Deep Recurrent Learning for Heart Sounds
Segmentation based on Instantaneous Frequency
Features
Aprendizaje profundo y recurrente para la segmentaci
´
on de sonidos card
´
ıacos basado en
caracter
´
ısticas de frecuencia instant
´
anea
´
Alvaro Joaqu
´
ın Gaona
∗1
, Pedro David Arini
∗†2
∗
Facultad de Ingenier
´
ıa, Universidad de Buenos Aires,
Instituto de Ingenier
´
ıa Biom
´
edica, (IIBM)
Avenida Paseo Col
´
on 850, C1063ACV, Buenos Aires, Argentina
1
agaona@fi.uba.ar
†
Instituto Argentino de Matem
´
atica ”Alberto P. Calder
´
on”, CONICET
Saavedra 15, C1083ACA, Buenos Aires, Argentina
2
pedro.arini@conicet.gov.ar
Abstract—In this work, a novel stack of well-known
technologies is presented to determine an automatic method
to segment the heart sounds in a phonocardiogram (PCG).
We will show a deep recurrent neural network (DRNN)
capable of segmenting a PCG into their main components
and a very specific way of extracting instantaneous frequency
that will play an important role in the training and testing
of the proposed model. More specifically, it involves an Long
Short-Term Memory (LSTM) neural network accompanied
by the Fourier Synchrosqueezed Transform (FSST) used to
extract instantaneous time-frequency features from a PCG.
The present approach was tested on heart sound signals
longer than 5 seconds and shorter than 35 seconds from
freely-available databases. This approach proved that, with
a relatively small architecture, a small set of data and the
right features, this method achieved an almost state-of-the-art
performance, showing an average sensitivity of 89.5%, an
average positive predictive value of 89.3% and an average
accuracy of 91.3%.
Keywords: phonocardiogram; fourier synchrosqueezed
transform; long short-term memory.
Resumen—En este trabajo se presenta un conjunto de
t
´
ecnicas bien conocidas definiendo un m
´
etodo autom
´
atico para
determinar los sonidos fundamentales en un fonocardiograma
(PCG). Mostraremos una red neuronal recurrente capaz de
segmentar segmentar un fonocardiograma en sus principales
componentes, y una forma muy espec
´
ıfica de extraer
frecuencias instant
´
aneas que jugar
´
an un importante rol en
el entrenamiento y validaci
´
on del modelo propuesto. M
´
as
espec
´
ıficamente, el m
´
etodo propuesto involucra una red
neuronal Long Short-Term Memory (LSTM) acompa
˜
nada
de la Transformada Sincronizada de Fourier (FSST) usada
para extraer atributos en tiempo-frecuencia en un PCG. El
presente enfoque fue evaluado con se
˜
nales de fonocardiogramas
mayores a 5 segundos y menores a 35 segundos de duraci
´
on
extra
´
ıdos de bases de datos p
´
ublicas. Se demostr
´
o, que con
una arquitectura relativamente peque
˜
na, un conjunto de
datos acotado y una buena elecci
´
on de las caracter
´
ısticas,
este m
´
etodo alcanza una eficacia cercana a la del estado del
arte, con una sensitividad promedio de 89.5%, una precisi
´
on
promedio de 89.3% y una exactitud promedio de 91.3%.
Palabras clave: fonocardiograma; transformada sincronizada
de fourier; long short-term memory.
I. INTRODUCTION
Phonocardiography is a method to record the acoustic
phenomena of the heart graphically. It is used to provide
information about the cardiac cycle by plotting sounds and
murmurs of the heart. The sounds result from the closure
of the heart valves, and it is possible to identify at least
two sounds. The first one, S
1
, corresponds to the closure
of the atrioventricular valves (mitral and tricuspid valve) at
the beginning of the systole. At this point, the ventricles
filled with blood from the atriums and muscle contractions
begin to eject the oxygenated and deoxygenated blood to the
pulmonary and systemic circuits respectively. After most of
the blood has been ejected from the ventricles, the aortic and
pulmonary valves close producing the second sound, S
2
.
