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<front>
<journal-meta>
<journal-id journal-id-type="pmc">CMC</journal-id>
<journal-id journal-id-type="nlm-ta">CMC</journal-id>
<journal-id journal-id-type="publisher-id">CMC</journal-id>
<journal-title-group>
<journal-title>Computers, Materials &#x0026; Continua</journal-title>
</journal-title-group>
<issn pub-type="epub">1546-2226</issn>
<issn pub-type="ppub">1546-2218</issn>
<publisher>
<publisher-name>Tech Science Press</publisher-name>
<publisher-loc>USA</publisher-loc>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">21582</article-id>
<article-id pub-id-type="doi">10.32604/cmc.2022.021582</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Article</subject>
</subj-group>
</article-categories>
<title-group>
<article-title>Prediction of Cardiovascular Disease Using Machine Learning Technique&#x2014;A Modern Approach</article-title>
<alt-title alt-title-type="left-running-head">Prediction of Cardiovascular Disease Using Machine Learning Technique&#x2014;A Modern Approach</alt-title>
<alt-title alt-title-type="right-running-head">Prediction of Cardiovascular Disease Using Machine Learning Technique&#x2014;A Modern Approach</alt-title>
</title-group>
<contrib-group content-type="authors">
<contrib id="author-1" contrib-type="author"><name name-style="western"><surname>Ambeth Kumar</surname><given-names>Visvasam Devadoss</given-names></name><xref ref-type="aff" rid="aff-1">1</xref>
</contrib>
<contrib id="author-2" contrib-type="author"><name name-style="western"><surname>Swarup</surname><given-names>Chetan</given-names></name><xref ref-type="aff" rid="aff-2">2</xref>
</contrib>
<contrib id="author-3" contrib-type="author"><name name-style="western"><surname>Murugan</surname><given-names>Indhumathi</given-names></name><xref ref-type="aff" rid="aff-1">1</xref>
</contrib>
<contrib id="author-4" contrib-type="author"><name name-style="western"><surname>Kumar</surname><given-names>Abhishek</given-names></name><xref ref-type="aff" rid="aff-2">3</xref>
</contrib>
<contrib id="author-5" contrib-type="author"><name name-style="western"><surname>Singh</surname><given-names>Kamred Udham</given-names></name><xref ref-type="aff" rid="aff-4">4</xref>
</contrib>
<contrib id="author-6" contrib-type="author"><name name-style="western"><surname>Singh</surname><given-names>Teekam</given-names></name><xref ref-type="aff" rid="aff-5">5</xref>
</contrib>
<contrib id="author-7" contrib-type="author" corresp="yes"><name name-style="western"><surname>Dubey</surname><given-names>Ramu</given-names></name><xref ref-type="aff" rid="aff-6">6</xref><email>rdubeyjiya@gmail.com</email>
</contrib>
<aff id="aff-1"><label>1</label><institution>Department of Computer Science &#x0026; Engineering, Panimalar Engineering College, Anna University</institution>, <addr-line>Chennai, 600123</addr-line>, <country>India</country></aff>
<aff id="aff-2"><label>2</label><institution>Department of Basic Science, College of Science &#x0026; Theoretical Studies, Saudi Electronic University</institution>, <addr-line>Riyadh-Male Campus 13316</addr-line>, <country>Saudi Arabia</country></aff>
<aff id="aff-3"><label>3</label><institution>Department of Computer Science &#x0026; IT, JAIN (Deemed to be University)</institution>, <addr-line>Bangalore, 560069</addr-line>, <country>India</country></aff>
<aff id="aff-4"><label>4</label><institution>Department of Computer Science and Information Engineering, National Cheng Kung University</institution>, <addr-line>Tainan 701</addr-line>, <country>Taiwan</country></aff>
<aff id="aff-5"><label>5</label><institution>Department of Mathematics, Graphic Era Hill University</institution>, <addr-line>Dehradun, 248002</addr-line>, <country>India</country></aff>
<aff id="aff-6"><label>6</label><institution>Department of Mathematics, J. C. Bose University of Science &#x0026; Technology, YMCA</institution>, <addr-line>Faridabad, 121006</addr-line>, <country>India</country></aff>
</contrib-group>
<author-notes>
<corresp id="cor1"><label>&#x002A;</label>Corresponding Author: Ramu Dubey. Email: <email>rdubeyjiya@gmail.com</email></corresp>
</author-notes>
<pub-date pub-type="epub" date-type="pub" iso-8601-date="2021-10-18"><day>18</day>
<month>10</month>
<year>2021</year></pub-date>
<volume>71</volume>
<issue>1</issue>
<fpage>855</fpage>
<lpage>869</lpage>
<history>
<date date-type="received"><day>07</day><month>7</month><year>2021</year></date>
<date date-type="accepted"><day>23</day><month>8</month><year>2021</year></date>
</history>
<permissions>
<copyright-statement>&#x00A9; 2022 Ambeth Kumar et al.</copyright-statement>
<copyright-year>2022</copyright-year>
<copyright-holder>Ambeth Kumar et al.</copyright-holder>
