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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>L1 and L2 Regularized Deep Residual Network Model for Automated Detection of Myocardial Infarction (Heart Attack) Using Electrocardiogram Signals</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Arijit Ukil</string-name>
          <email>arijit.ukil@tcs.com</email>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Leandro Marin</string-name>
          <email>leandro@um.es</email>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Antonio J. Jara</string-name>
          <email>jara@hopu.org</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>HOP Ubiquitous (HOPU)</institution>
          ,
          <country country="ES">Spain</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>TCS Research and Innovation, Tata Consultancy Services</institution>
          ,
          <addr-line>Kolkata</addr-line>
          ,
          <country country="IN">India</country>
        </aff>
        <aff id="aff2">
          <label>2</label>
          <institution>University of Murcia</institution>
          ,
          <addr-line>Murcia</addr-line>
          ,
          <country country="ES">Spain</country>
        </aff>
      </contrib-group>
      <abstract>
        <p>Automated interpretation of fundamental physiological signals like Electrocardiogram (ECG) plays an important role as part of smart healthcare ecosystem to build reliable and on-demand cardio-vascular diseases (CVD) screening system. Myocardial infarction is a life-threatening condition. Acute myocardial infarction leads to fatal condition commonly known as heart attack. It is medically established that myocardial infarction is often ignored initially, and treatment starts late. In this paper, we present an automated method of myocardial infarction detection from off-the-shelf single lead ECG signals so that early warning can be generated, and timely diagnosis can take place. We propose regularized deep neural network based model that is capable of classifying myocardial infarction condition from normal heart rhythm in single lead ECG signals. More precisely, we propose intensely regularized deep residual networks (ResNet) where both L2 (also known as Tikhonov regularization) and L1 (commonly known as Lasso) regularizations are used to construct a compact residual learning model. We demonstrate through empirical study on publicly available relevant ECG dataset from UCR timeseries archive that the proposed method demonstrates considerably superior performance over baseline methods and current state-of-the-art algorithms. We have also performed ablation study to depict the efficacy of the proposed intense regularization over only L2 or L1 regularizations.</p>
      </abstract>
      <kwd-group>
        <kwd>1 Deep Learning</kwd>
        <kwd>regularization</kwd>
        <kwd>residual networks</kwd>
        <kwd>Electrocardiogram</kwd>
        <kwd>time series</kwd>
        <kwd>sensor</kwd>
        <kwd>classification</kwd>
        <kwd>automation</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>
        Electrocardiogram (ECG) is one of the
fundamental markers for preliminary
investigation of Cardio-Vascular Diseases
(CVDs). Owing to the affordable availability of
personal ECG Sensors like Alivecor [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ], and
wide-scale adoption of Internet of Things (IoT)
infrastructure, remote diagnosis of critical CVD
like myocardial infarction (commonly known
as heart attack) is envisaged in smart clinical
management system. In this paper, we propose
a deep neural network based ECG classification
algorithm, which gets executed in a typical
cloud platform and the inference on the test or
on-field ECG recording is shared to the nearest
medical facility for automated emergency
services. While, the ECG gets recorded by the
individual at the comfort of their home, the
analysis requires engagement of trained
cardiologists, which is likely to hinder the
scalability and larger scale basic diagnosis of
the heart condition. Computerized analysis and
automated interpretation of ECG signal paves
the way to substantially reduce the frequency of
clinician
intervention
and
provides
quick
assessment of the heart condition. The future
smart
infrastructure
facility
is invariably
necessitating
remote
diagnosis
capability.
      </p>
      <p>Future smart cities with IoT based applications
and
eco-system
demand
such
automated
clinical management system that ensures
ondemand diagnosis and quick response to the
critical treatment requirements. In a general
setup, patients interact with their smartphone
applications to get associated in the smart
healthcare systems and derive the benefit of
remote assistance of healthcare facility with
digital therapeutics.
is inferred based on the rule of minimum DTW
distance of the training signals set. In fact,
similarity measure is often considered a good
approach for classification particularly in the
area
distance
of data</p>
      <p>
        mining. DTW-based
measurement
and
1-NN
elastic
based
classification is the conventional choice of
baseline time series classification algorithm [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ].
Lately, machine learning algorithms tailored
for time series signals are evolve [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ]. Collective
of transformation ensembles (COTE) is an
ensemble classifier in the time, autocorrelation,
power spectrum
      </p>
      <p>
        and shapelet domains [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ].
      </p>
      <p>Another important time series classification
algorithm
is</p>
      <p>Bag
of</p>
      <sec id="sec-1-1">
        <title>Symbolic</title>
      </sec>
      <sec id="sec-1-2">
        <title>Fourier</title>
        <p>
          Approximation (SFA) symbols (BOSS) [
          <xref ref-type="bibr" rid="ref5">5</xref>
          ].
BOSS considers a truncated Discrete Fourier
Transform (DFT) in extracting features through
sliding windowed time series. These algorithms
namely, COTE and BOSS are dependent on the
customized feature space development and
specific pattern recognition.