Additionally, two other segments of the phonocardiogram
(PCG) can be identified. The first one is the segment S
1
-
S
2
called isovolumetric contraction and the second one is
the segment. S
2
-S
1
called isovolumetric relaxation, which
usually is shorter than the first segment. Heart sounds
segmentation dates back to 1997 where H. Liang et al. used
a deterministic algorithm based on the normalized average
Shannon energy of a PCG signal achieving a 93% correct
ratio. This approach has, however, some drawbacks such
as corrupting noise. In the same year, H. Liang et al. [1]
proposed an algorithm based on wavelet decomposition and
reconstruction performing correctly in over 93% of cases.
Heart sounds segmentation boomed in 2010 when Schmidt
et al. [2] proposed a Hidden Markov Model (HMM) based
on time-duration called Dependent-duration Hidden Markov
Model (DHMM). Additionally, it introduced the use of
annotations derived from the EKG to label training sets to
train the proposed model, later used by Springer et al. [3]
to go even further and outperform the previous work by
adding logistic regression and modifying the implementation
of the Viterbi algorithm. In 2018, Renna et al. in [4] have
used Deep learning techniques to segment the PCG. Their
Revista elektron, Vol. 4, No. 2, pp. 52-57 (2020)
ISSN 2525-0159
52
Recibido: 15/08/20; Aceptado: 31/10/20
Creative Commons License - Attribution-NonCommercial-
NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
https://doi.org/10.37537/rev.elektron.4.2.101.2020
Original Article
approach, motivated by a novel convolutional neural network
called U-net [5] for neuronal structures segmentation in
electron microscopic stacks, used Schmidt and Springer
techniques such as labelling and feature extraction (Ho-
momorphic envelogram, Hilbert envelope, Wavelet envelope
and Power Spectral Density envelope) to outperform what
was at that time known as a state-of-the-art technique.
In this work, we propose an implementation based on
a DRNN to segment PCG signals into their main com-
ponents. The proposed method involves a Long Short-
Term Memory (LSTM) neural network accompanied by the
Fourier Synchrosqueezed Transform (FSST) used to extract
instantaneous time-frequency features in a PCG.
II. MATERIAL AND METHODS
Most of the work begins at deciding which approach and
what data is going to be used to achieve the desired goal.
Deep Learning has proved to the world that it is a
compelling strategy to address various kind of problems
and signal segmentation is no exception. Moreover, deep
learning techniques have not been used in PCG as it has
been used in electrocardiogram (EKG) signals lately. Long
Short Term Memory neurons are pretty powerful neural
network units that can achieve great accuracy when trained
on time-series data. This data must be well acquired and
processed before feeding it into the neural network. Both
stages, acquisition and processing, require a right amount
of effort to execute and, most of the times, much more than
training the network.
Lastly, the obtained model and results must be interpreted,
verified and validated by following different techniques such
as Cross-Validation (CV), Receiver Operation Characteristic
(ROC) curve and other performance metrics. A decent
examination of the recently referenced techniques will allow
selecting a model that is well fitted to segment the PCG
effectively.
A. Database
The PCG recordings, extracted from the so called Phys-
ioNet Database [6], was utilized.
The Challenge 2016 carried out by the Computing of
Cardiology (CinC) 2016 provided participants with a rea-
sonably big dataset comprised of PCG and EKG recordings
along with various annotations such as a patient identifier,
abnormality of the signal and so on. Nevertheless, this
challenge asked participants to classify PCG according to the
pathology presented in them. Additionally, the trial provided
a link to Springer’s implementation of Logistic Regression
Hidden Semi-Markov Model (LR-HSMM) for heart sounds
segmentation and with it, 792 PCG recordings from 37
patients with R wave and end of T wave annotations. These
wave annotations have correspondences in time with S1 and
S2 in the PCG respectively, according to [2], and Springer
et al. implemented a labelling algorithm in [3] to automati-
cally generate labels used for training models. Furthermore,
experts identified these recordings as healthy and unhealthy.
