Download An adaptive singular spectrum analysis approach to murmur

Medical Engineering & Physics 33 (2011) 362–367
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Medical Engineering & Physics
journal homepage: www.elsevier.com/locate/medengphy
An adaptive singular spectrum analysis approach to murmur detection from
heart sounds
Saeid Sanei a , Mansoureh Ghodsi b , Hossein Hassani b,c,∗
a
b
c
School of Engineering and Physical Sciences, University of Surrey, Guildford, UK
Statistics Group, School of Mathematics, Cardiff University, Cardiff, UK
Statistical Research and Training Center (SRTC), Tehran, Iran
a r t i c l e
i n f o
Article history:
Received 8 May 2010
Received in revised form 3 November 2010
Accepted 5 November 2010
Keywords:
Singular spectrum analysis
Murmur detection
Heart sounds
ASSA
a b s t r a c t
Murmur is the result of various heart abnormalities. A new robust approach for separation of murmur
from heart sound has been suggested in this article. Singular spectrum analysis (SSA) has been adapted
to the changes in the statistical properties of the data and effectively used for detection of murmur from
single-channel heart sound (HS) signals. Incorporating a cleverly selected a priori within the SSA reconstruction process, results in an accurate separation of normal HS from the murmur segment. Another
contribution of this work is selection of the correct subspace of the desired signal component automatically. In addition, the subspace size can be identified iteratively. A number of HS signals with murmur have
been processed using the proposed adaptive SSA (ASSA) technique and the results have been quantified
both objectively and subjectively.
© 2010 IPEM. Published by Elsevier Ltd. All rights reserved.
1. Introduction
The demand for automatic detection of murmur from auscultation of heart sound has been addressed by researchers and
clinicians recently [1–6]. In [1] patients with previously diagnosed
hypertrophic cardiomyopathy (HCM) (both obstructive and nonobstructive) have been assessed for the presence of heart murmur,
murmur characteristics, change in murmur loudness with postural change, and detectability of murmurs by an automated system.
In [2] the maximum intensity of the systolic murmur, its average frequency, and the mean spectral power were quantified. The
frequency at the point with the highest sound intensity in the spectrum and its time from the first heart sound, the highest frequency,
and frequency range were also determined. Separation of murmur
in this method however is based on segmentation and classification of the data and does not incorporate the basic heart sound
and the murmur detailed statistical parameters (within the overlapped regions) into account. In the method proposed in [3] the
spectrogram is used as an input to a multiple layer perceptron
(MLP) neural network trained to detect the presence of heart murmurs. Once the murmur is detected they are classified into seven
classes depending on their timing within the cardiac cycle using
smoothed pseudo Wigner–Ville distribution. The method is simple
and confirms that most of the signals’ information lies in the time-
∗ Corresponding author at: Statistics Group, School of Mathematics, Cardiff University, Cardiff, UK. Tel.: +44 7703367456.
E-mail address: [email protected] (H. Hassani).
frequency space. In this method the resolution constraint and the
time-frequency overlaps of the signal components are the major
drawbacks. Other workers applied some simple classifier to detect
and classify the systolic murmur for phonocardiogram screening
[4]. In another approach [6] the above two systems are somehow
combined and a neural network is used for classification of normal heart sound and murmur. Some other similar methods mainly
based on time-frequency analysis and feature classification have
also been reported [3].
A heart murmur is an extra or unusual sound heard during and
in between two heartbeats. Murmurs occur when a valve does not
close tightly (such as with mitral regurgitation) and blood leaks
backward. They also can occur when the blood flows through a narrowed or stiff valve [5]. The murmurs’ sound ranges from very faint
to very loud. They sometimes sound like a whooshing or swishing
noise. Normal heartbeats make a “lub-dupp” or “lub-dup” sound.
This is the sound of the heart valves closing as blood moves through
the heart. Murmur, on the other hand, has a noise type or “Puff”
sound and stretches from start of the heart sound for few seconds
or even the entire interval between the two heart beats.
The heart sounds and heart murmurs may be recorded using
electronic stethoscope connected to PC via an ADC and amplifier
interface. Cardiac murmurs can be divided into three categories
based on where they occur in the cardiac cycle. Short, quiet systolic
murmurs are generally benign or innocent. Long systolic murmurs,
diastolic murmurs and continuous murmurs are generally pathologic. People who have benign heart murmurs have normal hearts.