<license xlink:href="https://creativecommons.org/licenses/by/4.0/">
<license-p>This work is licensed under a <ext-link ext-link-type="uri" xlink:type="simple" xlink:href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution 4.0 International License</ext-link>, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.</license-p>
</license>
</permissions>
<self-uri content-type="pdf" xlink:href="TSP_CMC_21582.pdf"></self-uri>
<abstract>
<p>Cardio Vascular disease (CVD), involving the heart and blood vessels is one of the most leading causes of death throughout the world. There are several risk factors for causing heart diseases like sedentary lifestyle, unhealthy diet, obesity, diabetes, hypertension, smoking and consumption of alcohol, stress, hereditary factory etc. Predicting cardiovascular disease and improving and treating the risk factors at an early stage are of paramount importance to save the precious life of a human being. At present, the highly stressful life with bad lifestyle activities causes heart disease at a very young age. The main aim of this research is to predict the premature heart disease based on machine learning algorithms. This paper deals with a novel approach using the machine learning algorithm for predicting the cardiovascular disease at the premature stage itself. Support Vector Machine (SVM) is used for segregating the CVD patients based on their symptoms and medical observation. The experimentation results by using the proposed method will facilitate the medical practitioners to provide suitable treatment for the patients on time. A sophisticated model has been developed with the current approach to examine the various stages of CVD and the performance metrics used have given effective and fruitful results as compared to other machine learning techniques.</p>
</abstract>
<kwd-group kwd-group-type="author">
<kwd>Machine learning</kwd>
<kwd>support vector machine</kwd>
<kwd>classification</kwd>
<kwd> cardiovascular disease</kwd>
</kwd-group>
</article-meta>
</front>
<body>
<sec id="s1"><label>1</label><title>Introduction</title>
<p>Based on the estimated facts, World Health Organization (WHO) had claimed that about 17.9 million men and women died from Cardio Vascular Disease (CVD) in year 2016, which is nearly 31&#x0025; of the deaths worldwide [<xref ref-type="bibr" rid="ref-1">1</xref>]. Globally, CVD is the major cause of death in men and women who die annually from CVD [<xref ref-type="bibr" rid="ref-2">2</xref>]. It is also reported that one third of the deaths for people aged below 70 years occur by stroke and heart attacks [<xref ref-type="bibr" rid="ref-3">3</xref>]. Though there are leaping advances in medical field, it is still challenging to predict the heart disease in an earlier stage. Antenatal practices help in identifying the risk factors and modern technology is used to overcome the risk [<xref ref-type="bibr" rid="ref-4">4</xref>]. Still, the morbidity rate is very high due to the unpredicted and unexpected reasons. Currently, there are no proven and concrete interventions that reduce the risk of cardiovascular disease [<xref ref-type="bibr" rid="ref-5">5</xref>,<xref ref-type="bibr" rid="ref-6">6</xref>].</p>
<p>In cardiovascular disease, the data provided to the medical field is vast, multi-dimensional and critical, which makes it challenging and cumbersome to understand such extensive data. It is quite difficult to predict whether the patient has heart disease symptoms or not based on the patient&#x0027;s records [<xref ref-type="bibr" rid="ref-7">7</xref>,<xref ref-type="bibr" rid="ref-8">8</xref>]. Some of the typical symptoms for patients having CVD are chest pain, shortness of breath, radiating pain in the arms, left shoulders and elbows, discomfort while walking, high blood pressure, dizziness, nausea, fatigue, etc. while the risk factors causing CVD are cholesterol, hypertension, genetic or heredity, obesity, diabetes, dietary habits, aging, [<xref ref-type="bibr" rid="ref-9">9</xref>&#x2013;<xref ref-type="bibr" rid="ref-11">11</xref>], etc. Life Style modifications with regular cardio friendly exercises followed by a heart-healthy diet, quitting smoking and alcohol intake, usage of tobacco, salt, sugar and fat intake can prevent CVD. Based on the analysis of worldwide data on CVD patients, it is noted that CVD affects even young men and women and therefore, requires prediction and prevention at the incipient stage itself.</p>
<p>The key objective of this research is to predict cardiovascular disease at an earlier stage. To envisage the detection of CVD at the incipient stage and intervene appropriately, Support Vector Machine (SVM) is used for classifying the patients depending on their symptoms and risk factors. By using these machine learning algorithms, it becomes easy to understand the nature and type of heart disease in all aspects.</p>