The dataset maintains an equilibrium between normal and
abnormal signals which is essential for training models for
them to learn different features or patterns off of the data.
B. Annotations and labeling
In Supervised Learning extracting labels is a crucial step
to go through. It can be performed manually or automat-
ically. The former is commonly done by specialists in the
field, and the later is fundamentally an algorithm responsible
for computing them.
In this work, labels were extracted using a labelling
algorithm provided by Springer [3]. This algorithm leverages
annotations provided in the dataset corresponding to the
EKG waves (R-wave and end of T-wave) and the homo-
morphic envelope [2] which is depicted in Figure 1. Based
on each annotation, a lower and upper bound is defined to
label S1 and S2. Between S2 and the S1 from the following
cardiac cycle lies the diastolic interval and the is assumed
to be the systolic interval.
Fig. 1: Homomorphic envelope (normalized) used for PCG
labeling. In red, a smoother signal, corresponding the enve-
lope, and in black, the PCG.
It is worth mentioning that the previously mentioned
algorithm should only be used offline. The training labels
this algorithm yields, should only be used to train the
neural network. It is not advisable to use this algorithm in
real-time applications due to the dependency of the EKG
signal. If so, performing PCG segmentation online could
be quite troublesome. Moreover, the algorithm has to be
tuned manually to retrieve reliable labels. Thus, the need to
develop a method independent of EKG signals, and a trained
deep neural network is a good way of solving this problem.
Additionally, it can be implemented in real-time embedded
systems with special care to perform an online segmentation,
if that would be goal. An example of a automatically labelled
PCG signal is illustrated in Figure 2
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Fig. 2: Automatically labeled PCG (normalized). Four states
are identified in four different colors, showing the beginning
and ending of each one.
III. APPROACH AND DRNN MODELS
Fig. 3: Heart sounds segmentation approach.
A. Preprocessing
Neural networks cannot ingest data without being ade-
quately transformed. Otherwise, these would not perform at
their best in both training and testing stages. Classification
techniques expect classifying observations into the right
class by observing explanatory variables or features. Most
of the times, these features are not on the same scale. Thus,
standarization is an excellent technique to perform on the
data before feeding it into the network.
Fig. 4: Fourier Synchrosqueezed Transform across a portion
of a PCG. It is possible to see the two main sounds (depicted
in green), and both systole and diastole intervals, associated
with higher and smaller energy levels, respectively.
Z
i
=
X
i
− µ
i
σ
i
, i = 1, . . . , p (1)
Where p is the number of features. Secondly, the fre-
quency content in a PCG signal has been determined to
be between 25 - 400 Hz in Schmidt work. However, we
have identified that most of the frequency energy needed is
contained in the 20 - 200 Hz range, as it is show in Figure
4.
B. Framing
Due to Deep Neural Networks (DNN) having a fixed input
length and the signals not having the same duration, it is
essential to perform a framing process on them.
N-dimensional patches were extracted from an N-
dimensional signal x
k
∈ R
T
with a given stride τ for
k = 0, 1, . . . , T − 1. These patches z
i
are the inputs which
the network is fed with. Thus, z
i
∈ R
L
is constructed by
computing Equation (2).
z
i
=
x
i·τ
.
.
.
x
i·τ +L−1
(2)
Where N = b
T −1−L
τ
c and L is the fixed length of the
patches and i = 0, 1 . . . , N and bxc denotes the greatest
integer lower or equal than x. It is worth considering that
after you select L you cannot frame signals whose length is
lower than the selected length, therefore those signals will
not be taken into account. Therefore, a good choice of L is
equal to the lowest signal length.