On the other hand, people who have abnormal murmurs may have
other signs or symptoms of heart problems. Most abnormal mur-
1350-4533/$ – see front matter © 2010 IPEM. Published by Elsevier Ltd. All rights reserved.
doi:10.1016/j.medengphy.2010.11.004
S. Sanei et al. / Medical Engineering & Physics 33 (2011) 362–367
Fig. 1. Normal heart sound (a) and heart sounds with (b) aortic regurgitation murmur, (c) aortic stenosis murmur, (d) mitral regurgitation murmur, (e) mitral stenosis
murmur, (f) precardial friction murmur, and (g) pulmonary stenosis murmur.
murs in children are due to congential heart defects. These are heart
defects that are present at birth. In adults, abnormal murmurs are
most often due to heart valve problems caused by infection, disease, or aging. Fig. 1 shows the sound signal of a normal heart and
a number of popular sounds of heart with murmur [7]. These signals have been recorded with 22 kHz sampling frequency using a
Welch Allyn Tycos stethoscope. The stethoscope was connected to
the PC through a multichannel ADC card and signal conditioner and
amplifier (Traveler-MK3 Portable bus-powered audio interface).
The maximum frequency band of these signals is below 300 Hz.
Therefore, they have been down-sampled here to 1600 sample/s in
order to reduce the computation cost while no information is lost.
The most important types of murmur are briefly described here.
Aortic regurgitation is the diastolic flow of blood from the aorta
into the left ventricle. The hallmark of aortic regurgitation or insufficiency is a high-pitched decrescendo diastolic murmur at the
left sternal border after the second heart sound. This abnormality causes significant morbidity within few years after diagnosis
mainly after the age of 50 [7]. Aortic stenosis is a narrowing or
obstruction of the aortic valve. The aortic component of the second heart sound, is usually diminished or absent because the aortic
valve is calcified and immobile and/or aortic ejection is prolonged
and it is obscured by the prolonged systolic ejection murmur. An
ejection click is common in children and young adults with congenital aortic stenosis but rare in elderly individuals with acquired
calcific aortic stenosis. This sound occurs approximately 40–60 ms
after the onset of S1 and is frequently heard best along the mid to
lower left sternal border. The more severe the stenosis, the longer
the duration of the murmur and the more likely it peaks at mid-tolate systole. When the left ventricle fails and cardiac output falls,
the aortic stenosis murmur becomes softer and may be barely audible. Atrial fibrillation with short R–R intervals can also decrease the
murmur intensity or make it appear absent [7]. Mitral regurgitation is a high-pitched holosystolic murmur beginning with the first
heart sound and extending to the second heart sound. The intensity
usually is constant throughout systolic ejection, often radiating to
the axilla. The harshness of the murmur does not correlate with the
magnitude of the valvular defect. Patients with severe disease often
have a third heart sound. In acute mitral regurgitation, the examination usually is consistent with acute pulmonary edema and left
ventricular failure. The murmur often is harsh. It may be heard over
the back of the neck, vertebra, and/or sacrum and may radiate to
the axilla, back, and left sternal border [7]. Mitral stenosis is a narrowing of the inlet valve into the left ventricle that prevents proper
opening during diastolic filling. The most common cause of mitral
stenosis is rheumatic fever [7]. In examination of the subjects with
363
mitral stenosis often low-pitched, rumbling murmur is observed.
The duration, and not intensity, of the murmur is a guide to the
severity of mitral valve narrowing. However, murmur may diminish in intensity as the stenosis increases. Pericarditis and cardiac
tamponade are clinical problems that involve the potential space
surrounding the heart or pericardium. Pericarditis is one cause of
fluid accumulation in this potential space; cardiac tamponade is
the hemodynamic result of fluid accumulation. Pericardial friction
rub is best heard at the lower left sternal border or apex when
the patient is positioned sitting forward or on hands and knees.