<p>The important aspect of this method is to train the machine to analyze a massive set of data with the known inputs and outputs, i.e., Supervised machine learning is applied [<xref ref-type="bibr" rid="ref-12">12</xref>]. The main objective of the work is to improve the accuracy of prediction of cardiovascular disease [<xref ref-type="bibr" rid="ref-13">13</xref>,<xref ref-type="bibr" rid="ref-14">14</xref>], which can help for preventive treatments and reduce the cases having CVD.</p>
<p>The rest of the paper deals with various sections viz.., the related works are discussed in Section 2, while in Section 3, the various stages of CVD are elaborated and the techniques involved for the prediction of cardiovascular disease are explained thoroughly. Section 4 highlights the Experimental results, Comparison of results using multiple techniques, Summarization of the methods and percentage of CVD based on the collected datasets. Finally, in Section 5, the conclusion of research and the thrust for more related research work is highlighted.</p>
</sec>
<sec id="s2"><label>2</label><title>Related Works</title>
<p>The clinical study was designed as a controlled clinical study, open-label [<xref ref-type="bibr" rid="ref-15">15</xref>]. To estimate the event-free rate, Kaplan-Meier has been used [<xref ref-type="bibr" rid="ref-16">16</xref>,<xref ref-type="bibr" rid="ref-17">17</xref>]. The logistic regression (LR) model reveals that a Coronary Artery Calcium (CAC) score of &#x003E;&#x003D;100 rather than a Cardio Ankle Vascular Index (CAVI) of &#x003E;&#x003D;9 had a higher predictive value for all cardiovascular events [<xref ref-type="bibr" rid="ref-18">18</xref>]. The absolute risk was calculated using charts and adjusted according to these notes. More than 20&#x0025; chances of developing a cardiovascular event due to the prevalence of WHO/ISH of high CVD risk [<xref ref-type="bibr" rid="ref-19">19</xref>]. From the Receiver Operating Characteristic (ROC), a cross-sectional study was conducted. The risk of carotid arteriosclerosis was positively associated with CAVI [<xref ref-type="bibr" rid="ref-20">20</xref>].</p>
<p>The study includes neural networks, support vector machine, Decision Tree models, ID3 algorithm, and association rules [<xref ref-type="bibr" rid="ref-21">21</xref>]. To analyze the application of data mining algorithms, a study has been done [<xref ref-type="bibr" rid="ref-22">22</xref>]. Principal Component Analysis (PCA) is a method in which the large data set is reduced by PCA, wherein the original data is transformed into new dimensions. The bivariate model was used to find the relationship between two variables. In the future, the research can be extended by using different techniques like an outlier and link analysis used to associate rule mining on a large number of patients. Usage of various techniques and association of rule mining has been referred for many patients [<xref ref-type="bibr" rid="ref-23">23</xref>,<xref ref-type="bibr" rid="ref-24">24</xref>]. The methods used here are classification methods such as DT and SVM. The results present a better accuracy of 99.42&#x0025; by using the decision tree, whereas the support vector machine gives an accuracy of 89&#x0025; [<xref ref-type="bibr" rid="ref-25">25</xref>].</p>
<p>The KNN algorithm is based on the similarity measure and the distance has been evaluated [<xref ref-type="bibr" rid="ref-26">26</xref>]. To develop predictive models, machine learning techniques like SVM, DT and ANN are used. The main aim is to compare the three algorithms using the performance measure algorithms like sensitivity, accuracy, and specificity [<xref ref-type="bibr" rid="ref-27">27</xref>]. Nephritis of renal pelvis origin is a disease that affects the urinary system [<xref ref-type="bibr" rid="ref-28">28</xref>]. The machine learning algorithms used here are SVM, Naive Bayes, Logistic regression, J48, and one R. The highest accuracy is still unable to exceed the accuracy of 80&#x0025; with the best performing algorithm [<xref ref-type="bibr" rid="ref-29">29</xref>]. The techniques used here are machine learning, such as logistic regression and classification trees [<xref ref-type="bibr" rid="ref-30">30</xref>].</p>