Example 1. We want to create patches of length L = 2000
from a signal whose length is T = 35000. After these two
parameters are set up, we just need to define how much
overlapping we want between patches, defined by parameter
τ. This means if we set τ = 1000, 50% of the samples in
each patch will be repeated in the adjacent ones and if it
is set to τ = 2000, patches will not intersect. Suppose we
choose τ = 1000, then N is equal to 32, meaning that the
signal will be framed into 32 patches. It is important to note
that if T − 1 − L is not multiple of τ some samples will be
discarded due to the floor function b·c.
C. Feature extraction
Many features have been used to perform PCG segmen-
tation. Mostly envelopes were used by Schmidt [2] and
Springer [3]. The former used the so-called Homomorphic
Envelope, and the latter added three more envelopes, such as
the Discrete Wavelet (DWT) Envelope, the Power Spectral
Density (PSD) Envelope, and the Hilbert Envelope.
Nevertheless, in this work, we proposed a different
approach to accomplish PCG segmentation. Fourier Syn-
chrosqueezed Transform (FSST) [7] is a technique based
on Short-time Fourier Transform (STFT) that maps STFT
frequencies into instantaneous frequencies of the signal at a
given time t. After computing the FSST on a PCG signal,
just a frequency range is extracted from it. Frequencies in
the range of 20 - 200 Hz were kept.
Example 2. To illustrate how extracted features from the
FSST impact on the choice of the input layer size, consider a
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framed signal by the method in III-B yielding a patch length
of 2000. As Figure 3 suggests, we have to extract the features
from the given patches, but for the sake of this example we
take into account only one patch. The FSST will compute
time-frequency characteristics of the given patch providing a
fixed amount of instantaneous frequencies. For instance, we
will get a feature matrix F ∈ C
q×p
, where q is number of
computed frequencies and p the number of timestamps (the
later matches the length of the patch). However, we might be
interested in a range of frequencies, and by selecting those,
we get a smaller fixed number of frequencies that we can
feed the input layer with, and so the architecture of the input
layer should be properly configured.
D. Neural Network
The proposed approach in this work is DRNNs specialized
in time-series data. Knowledge about past and future times
is a great feature to have for neural networks and Long
Short-Term Memory (LSTM) excel in this subject. One
shortcoming in RNNs is the vanishing gradient problem.
Networks that are deep and have a large number of units
tend to vanish the gradient when Backpropagation Through
Time (BPTT) algorithm is computed. So LSTM has proved
to be a robust solution to the vanishing gradient problem
and, at the same time, keeping the well-known benefits of
RNNs.
1) Long Short-Term Memory (LSTM) Block: The LSTM
network is a type of RNNs. It consists of several memory
blocks. Figure 5 reflects the operations taking place within
each one of them at a specific layer.
Fig. 5: Fundamental block in LSTM networks
For a given block and features x
t
at a given time t in an
LSTM layer, l, the following equations are computed:
i
(l)
t
= σ(W
(l)
ii
x
(l)
t
+ b
(l)
ii
+ W
(l)
hi
h
(l)
t−1
+ b
(l)
hi
) (3)
f
(l)
t
= σ(W
(l)
if
x
(l)
t
+ b
(l)
if
+ W
(l)
hf
h
(l)
t−1
+ b
(l)
hf
) (4)
g
(l)
t
= tanh(W
(l)
ig
x
(l)
t
+ b
(l)
ig
+ W
(l)
hg
h
(l)
t−1
+ b
(l)
hg
) (5)
o
(l)
t
= σ(W
(l)
io
x
(l)
t
+ b
(l)
io
+ W
(l)
ho
h
(l)
t−1
+ b
(l)
ho
) (6)
c
(l)
t
= f
(l)
t
c
(l)
t−1
+ i
(l)
t
g
(l)
t
(7)
h
(l)
t
= o
(l)
t
tanh(c
(l)
t
) (8)
Where in Figure 5, h
t
is the hidden state at time t, c
t
is
the cell state at time t, x
t
is the input at time t, h
t−1
is
the hidden state of the layer t − 1 or the initial hidden state
at time 0, and i
t
, f
t
, g
t
, o
t
are the input, forget, cell and
output gates, respectively. σ is the sigmoid function, and
is the Hadamard product.
