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

agaona@fi.uba.ar

†

Instituto Argentino de Matem

atica ”Alberto P. Calder

on”, CONICET

Saavedra 15, C1083ACA, Buenos Aires, Argentina

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

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

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

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

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

, 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

Additionally, two other segments of the phonocardiogram

(PCG) can be identiﬁed. The ﬁrst one is the segment S

called isovolumetric contraction and the second one is

the segment. S

-S

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)

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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.

− µ

, 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

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

∈ R

with a given stride τ for

k = 0, 1, . . . , T − 1. These patches z

are the inputs which

the network is fed with. Thus, z

∈ R

is constructed by

computing Equation (2).







i·τ

i·τ +L−1







(2)

Where N = b

T −1−L

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

at a given time t in an

LSTM layer, l, the following equations are computed:

(l)

= σ(W

(l)

+ b

(l)

+ W

(l)

t−1

+ b

(l)

) (3)

(l)

= σ(W

(l)

+ b

(l)

+ W

(l)

t−1

+ b

(l)

) (4)

(l)

= tanh(W

(l)

+ b

(l)

+ W

(l)

t−1

+ b

(l)

) (5)

(l)

= σ(W

(l)

+ b

(l)

+ W

(l)

t−1

+ b

(l)

) (6)

(l)

= f

(l)

 c

(l)

t−1

+ i

(l)

 g

(l)

(7)

(l)

= o

(l)

 tanh(c

(l)

) (8)

Where in Figure 5, h

is the hidden state at time t, c

the cell state at time t, x

is the input at time t, h

t−1

the hidden state of the layer t − 1 or the initial hidden state

at time 0, and i

, f

, g

, o

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)

of a

previous layer can be multiplied by a drop-out δ

(l−1)

co-

efﬁcient where each δ

(l−1)

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

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

updated into the new state c

. Finally, the hidden state h

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

) 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)

T P

T P + F P

(10)

Se =

T P

T P + F N

(11)

= 2

· Se

+ 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

(%)

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

(%)

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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