<p>Using ANN, the multi-layer feed-forward neural network with Levenberg-Marquardt learning algorithm was used on CVD and diabetes mellitus patients [<xref ref-type="bibr" rid="ref-31">31</xref>,<xref ref-type="bibr" rid="ref-32">32</xref>]. The proposed system&#x0027;s primary method was a neural network ensemble method.89.01&#x0025; of classification accuracy has been taken from the Cleveland Heart Disease database [<xref ref-type="bibr" rid="ref-33">33</xref>]. Iris image was cropped from the region of interest, and the discrete wavelength transformation feature, statistical, texture is extracted from the area of interest [<xref ref-type="bibr" rid="ref-34">34</xref>].</p>
<p>In the proposed system, the main aim is to investigate the CAD system for breast cancer. The database used here was the Springer link (SL), inclusion and exclusion criteria [<xref ref-type="bibr" rid="ref-35">35</xref>]. Data mining methods, like feature extraction and selection, have been used. K means and SVM has been used for diagnosing tumors and extracting useful information [<xref ref-type="bibr" rid="ref-36">36</xref>]. Based on the classification technique, machine learning had been approached. For solving the classification of problems, the Genetically Optimized Neural Network (GONN) algorithm had been used [<xref ref-type="bibr" rid="ref-37">37</xref>]. In the proposed system, by using the data, the prediction of chronic disease has been done by using machine learning algorithms. MLT like KNN, SVM, decision tree and logistic regression has been used [<xref ref-type="bibr" rid="ref-38">38</xref>]. In the proposed research, the pre-processing techniques like removal of missing data, deletion of noisy data, if applicable, will fill the default values. The performance has been measured using methods like classification, sensitivity, accuracy and specificity analysis [<xref ref-type="bibr" rid="ref-39">39</xref>&#x2013;<xref ref-type="bibr" rid="ref-41">41</xref>]. Advanced data mining techniques has been used to discover the relationship and hidden pattern. The dataset used here was the Iranian Center for Breast Cancer (ICBC) [<xref ref-type="bibr" rid="ref-42">42</xref>&#x2013;<xref ref-type="bibr" rid="ref-44">44</xref>].</p>
</sec>
<sec id="s3"><label>3</label><title>Proposed Work</title>
<p>In the past several years, Cardio vascular disease (CVD) is one of the main contributing factors that cause innumerable fatalities worldwide. The medical condition that affects the heart and blood vessels is called CVD. Risk assessment and risk predictions have become essential in preventing CVD. Even though risk prediction tools are recommended, they are not adequately implemented in clinical practice. If the CVD patient is not properly assessed and intervened on time, there is every chance of resulting in fatality. To reduce the mortality rate and improve the heart health conditions, a new method is proposed. This proposed method analyzes the parameters (hypertension, diabetes, obesity, blood pressure, heredity), and also the typical and atypical symptoms associated with the heart patients. To identify and classify the stages of CVD affected patients, new classification methods are designed. The proposed classification methods have high accuracy in predicting CVD patients. It also has a fast-training process and therefore easy to indicate whether the patients are affected by CVD or not.</p>
<p>The various stages of CVD are shown in <?A3B2 "fig1",5,"anchor"?><xref ref-type="fig" rid="fig-1">Fig. 1</xref> constituting various stages as</p>
<fig id="fig-1"><label>Figure 1</label><caption><title>Stages of CVD</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_21582-fig-1.png"/></fig>
<sec id="s3_1"><label>3.1</label><title>STAGE A: No Heart Disease and No Symptoms (High Risk)</title>
<p>Stage A is considered to be at high risk for heart failure but without structural heart disease or heart failure symptoms. The patient with symptoms of hypertension, cholesterol, diabetes, obesity, and blood pressure should have a standing goal therapy to self-care, carry out regular exercise and control metabolic syndrome and avoid alcohol intake. Drugs used for Stage A are ACEI or ARB in appropriate patients for vascular disease.</p>
</sec>
<sec id="s3_2"><label>3.2</label><title>Stage B: Structural Heart Disease Without Symptoms</title>
<p>Stage B is considered to be a structural disease without symptoms, and there is also a risk of heart failure. The symptoms of Stage B are patients having chest pain and left and right-side heart failure. The goal therapy for Stage B is same as that of Stage A. The drugs used for Stage B is ACEI or ARB as well as beta-blockers for in appropriate patients.</p>
</sec>
<sec id="s3_3"><label>3.3</label><title>Stage C: Structural Heart Disease with Symptoms</title>
<p>Stage C includes the problem of forming a structural heart disease with typical symptoms. There will be difficulty in breathing while doing exercises. Diuretics for fluid retention, ACEI and beta-blockers are the drugs used for daily routine.</p>