        </p>
        <p>
          Recently Residual Network (ResNet) have
been emerged to solve time series classification
problem. In fact, ResNet based approach seems
to be a promising one [
          <xref ref-type="bibr" rid="ref6">6</xref>
          ]. Similarly, we get
inspired by the promise of the capability of deep
residual network’s representation learning by
residual mapping, we propose a regularized
deep residual neural network with both L2 and
L1 penalties such that a compact learned model
can be constructed. We investigate on publicly
available ECG datasets with normal rhythm and
myocardial infarction labels and comparative
study indicates superior performance of our
proposed method over baseline algorithms and
state-of-the-art methods.
        </p>
      </sec>
    </sec>
    <sec id="sec-2">
      <title>2. Proposed deep residual network architecture</title>
      <p>Myocardial infarction detection from ECG
signal considers number of input ECG signals
as part of the overall training space. We can
represent
each
of
them
as:

=
[ 1,  2,  3, … ,   ] ∈ ℝ
 is an ordered set of
real values</p>
      <p>number of time steps at each of
the training samples. Each of the training
samples is associated with a with class label  ∈
[
,</p>
      <p>], where 
rhythm
and
indicates normal sinus
indicates
myocardial
infarction. Thus, the training dataset consists of
labeled ECG signals as Ω = {  ,   }, for  =
1,2,3, … , 
examples.</p>
      <p>with total</p>
      <p>number of training</p>
      <p>
        Typically, normal sinus rhythm consists of
regular ECG morphology while ECG signal of
myocardial infarction patients have different
morphology [
        <xref ref-type="bibr" rid="ref7">7</xref>
        ] as shown in Figure 2.
propagation and thus, it helps to prevent the
phenomenon of propagation loss of signal
characteristics.
      </p>
      <p>
        In order to extract the distinctive features
from ECG signal to distinguish normal rhythm
and myocardial infarction, we use deep residual
network based representation learning [
        <xref ref-type="bibr" rid="ref8">8</xref>
        ].
      </p>
      <p>
        The immense success of deep residual
networks for computer vision applications
motivates us. In deep residual networks, the
underlying layers fit a residual mapping instead
of directly stacking layers to overcome learning
degradation problem through layer-wise
recursive learning using skip-connection [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ].
Let us consider a deep neural network that
consists of  number of layers, where each of
the layer implements a non-linear
transformation ℋ (∙), where a layer is indexed
by  . In accordance to the ResNet topology as
shown in Figure 3, the residual mapping ℛ of
 th layer is denoted as:
      </p>
      <p>ℛ = ℛ −1 + ℋ (ℛ −1)</p>
      <p>The main intuition of a residual network is
that the skip connection or short-circuit
connection provides direct path of input signal</p>
      <p>We can conceptualize residual networks as
micro-structures of residual blocks connected
sequentially along with skip connection as
shown in Figure 3.</p>
      <p>We construct a pretty deep residual neural
network with total fifteen convolution layers.
There are three residual blocks. First residual
block consists of five convolution layers. There
are eight convolution layers in second residual
block, while third residual block consists of six
convolution layers. Including the three skip
connection layers, total twenty layers are
present in the proposed deep learning model,
with nineteen effective convolution layers.</p>
      <p>
        We have used Batch Normalization (BN)
and Rectified Linear Unit (ReLU) as the
activation layer. After the last convolution
layer, we use Global Average Pooling, which
acts a structural regularizer. In fact, it natively
prevents overfitting for the overall structure
with added advantage of no need for
hyperparameter optimization [
        <xref ref-type="bibr" rid="ref9">9</xref>
        ]. Softmax activation
function is used at the output layer for the
classification purpose along with cross-entropy
as the loss function. We depict the proposed
model in Figure 4.
      </p>
      <p>
        It is understood that ECG signal annotation
is an expensive process and it is likely to have
scarce number of training examples. While the
proposed deep neural network has a
sophisticated capability of representation
learning over the training space, there exists
higher chance of overfitted model generation.
