
increase the ratio and percentage of correct diagnosis. In
ICA processing, at times some of the components are more
emphasized or some components are either missing or
reduced and therefore, it can be used as a good statistical
tool for automated heart monitoring and its variability
measures.
Table 8 Values of estimated |Kurt| and Varvar for the two ICA
components AF and AR
Index ICA1 ICA2
|Kurt| 23.6985 3.1324 (Noise)
Varvar 0.0035 0.0050
Table 9 Values of estimated |Kurt| and Varvar for the ICA compo-
nents for leads AF and AL
Index ICA1 ICA2
|Kurt| 23.6674 3.1332 (Noise)
Varvar 0.0035 0.0050
Table 10 Values of estimated |Kurt| and Varvar for ICA components
of AL and AR
Index ICA1 ICA2
|Kurt| 23.6834 3.1353 (Noise)
Varvar 0.0035 0.0050
Neural Comput & Applic
123
8 Conclusion
Principal component analysis used in this case is used for
denoising, dimensionality reduction and data compression,
whereas ICA is utilized for removal of artifacts and noise.
In this paper, a new statistical algorithm based on PCA–
ICA together for six leads of a 12-channel ECG data is
developed. In this analysis, ICs are extracted, but as
evident from the results, they contained sufficient amount
of noise which was removed using statistical measures,
modulus of kurtosis and variance of variance (Varvar) as
proposed in [6]. After obtaining the corrected ECG signals,
further investigations can be done for ECG segment anal-
ysis and different ECG interval classification. Based on the
combinations of the leads chosen, the useful ECG data at
times give better feature selection using ICA and better
Fig. 8 a Plot of signals AF and
AR before and after ICA
mixing. b Extracted
independent components and
reconstructed clean ECG signal
for leads AR and AF
Neural Comput & Applic
123
Fig. 9 a Source signals AL and
AF before and after ICA
mixing. b Extracted
independent components and
reconstructed ECGs for leads
AL and AF after statistical
corrections
Neural Comput & Applic
123
Fig. 10 a Source signals for
leads AL and AR before and
after ICA mixing. b Extracted
independent components and
reconstructed clean ECG signals
of the leads AL and AR
Neural Comput & Applic
123
denoising of ECG data using PCA. Simulation cases
illustrating the capability to adapt to time-varying mixing
systems and source distributions of unknown kurtosis are
presented using CSE data base ECG signals. The track of
the sign of difference of kurtosis coefficients, i.e., (k1 - k2)
for the two ECG channels is presented in the respective
graphs for physiological interpretation of electrocardio-
grams and gaussanity. The results demonstrate that the
integration of PCA and ICA techniques can efficiently
remove the noise and artifacts from the ECG signals, even
after ECG data reduction preserving morphological ECG
features. PCA and ICA scatter plots of various ECG leads
and their combinations give different orientations of the
same heart information with more probability of attaining
diagnostic features. Different case studies have been
carried out for 12-lead ECG data and results have been
obtained for combinations to find correlations between
various leads, viz. V1, V3, V6, AF, AR and AL. PCA in
this case is used for removal of redundant data reduction,
denoising and data shrinkage, whereas ICA is used not only
for removal of artifacts and noise, but also for feature
extraction. For various lead combinations, ICA and
PCA scatter plots have been obtained. Based on the
combinations of the leads chosen, the position of noise and
useful ECG data in various quadrants can be done using
ICA as well as PCA scatter plots.
9 PCA and ICA: alternative statistical tools
for medical researchers
The proposed approach allows for the consideration of
priors on the structural nature of the different class of ECG
signals that are to be separated. These investigations are
expected to throw some light on the physiological phe-
nomenon of heart and its abnormalities if existing in the
ECG data sets. The observation made by the author after
this comparative study, is that, these higher order statistical
tools could be effectively utilized by the clinicians and
medical research community for morphological and feature
extraction of ECG. PCA and ICA methods demonstrate
that their combination to ECG applications offers signifi-
cant advantageous as well as comparable results over
classical approaches for better classification and a basis for
extensive feature selection. Abnormal signals were suc-
cessfully detected in ICA and corrected using statistical
parameters as compared to the original source ECG signals,
which may be used as a basis at times to reduce the need of
further sophisticated processing generally required in
conventional filtering methods. However, the results are
not always completely satisfactory, because there are only
three measured ECG signals to demix. If there were more
measured signals, ICA is expected to still provide better
results. To conclude, these techniques can be very well
accepted for ECG data compression, denoising and cor-
rection of ECG signals as done using wavelet analysis and
high-order digital filters like butterworth, etc. Based on the
combinations of the leads chosen, the useful ECG data at
times give better feature selection using ICA and better
denoising and compression of ECG data using PCA
maintaining diagnostic morphology.