In a multi-layer scheme the hidden state h
(l−1)
t
of a
previous layer can be multiplied by a drop-out δ
(l−1)
t
co-
efficient where each δ
(l−1)
t
is a random Bernoulli variable
with probability p.
LSTM cells decide whether to keep information from a
previous time t − 1 using the forget gate by taking into
account x
t
and h
t−1
. Then using the input gate and the cell
gate can choose what information is a candidate to be stored
in the cell. Once the information has been chosen c
t−1
is
updated into the new state c
t
. Finally, the hidden state h
t
is computed in Equation (8).
2) Bidirectional Long Short-Term Memory (BiLSTM):
BiLSTM networks are an extension to LSTM, in which
training is performed in both time directions simultaneously
possible by using two embedded RNN layers. One back-
ward and another one forward depicted in Figure 6. Both
backward and forward hidden-states are then fed into the
next layer. In some instances, it can be another BiLSTM
layer. It is worth mentioning that each block comprises the
computations described in Section III-D1.
Fig. 6: BiLSTM network
Bidirectional Recurrent Neural Networks (BRNN) can
also be built upon different RNN schemes such as Bidi-
rectional Gated Recurrent Units (BGRU).
3) Architecture: The LSTM architecture in Figure 7 is
comprised of three hidden layers besides the input and
output layer. The input layer has a dimensionality of 44
correspondings to the features of interest. It is connected to
a first 200-unit BiLSTM hidden layer activated by a ReLU
function which is also connected to a second hidden layer
with the same characteristics. Its output is then fed into a
fully-connected or dense layer to compute the corresponding
scores. Finally, a softmax layer is liable for computing the
likelihood of belonging to a particular class. This architec-
ture could seem straightforward and paltry, but it does the
job classifying with a more than worthy performance.
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Fig. 7: Proposed DRNN.
4) Drop-out Regularization: Deep neural networks usu-
ally tend to be very deep. Convolutional Neural Networks
(CNN) is one good example. Networks having a large
number of hidden layers yields to have a large number
of parameters to optimize. Nevertheless, the more layers a
DNN has, the more likely it is to overfit. Suggesting that
it will learn every detail off of the data trained with and it
will lose generality.
Drop-out is a technique for addressing this problem. The
central idea is to randomly drop units from the network
during training and preventing neurons from co-adapting too
much. In broad, drop-out is implemented by deactivating
neurons in each iteration with a probability p. During the
whole training process, all neurons will have been deacti-
vated the same amount of times.
This technique significantly reduces overfitting and gives
significant improvements over other regularization methods.
E. Model training & testing
Training was performed using cross-validation techniques,
namely K-Fold Cross Validation. Training. Validation and
test folds were deliberately chosen to begin training the
neural network. With K being the number of folds which
was picked to be 10. Along these lines, every observation
was used to train and test the model. Say that the picked
model is the one performing at its best on the testing dataset.
Most of the time contributed in training is used to choose
the appropriate hyperparameters of the model. Generally,
this is done by trial and error. The chosen hyperparameters
that best performed are shown in Table I.
A gradient threshold is defined to avoid any issues with
gradient explosions. Therefore, if the gradient in absolute
value is greater than the threshold, it will be clipped. Another
technique to avoid overfitting is using a validation set to
control how close the validation loss is to the training loss
called Early Stopping. The stopping is set by defining a
validation patience which outlines how many times the
validation loss can be higher than the minimum validation
loss computed at a given iteration. If this criterion is met,
then the training progress stops.
The optimizer is another option to set up. Adaptive
Moment Estimation (ADAM) is a stochastic gradient-based
optimization method to find the weights in a neural network.
It requires that a learning rate is set and it can also be
adaptive. It implies that every a fixed amount of epochs the
learning rate decreases by some factor.