A friction rub may be distinguished from a cardiac murmur by its
changing character from heartbeat to heartbeat and patient position changes [7]. Pulmonic stenosis refers to a dynamic or fixed
anatomic obstruction to flow from the right ventricle (RV) to the
pulmonary arterial vasculature. Although most commonly diagnosed and treated in the pediatric population, individuals with
complex congenital heart disease and more severe forms of isolated
PS are surviving into adulthood and require ongoing assessment
and cardiovascular care. Functional or physiologic peripheral pulmonary stenosis is a common cause of a systolic murmur in infants.
The murmur of peripheral pulmonary stenosis may be continuous,
softer, and higher pitched [7].
For majority of murmurs, as can be seen in Fig. 1, the morphology
of murmur is different from actual heart sound and therefore, it is
expected that an effective subspace separation technique is the best
solution for this problem.
In this paper a new robust and adaptive approach based on
subspace analysis using SSA for detection of murmur is suggested.
This stems from the fact that in usual cases the subspaces of heart
sound and murmur are distinct and separable. SSA as a powerful technique in time series analysis and signal processing has
been introduced and applied to many practical problems. Here
a constrained SSA with adaptive selection of subspaces has been
introduced to extract the murmur signal. SSA incorporates the elements of classical time series analysis, linear algebra, multivariate
statistics, multi-variate geometry, dynamical systems and signal
processing [8]. This approach overcomes many limitations such
as nonlinearity and nonstationarity of the signals. Moreover, contrary to the traditional methods of time series analysis and signal
processing, the basic SSA method is non-parametric and does not
require any prior assumption about the data. Furthermore, SSA
decomposes a series into its component parts, while excluding the
random (noise) component which is very important for the murmur extraction. Of the main feature of the proposed technique is
that the extraction of murmur signal is achieved through successive
extraction (or filtering) in an algebraically orthogonal projection. It
also exploits the statistical differences between the two components in definition of a proper constraint. The rest of the paper is
organized as follows: In Section 2 the Basic SSA is described, Section
3 introduces the proposed constrained adaptive SSA, the proposed
algorithm for murmur extraction and empirical results are represented in Section 4, and finally Section 5 is devoted to summary
and conclusions.
2. Singular spectrum analysis
The basic SSA method consists of two complementary stages:
decomposition and reconstruction; each stage includes two separate stages. In the first stage the observed signal (often called
time series) is decomposed and in the second stage the original source signal is reconstructed and used for further analysis.
The main concept in studying the properties of SSA is separability, which characterizes how well different components can be
separated from each other. The absence of approximate separability is often observed in series with complex structure. For
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S. Sanei et al. / Medical Engineering & Physics 33 (2011) 362–367
these series and series with special structure there are different
ways of modifying SSA leading to different versions such as SSA
with single and double centering, Toeplitz SSA, and sequential SSA
[8].
The SSA is used in forecasting procedures for time series; see
[9,10,12]. In [8] SSA has been utilized for change-point detection in
time series. A comparison between SSA and other classical methods
you can see [11,12]. In addition, the method has several essential
extensions. The multivariate version of the method permits simultaneous expansion of several time series, e.g. in [13]. Automatic
methods of identification within the SSA framework can be seen in
[14] and recent work in ‘Caterpillar’-SSA software as well as new
developments in [15]. In the area of nonlinear time series analysis SSA can compete with other conventional methods. There are a
number of research that have considered SSA as a filtering method,
e.g. in [16] and the references therein. In another research, the information lied within noise subspace has been used as a diagnostic
information [17]. It has been shown that noise reduction is important for curve fitting in growth curve models, and that SSA can be
employed as a powerful tool for noise reduction for longitudinal
measurements [18]. A brief description of the SSA stages is given in
the following subsections [8].
2.1. Decomposition
This stage includes an embedding operation followed by singular value decomposition (SVD). In the embedding stage a
one-dimensional time series f of length N is mapped into an l × k
matrix with rows of length l as
⎡
⎢
⎢
X = {xij } = [x1 , x2 , ..., xk ] = ⎢
⎢
⎣
f0
f1
f2
..
.
ft−1
f1
f2
f3
..
.
f1
f2
f3
f4
..
.
fl+1
...
...
...
..
.
...