Acknowledgments The author is thankful to Department of elec-
trical engineering, Indian Institute of Technology, Roorkee, India for
providing the required facilities to carry out this research. He is
extremely indebted to G.S. Inst. of Tech & Sc., Indore, India and
AICTE, GOI for sponsoring for his PhD.
References
1. Chawla MPS, Verma HK, Vinod Kumar A (2007) New statistical
PCA–ICA algorithm for location of R-peaks in ECG (Elsevier).
Int J Cardiol (in press)
2. Chawla MPS, Verma HK, Vinod Kumar (2006) ECG modeling
and QRS detection using principal component analysis. In: Pro-
ceedings of IET international conference, paper no. 04,
MEDSIP06, Glasgow, UK
Fig. 11 a ICA scatter plot of leads AL and AF. b ICA scatter plot of
leads AR and AF. c ICA Scatter plot of AL and AR
Neural Comput & Applic
123
3. Chawla MPS (2008) PCA–ICA method for detection of QRS
complexes and location of R-peaks in electrocardiograms, DSP,
Elsevier (revised and resubmitted on 30 April 2008)
4. Hao Z, Li-Qing Z (2005) ECG analysis based on PCA and sup-
port vector machines (IEEE). Transactions 0-7803-9422-4/05, pp
743–747
5. Chawla MPS, Verma HK, Vinod Kumar (2007) Artifacts and
noise removal in electrocardiograms using independent compo-
nent analysis (Elsevier). Int J Cardiol (in Press)
6. Taigang He, Gari Clifford, Lionel Tarassenko (2005) Application
of independent component analysis in removing artifacts from the
electrocardiogram. In: Neural computing and applications.
Springer-Verlag London Limited, pp 1–19
7. Chawla MPS (2007) Parameterization and correction of electro-
cardiogram signals using Independent component analysis
(WSPC, Singapore). Int J Mech Med Biol (JMMB) 7(4):355–379
8. Chawla MPS (2007) Parameterization and R-peak error estima-
tions of ECG signals using independent component analysis
(Taylor & Francis). Int J Comp Math Methods Med (CMMM)
8(4):263–285
9. Jalaleddine S, Hutchens C, Strattan R, Coberly W (1990) ECG
data compression techniques: a uniform approach (IEEE). Trans
Biomed Eng BME 37(4):329–343
10. Chawla MPS, Verma HK, Vinod Kumar (2006) Modeling and
feature extraction of ECG using independent component analysis.
In: Proceedings of IET international conference, paper no. 40.
APSCOM06, Hongkong, Oct 31–Nov 2
11. Chawla MPS (2008) Data reduction and removal of base-line
wander using principal component analysis, DSP, Elsevier
(revised and resubmitted on 30 April 2008)
12. Kohler BU, Hennig C, Orglmeister R (2002) The principles of
software QRS detection (IEEE). Eng Med Biol Mag 21:42–57
13. Chawla MPS, Verma HK, Vinod Kumar (2006) Independent
component analysis: a novel technique for removal of artifacts and
base-line wander in ECG. In: Proceedings of national conference,
pp 14–18. CISCON-06, MIT, Manipal, India, November 3–4
14. James CJ, Hesse CW (2005) Independent component analysis for
biomedical signals. Physiol Meas 26:R15–R39
15. Gupta D, James CJ, Gray W (2006) Denoising epileptic EEG
using ICA and phase synchrony. In: Proceedings of IET inter-
national conference, paper no. 085. MEDSIP06, Glasgow, UK,
July, 17–19
16. Chawla MPS, Verma HK, Vinod Kumar (2006) A new approach
to ECG modeling using principal component analysis. In: Pro-
ceedings on national conference, paper no. BM4.NCCCB06,
Engineering college, Kota, India, March 8–10
17. Koutsogiannis GS, Soraghan JJ (2002) Selection of number of
principal components for denoising signals. Electron Lett
38:664–666
18. Gao P, Chang EC, Wyse L (2003) Blind separation of fetal ECG
from single mixture using SVD and ICA. In: Proceedings of
ICICS-PCM 2003, Singapore, pp 15–18
19. Bernat EM, Williams WJ, Gehring WJ (2005) Decomposing ERP
time-frequency energy using PCA. Clin. Neurophysiol.