In order to eliminate the risk of overfitting to
the training examples, we regularize the model
using  2 and  1 regularizations [
        <xref ref-type="bibr" rid="ref10">10</xref>
        ]. The
regularized cost function  ∗ with network
parameters  is:
      </p>
      <p>∗( ) =  ( ) +    ( )</p>
      <p>Where,   ( ) is the penalty function and
 is the regularization co-efficient, with  ∈
[0, ∞]. The  2 or Tikhonov regularization is
expressed as:
 ∗2( ) =  ( ) +  2
 Τ
2
Where,   ( ) =  Τ2 .</p>
      <p>Where, the network parameter gradient is:
Similarly, the Lasso or  1 regularization is
defined as:</p>
      <p>∗1( ) =  ( ) +  1‖ ‖1</p>
      <p>Where,  2 and  1 are  2 regularization and
 1 regularization factors respectively.</p>
      <p>∗</p>
      <sec id="sec-2-1">
        <title>Our proposed cost function is:</title>
        <p>Τ
( ) =  ( ) +  2
2
+  1‖ ‖1</p>
        <p>We intend to emphasize that regularization
impacts on network parameters for  2 and
 1 regularizations are different. With or
 1 regularization, we have sparser parameter
matrix while  2 regularization clips the values
of the parameters. Thus, a sparser yet controlled
network parameter space model is constructed.</p>
      </sec>
    </sec>
    <sec id="sec-3">
      <title>3. Experimental</title>
    </sec>
    <sec id="sec-4">
      <title>Results</title>
    </sec>
    <sec id="sec-5">
      <title>Analysis and</title>
      <p>
        We consider relevant dataset ECG200 from
publicly available UCR time series archive
[
        <xref ref-type="bibr" rid="ref11">11</xref>
        ]. The intent is to construct a classification
model that demonstrates better performance
accuracy than state-of-the-art algorithms like
DTW_R1_1NN [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ], BOSS [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ], ResNet [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ],
HIVE-COTE [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ]. From UCR time series
archive, the representative dataset ECG 200 is
considered. ECG200 dataset is binary-labelled
with normal heartbeat and myocardial
infarction classes. There are distinct 100
instances for training and 100 instances for
testing purposes.
      </p>
      <p>
        For this experimentation purpose, we
consider the hyperparameters as described in
Table 1.
[
        <xref ref-type="bibr" rid="ref5">5</xref>
        ] is the benchmark algorithm, and our
proposed method shows 2% test accuracy gain
ver BOSS [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ] and 4% test accuracy gain over
ResNet [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ]. In fact, our method demonstrates
substantial performance gain with similar type
of deep learning model- ResNet [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ].
 ∗( ) =  ∗2( ) or  ∗( ) =  ∗1( ), whereas our
ResNet
has
cost function
      </p>
      <p>as:
i.e.</p>
      <p>when
( ).</p>
      <p>Ablation study to depict the efficacy of the
proposed method, showing that L1 and L2
regularization is more effective than L1 or L2
regularizations.</p>
      <p>Regularization</p>
      <p>L1</p>
      <p>L2</p>
      <p>Our method (L1 and L2)</p>
    </sec>
    <sec id="sec-6">
      <title>4. Plausible</title>
    </sec>
    <sec id="sec-7">
      <title>Architecture</title>
      <p>Test accuracy
0.80
0.86
0.91</p>
    </sec>
    <sec id="sec-8">
      <title>Deployment</title>
      <p>
        We
illustrate
a
plausible
deployment
architecture of remote diagnosis of myocardial
infarction (CVDs in larger scope) in Figure 5.
The
proposed ECG
analysis
algorithm is
supposed to be hosted
over cloud and a
smartphone-based application interacts with the
user to send the captured ECG signal to the
cloud. For ECG signal capturing purpose,
offthe-shelf sensors like Alivecor can be used. The
cloud server responds the inference result to the
user through the same smartphone application
Residual block #3
state-of-the-art algorithms. Currently, BOSS
as well as alerts nearby medical facilities if
abnormal cardiac activity is detected and
myocardial infarction is suspected. Thus, a
complete diagnosis eco-system can be built
using the proposed method, which will have
immense benefit in providing early-warning
alarms to initiate necessary medical attention.
However, it is imperative to mention that
physiological signals like ECG consists of
potential sensitive information and appropriate
trust [
        <xref ref-type="bibr" rid="ref13 ref15">13, 15</xref>
        ], data security [
        <xref ref-type="bibr" rid="ref14 ref17">14, 17</xref>
        ] and data
privacy [
        <xref ref-type="bibr" rid="ref12 ref16 ref17">12, 16, 17</xref>
        ] mechanisms are to be
implemented in order to ensure wide-scale
acceptability in the public domain.
      </p>
    </sec>
    <sec id="sec-9">
      <title>5. Conclusion</title>
      <p>In this paper, our focus is to develop a
classification algorithm to reliably detect
myocardial infarction or heart attack condition
using ECG signal. The performance of the
proposed model is superior than the currently
available relevant methods. We are confident
that ECG analytics as part of a smart healthcare
ecosystem will ensure the necessary impetus
for human-centered purpose in contributing
better quality of life through the development
of technology-driven early detection and
treatment for life-threatening CVDs like
myocardial infarction.</p>
    </sec>
    <sec id="sec-10">
      <title>6. Acknowledgements</title>
      <p>Leandro Marin is partially funded by Project
PID2020-112675RB-C44 funded by
MCIN/AEI/10.13039/501100011033.</p>
      <p>Antonio J. Jara is funded by the European
Union’s Horizon 2020 research and innovation
programme under grant agreement No 732679,
ACTIVAGE project
https://www.activageproject.eu/.</p>
    </sec>
    <sec id="sec-11">
      <title>7. References</title>
    </sec>
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