⎤
fk−1
fk ⎥
⎥
fk+1 ⎥
.. ⎥
. ⎦
fr−1
(1)
d
i=1
Xi =
d
i ui vTi
1 u1 v1 associated
2.2. Reconstruction
In the reconstruction stage the elementary matrices are first
split into several groups (depending on the number of components
in the time series – in this application heart and murmur sound
sources, the matrices within each group are added together). The
size of the group or in other words, the length of each subspace may
be specified based on some a priori information. In the case of murmur detection this feature and the desired component are jointly
(and automatically) identified based on a constraint on the statistical properties of the signal to be extracted. Let I = {i1 , . . ., ip } be the
indices corresponding to the p eigenvalues of the desired component.
Then, the matrix X̂I corresponding to the group I is defined as
ip
Xj . In splitting the set of indices J = {1, . . ., d} into disjoint
X̂I =
j=i
1
subsets I1 to Im we always have
X=
Im
X̂j
(3)
j=I1
The procedure of choosing the sets I1 , . . ., Im is called the
eigentriple grouping. For a given group I the contribution of the
component XI in expansion (3) is measured by contribution of the
d
/ i=1 i
corresponding eigenvalues:
i∈I i
In the next step the obtained matrix is transformed into the
form of a Hankel matrix which can be subsequently converted to a
time series. If zij stands for an element of a matrix Z, then the k-th
term of the resulting series is obtained by averaging zij over all i,j
such that i + j = k + 1. This procedure is called diagonal averaging, or
Hankelization of matrix Z.
3. Constrained SSA
with vectors xi = [fi−1 , fi , . . ., fi+l−2 ]T ∈ RL , where k = r − l + 1 is the
number of windows (1 ≤ l ≤ r), and subscript T denotes the transpose of a vector. Vectors xi are called l-lagged vectors (or, simply,
lagged vectors). The window length l should be sufficiently large.
Note that the trajectory matrix X is a Hankel matrix, which means
that all the elements along the diagonal i + j = const. are equal. This
represents a Hankel matrix.
In the SVD stage the SVD of the trajectory matrix is computed
and represented as a sum of rank-one bi-orthogonal elementary matrices. Consider the eigenvalues of the covariance matrix
Cx = XXT are denoted by 1 , . . ., l in decreasing order of magnitude
(1 ≥. . .≥ l ≥ 0) and the corresponding orthogonal eigenvectors
by u1 , . . ., u
l . Set d = max(i; such that i > 0) = rank(X): If we denote
vi = XT ui / i , then the SVD of the trajectory matrix can be written
as:
X=
centrated in the most dominant matrix X1 =
with the first singular value 1 ).
(2)
i=1
The SVD is used to decompose any trajectory matrix X into two
or several orthogonal components. Here, the objective is to separate the subspace of the two constituent components of heart
sounds (considering that the noise is negligible) of basic idea is
to identify the murmur and noise components. These components
are separated through a successive and constrained procedure of
configuring X and the SVD operation. Since the desired signal
might have different energy level, in this work, there won’t be any
assumption about the relationship between the order of the eigenvalues and the physiologically dominant component (note that for
example, if 1 > > 2 , then, the signal energy will be mostly con-
Comparing the normal heart sound and those with murmur, it
is concluded that the normal heart sound is the one which is limited in time duration and often with relatively larger amplitude.
As a result, the distribution of such a signal is sharper than (and
often skewed toward left compared with) a quasi-Gaussian distribution, which makes the kurtosis larger than that of the rest of the
signal (murmur). Therefore, the distribution is super-Gaussian for a
normal heart sound signal and clearly Gaussian or sub-Gaussian for
the murmur. This property can be enforced into the SSA reconstruction algorithm as a constraint. Approximately, a similar constraint
can be imposed by means of the distribution skewness. In practice,
the first signal component is reconstructed from the eigenvectors
and eigenvalues of the covariance of the Hankel matrix by sliding a
window over the eigenvalues and select m out of M of them where
m M. The desired reconstructed signal (heart sound) will be sum
of the signals reconstructed from the eigenvalues (and their corresponding eigenvectors) within the window to have maximum
kurtosis. Another simple criterion can be the peak to variance ratio
of the reconstructed signals.