116:1314–1334
20. Lee TW (1999) Independent component analysis using an
extended infomax algorithm for mixed subgaussian and super-
gaussian sources. Neural Comput 11(2):409–433. doi:10.1162/
089976699300016719
21. Ungureanu M, Bigan C, Strungaru R, Lazarescu V (2004) Inde-
pendent component analysis applied in biomedical signal
processing. Meas Sci Rev 4(sect 2):1–8
22. Draper B, Baek K, Bartlett MS, Beveridge JR (2003) Recog-
nizing faces with PCA and ICA. Comput Vis Image Underst
(Special Issue on Face Recognition) 91(1–2):115–137
23. Dyrholm M. Independent component analysis in a convoluted
world, Kongens, Lyngby, Denmark, IMM-Ph.D-2005-158
24. Enescu M (2002) Adaptive methods for blind equalization and
signal separation in MIMO systems, DSC-Tech, Thesis August,
2002, Helsinki University of Technology, Signal Processing
Laboratory
25. Roweis S, Saul L (2000) Nonlinear dimensionality reduction by
local linear embedding. Science 290(5500):2323–2326
26. Ziehe A, Lasko P, Muller K, R. Nolte G (2003) A linear least-
squares algorithm for joint diagonalization. In: Proceedings of
international conference on independent component analysis and
blind signal separation, pp 469–474 (ICA-03, Nara, Japan)
27. Hamilton PS, Tompkins WJ (1986) Quantitative investigation of
QRS detection rules using the MIT/BIH arrhythmia database.
IEEE Trans Biomed Eng 1:115–165
28. Gritzali F, Frangakis G, Papakonstantinou G (1989) Detection of
the P and T waves in an ECG. J Comput Biomed Res 22:83–91
29. Friesen GM, Jannett TC, Jadallah MA, Yates SL, Quint SR,
Nagle HT (1990) A comparison of the noise sensitivity of nine
QRS detection algorithms (IEEE). Trans BME 37:85–98
30. Bruno A, Fabio F, Nadia M, Francesco Carlo M (2005) A New
approach based on wavelet-ICA algorithms for fetal electrocar-
diogram extraction, ESANN’2005. In: Proceedings of European
symposium on artificial neural networks bruges (Belgium),
pp 193–198
31. Thakor N, Sun Y, Rix H, Caminal P (1993) Multi-wave: a
wavelet-based ECG data compression algorithm. Trans Info Syst
E76-D(12):1462–1469 (IElCE)
32. Tarvainen MP, Niskanen J-P, Karjalainen PA, Laitinen T, Lyyra-
Laitinen T (2006) Noise sensitivity of a principal component
regression based RT interval variability estimation method. In:
Proceedings of 28th, EMBS, annual international conference, pp
3098–3101. IEEE, New York City, USA, August 30–September 3
33. James CJ, Lowe D (2003) Extracting multi-source brain activity
from a single electromagnetic channel. Med Artif Intell 28:89–
104
34. Enescu M, Koivunen V (2000) Recursive estimator for separation
of arbitrarily kurtotic sources. IEEE 301–305
35. Cardoso J-F (1998) Blind signal separation: statistical principles.
Proc IEEE 86(10):2009–2025. doi:10.1109/5.720250
36. Nagasaka Y, Iwata A (1993) Data compression of long time ECG
recording using BP and PCA neural networks (IEICE). Trans Info
Syst E76-D(12):1434–1442
37. Amari S-I, Chen TP, Cichocki A (1997) Stability analysis of
adaptive blind source separation. Neural Netw 10(8):1345–1351.
doi:10.1016/S0893-6080(97)00039-7
38. Amari S-I, Cichocki A (1998) Adaptive blind signal processing-
neural network approaches. Proc IEEE 86(10):2026–2048. doi:
10.1109/5.720251
39. Fisher AC, Hagan RP, Brown MC, El-Deredy W (2006) Lisboa
PJG ICA-based blind source separation (BSS) recovery of the
pattern electroretinogram from single channel records with poor
SNR. In: Proceedings of IET international conference, paper no-
087 (MEDSIP-06, Glasgow, UK, July 17–19)
40. Belouchrani A, Amin MG (1998) Blind source separation based
on time-frequency signal representations (IEEE). Trans Signal
Process 46(11):2888–2897
41. Zhou SK, Wang JT, Xu JR (1988)The real-time detection of QRS
complex using the envelope of ECG, (New Orleans, LA). In:
Proceedings of the 10th annual international conference on
engineering in medicine and biology society, p 38.IEEE, New
Orleans, LA
42. Sornmo L, Laguna P (2005) Bioelectrical signal processing in
cardiac and neurological applications. Elsevier Academic Press,
London
Neural Comput & Applic
123