The hyperparameters in Table I were chosen with certain
criterion. For instance, the mini-batch size, initial learning
rate, the learn rate drop period and gradient threshold are
the most common values in the literature, which were found
to have the best results based on the architecture and data
selected. Ultimately, the number of epochs generally are
defined between 10-30, although via trial and error, after
6 epochs we noticed the performance of did not improve
whatsoever if the network was trained for longer epochs, and
in some cases, the network was prone to overfit. Thereby, 6
epochs seems a reasonable value to reduce the training time
and the possibility of overfitting. Addtionally, a validation
patience was added, and in this case chosen to be 6 because
we have seen that the accuracy did not improve after 6
failures.
TABLE I: CHOSEN HYPERPARAMETERS
Hyperparameter Value
Optimizer ADAM
Epochs 6
Mini-Batch Size 50
Initial Learning Rate 0.01
Learn Rate Drop Period 3
Gradient Threshold 1
Validation Patience 6
IV. RESULTS
Performance of a model is a crucial step to select the
appropriate model. Most common metrics reported are pre-
cision (P
+
), sensitivity (Se), F1-score (F
1
) and accuracy
(ACC) computed based on true positives (TP), true negatives
(TN), false positives (FP) and false negatives (FN).
ACC =
T P + T N
T P + T N + F P + F N
(9)
P
+
=
T P
T P + F P
(10)
Se =
T P
T P + F N
(11)
F
1
= 2
P
+
· Se
P
+
+ Se
(12)
Fig. 8: Receiver Operating Characteristic curves. Curves
corresponding to each class (S1, sys, S2, dias).
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Another necessary result to report is the so-called ROC
curve, computed off the scores from the last hidden layer and
test labels. In Figure 8, a ROC curve is depicted for a given
fold, which is constructed by plotting True Positive Rate
(TPR) and False Positive Rate (FPR). TPR is also known as
sensitivity defined in Equation (11) and FPR is also known
as fall-out formulated in Equation (13).
F P R =
F P
F P + T N
(13)
Once the ten models have been trained, one has to be
selected. Area Under the Curve (AUC) is computed for
each model in Table II, and the highest is picked. Since
there are four classes, the average is computed and used for
comparison.
TABLE II: AUC SCORES
K-Fold AUC (%)
1 99.1
2 98.5
3 98.5
4 97.2
5 98.9
6 98.1
7 98.5
8 98.9
9 98.9
10 98.9
Lastly, Equations (9) to (12) are averaged across all
trained models to report the final results in Table III.
TABLE III: FINAL RESULTS UPON CROSS-VALIDATION.
State P
+
(%) Se (%) F
1
(%)
S1 85.7 86.5 86.0
Sys 90.0 90.0 90.0
S2 87.1 86.7 86.9
Dias 94.9 94.6 94.8
Average 89.3 89.5 89.4
ACC (%) 91.34
TABLE IV: STATE-OF-THE-ART ALGORITHMS COMPARI-
SON.
Algorithm ACC (%) P
+
(%) Se (%) F
1
(%)
BiLSTM 91.34 89.3 89.5 89.4
LR-HSSM [3] 92.52 95.92 95.34 95.63
CNN+HMM [4] 93.7 95.7 95.7 95.7
V. CONCLUSION
In this work, a novel heart sounds segmentation model
has been presented. An LSTM model is accompanied by a
time-frequency feature extraction procedure carried out by
the Fourier Synchrosqueezed Transform (FSST). It is shown
that choosing the right method to extract features and the
right neural network architecture yields, in comparison to
other proposals, an almost state-of-the-art performance as
shown in Table IV. For instance, the modified U-Net neural
network used by Renna et al. [4] with more than 20 layers.
Data augmentation and data addition can also be increased
to make the network deeper and to train it for a more sig-
nificant number of epochs. This means that using an LSTM
network can achieve higher performances by developing a
more complex architecture since these cells are specialized
in time-series data.
A possible future extension from this approach is to
implement a post-processing stage in order to imply correct
transitions between states, which is the main limitation of
this approach. Thus, improving the performance.
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