Another important parameter is the subspace size of the desired
component. For stronger signals the eigenvalues are in the lower
subspaces and for weaker signals there values fall within higher
subspaces (usually where the noise components are). In this work
we have both cases. Therefore, in order to select an optimum m
(may be denoted as W) the following constrained problem can be
solved iteratively using a hierarchical search procedure:
mopt = W = min(m) subject to max(Kurt[st ])
m
(4)
where Kurt denotes kurtosis operation and shows how peaky the
signal distribution is and st refers to the source of interest which
S. Sanei et al. / Medical Engineering & Physics 33 (2011) 362–367
in this case is the heart sound without murmur. The W value also
slightly varies with the total set value for d. Due to the limited window length and the number of sliding lags the overall searching
time is short (∼m × d). For smaller d the computation cost is lower.
However, d should be large enough to allow distinct subspaces.
The murmur component is then easily extracted by subtracting the
reconstructed heart sound from the original signal, i.e.
murmur = st = yt −
j+W
ŷt
365
Table 1
The normalized kurtosis values for the recorded and separated sound signals.
Kurtosis murmur types
Heart and
murmur sound
Murmur
sound
Heart
sound
Aortic stenosis
Mitral regurgitation
Precardial friction
Pulmonary stenosis
0.87
1.43
0.16
1.53
0.034
0.072
0.066
0.091
11.62
6.87
1.24
7.39
(5)
k=j+1
Assuming that the signal with (j + 1)th to (j + W)th eigenvalues
has the maximum kurtosis (or peak to variance ratio). Here, ŷt is
the kth reconstructed component of the signal. It is interesting to
know that sometimes the subspace of the heart sounds falls within
few last eigenvalues where the noise subspace is. In such cases, the
murmur signal is very strong as for aortic regurgitation murmur in
Fig. 1.
4. Murmur detection experiment
For this experiment the signals were recorded from subjects of
30–60 years old, with 22 kHz sampling frequency using a Welch
Allyn Tycos stethoscope. The stethoscope was connected to the
PC through a multichannel ADC card and signal conditioner and
amplifier (Motu Traveler-MK3 Portable bus-powered audio interface). The signals were down-sampled to 1600 sample/s. Applying
the above constrained SSA technique with d = 12 the heart and murmur sounds can be well separated. Increasing d up to 50 does not
change the results significantly since the signal subspace is then
selected adaptively. However, it increases the computation time
for the adaptive search algorithm. Therefore, it is favorable to select
the lowest d which best discriminate the eigentriples. This has been
achieved empirically. For large values of d the heart signal is not
perfectly separated and some parts of that are extracted as murmur.
The subspace sizes (W) for the heart sound (without murmur)
are automatically estimated as 3, 2, 4, and 2 for the signals with aortic stenosis, mitral regurgitation, precardial friction, and pulmonary
stenosis murmurs, respectively. Fig. 2 demonstrates the separation
for the above most difficult types of heart murmurs (in terms of
analysis/detection). In order to better illustrate the performance
of the algorithm the figures are zoomed to show one cycle of the
sounds. Both heart sound and the murmur are well separated and
are audible using the processed sounds. A zero amplitude line as
the bottom signal of Fig. 2(a)–(d) shows there is no murmur and the
heart is normal. Table 1 shows the values of kurtosis for each signal
and their constituent components. Another significant conclusion
here is that in most of the sound signals the murmur has considerable overlap with the main heart sound (S1 or S2 ). Obviously,
it is very easy to distinguish a murmur from the bottom signals
using an automatic approach. Indeed, it is also possible to design a
classifier to identify various murmurs from the separated murmur
sound signals. As an example, a simple k-means clustering algorithm can guarantee such identification with zero percent error
(the algorithm can be trained using small number of signals and
small number of first and second order features).
Fig. 2. Separation of murmur from single channel heart sounds: top signal is the recorded sound, middle signal is the heart sound without murmur, and bottom signal is the
murmur sound; (a) aortic stenosis murmur, (b) mitral regurgitation murmur, (c) precardial friction murmur, and (d) pulmonary stenosis murmur.
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S. Sanei et al. / Medical Engineering & Physics 33 (2011) 362–367
Table 2
The correlation values (|| ≤ 1) between the separated components, heart sound and
murmur signals.
Murmur types
Aortic stenosis
Mitral regurgitation
Precardial friction
Pulmonary stenosis
0.0012
0.0057
0.0094
0.0033
time-frequency approaches due to the overlap in this domain and
the fact that the transform is sub-optimal in which the basis do not
perfectly represent the signal subspaces. In terms of computation
speed, although ASSA is comparable to time-frequency based methods, it has less complexity than those using neural networks mainly
due to their extensive search operations. The proposed method is
also nonlinear and can cope with nonstationary data. Lowest values (shortest bars) in Fig. 3 refer to better separation/detection
performances of the algorithms. On the other hand, unlike the
feature-based [3] and TF-NN based [5] approaches, in which the
aim is detection of murmur, here a complete separation of the two
sounds is envisaged and followed. Therefore, the results provide
more detailed diagnostic information about both heart sound and
murmur.
6. Summary and conclusions
Fig. 3. Comparison between the results by employing the time-frequency neural
network based, the feature based, and the proposed ASSA methods using bars from
left to right respectively.
As another measure of performance of the method, the correlations between the separated heart and murmur sound signals
for each abnormality was calculated ( = corr(extracted murmur,
extracted heart sound)). The correlation values for the above different murmur types are depicted in Table 2.
5. Comparison with other methods
The approaches by Javed et al. [3], and Andrizevic et al. [6],
which are somehow similar and are time-frequency (TF) and neural network (NN) based systems, as two recent techniques (using
somehow sub-optimal transforms) were simulated. In the method
proposed in [6], first, the input data (digital recordings of heart
sounds), via wavelet packet analysis is denoised. Second, principal
component analysis (PCA) is employed for block processing of the
data. Third, a perceptron NN is utilized for classification. In [3] a
similar approach has been followed. In that work the signals are
segmented into individual cycles as well as individual components
using the spectral analysis of heart. Then, the features are extracted
from the individual components using spectrogram and are used as
an input to a multiple layer perceptron NN that is trained to detect
the presence of heart murmurs. Once the murmur is detected they
are classified into seven classes depending on their timing within
the cardiac cycle using smoothed pseudo Wigner–Ville distribution. Obviously, the major disadvantage of both above systems is
that the sounds are not exactly separated but the signals are segmented into heart and murmur sounds. These processes completely
ignore the overlap and the correlation between the two sounds.
All three methods were applied to real heart sound signals using
MATLAB and the results were compared in terms of correlation
values as defined above and also in terms of computational cost.
Records from 12 subjects were used (four aortic stenosis murmur,
three mitral regurgitation murmur, two precardial friction murmur, and three pulmonary stenosis murmur). All three methods
were applied to 8 temporal segments, 20 s each, from each subject
and the results averaged both across temporal segments and across
subjects for each abnormality (murmur). The results are depicted
in Fig. 3. It can be seen that, the proposed (ASSA) method here outperforms the other two significantly mainly since the data statistics
are well exploited in this approach. This would not be the same for
An effective constrained SSA method has been developed and
used to separate murmur from the recorded heart sounds. This
method is new and robust since the variables of the SSA are adapted
to the changes in the heart sound and murmur subspaces. In addition, one important advantage of this method compared with other
techniques such as PCA is that, it can cope with nonstationary data
since shifted segments of the data are stacked in the Hankel matrix
before decomposition of the covariance matrix. During the reconstruction process the subspace size is adaptively selected in order to
maximize the information regarding the signal of interest. The outcome is significant due to two major reasons; firstly, the algorithm
operates on single-channel sound signals rather than multichannel
ones. Secondly, the subspace of the desired signal is automatically and adaptively estimated based on some a priori knowledge
about the desired signal. As the result, approximately all types of
murmurs are separated and identified. A comparison between the
proposed algorithm and those of other two popular techniques
clearly shows that the ASSA outperforms the others in terms of
both quality of the results (denoted by less correlation between
the separated components) and also the overall computation cost
or speed. One of the major advantages of the proposed technique
is in perfectly separating the two sounds even over the temporally
overlapped regions. This is clearly denoted by the low values of the
correlation in almost all types of murmurs. The separated signals
can be used by clinicians for diagnosis of other possible heart problems and quantified for retrieving other biostatistics of the heart.
Physiologically, it is interesting to notice that the two components
have completely disjoint subspaces and they can be perfectly separated. This fact can possibly bring more insights in modeling the
cardiovascular system, as desired by many researchers around the
globe, and recognition of heart function.
Conflicts of interest
There are no possible conflicts of interest, sources of financial support, corporate involvement, patent holdings, etc. for each
author.
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