</sec>
<sec id="s3_4"><label>3.4</label><title>Stage D: Refractory HF</title>
<p>Stage D is a refractory heart failure requiring specialized interventions for those patients having marked symptoms at rest despite maximal therapy. The goal therapy is the appropriate measures given for Stages A, B, C.</p>
</sec>
<sec id="s3_5"><label>3.5</label><title>Predicting CVD Using SVM</title>
<p>SVM is a supervised machine learning algorithm, which is mainly used to classify the symptoms and common risk factors. Linearly separable data is used for data classification. The kernel function is used for nonlinear data. By using a &#x201C;hyperplane,&#x201D; the variation between two data can be detected. To separate the given data into two classes, the hyperplane should have the largest margin in a large-dimensional space. The margin between the two categories is represented in the longest distance between the classes closest to data points, as shown in <?A3B2 "fig2",5,"anchor"?><xref ref-type="fig" rid="fig-2">Fig. 2</xref>.</p>
<fig id="fig-2"><label>Figure 2</label><caption><title>Predicting CVD using SVM</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_21582-fig-2.png"/>
</fig>
<p>Various types of heart disease are shown in <?A3B2 "tbl1",5,"anchor"?><xref ref-type="table" rid="table-1">Tab. 1</xref>.</p>
<table-wrap id="table-1"><label>Table 1</label><caption><title>Types of cardio vascular disease (CVD)</title></caption>
<table frame="hsides">
<colgroup>
<col align="left" charoff="6"/>
<col align="left" charoff="7"/>
<col align="left" charoff="8"/>
<col align="left" charoff="8"/>
<col align="left" charoff="8"/>
</colgroup>
<thead>
<tr>
<th align="left">Cardiovascular disease</th>
<th align="left">Description</th>
<th align="left">Risk factor</th>
<th align="left">Symptoms</th>
<th align="left">Treatment</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left">Coronary heart disease</td>
<td align="left">It includes diseased vessels, structural problem, and blood clots</td>
<td align="left">Cholesterol, HBP,<break/>genetic, smoking,<break/>diabetes and Obesity</td>
<td align="left">Chest pain,<break/>Nausea, sweating,<break/>Shortness of breath</td>
<td align="left">Self-care, medications, medical procedure, and surgery</td>
</tr>
<tr>
<td align="left">High blood pressure (HBP)</td>
<td align="left">The force of blood against the artery wall is too high.</td>
<td align="left">Diabetes, hypertension, unhealthy diet, Obesity, genetic and family history</td>
<td align="left">HBP</td>
<td align="left">Self-care, medications</td>
</tr>
<tr>
<td align="left">Cardiac Arrest</td>
<td align="left">There is a sudden, unexpected loss of heart function, consciousness, and breathing</td>
<td align="left">Smoking, HBP,<break/>High Blood Cholesterol, Obesity, diabetes</td>
<td align="left">Chest pain, lightheadedness, shortness of breath</td>
<td align="left">Self-care, medications, medical procedure</td>
</tr>
<tr>
<td align="left">Heart failure (HF)</td>
<td align="left">The heart does not pump blood</td>
<td align="left">High blood pressure<break/>(HBP)</td>
<td align="left">Chest pain, dry cough, the inability to exercise, fast breathing, shortness of breathing, weight gain, swollen legs and feet</td>
<td align="left">Treatment depends on the severity, self-care, medications, medical procedure, surgery</td>
</tr>
<tr>
<td align="left">Arrhythmia</td>
<td align="left">Improving the beating of the heart, whether irregular, too fast, or too slow</td>
<td align="left">-</td>
<td align="left">Chest pain, lightheadedness, slow heart rate, shortness of breath</td>
<td align="left">Medication, medical procedures, devices, and supportive care.</td>
</tr>
<tr>
<td align="left">Peripheral artery disease</td>
<td align="left">Narrowed blood vessels reduce</td>
<td align="left">HBP, High blood cholesterol, obesity, diabetes mellitus</td>
<td align="left">Symptoms in leg pain, mainly when walking</td>
<td align="left">Self-care, medications and, medical procedure</td>
</tr>
<tr>
<td align="left">Stroke</td>
<td align="left">Damage in the brain from interference of its blood supply</td>
<td align="left">-</td>
<td align="left">Trouble speaking, walking.</td>
<td align="left">Medications, supportive care, Surgery, Therapies</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>To find the optimal hyperplane, the separation of the symptoms of CVD has been done by using the vectors with one category as a target variable (risk factor) on one side of the plane with another class on the other side of the plane. Support vector is the vector near the hyperplane. In <?A3B2 "fig3",5,"anchor"?><xref ref-type="fig" rid="fig-3">Fig 3</xref>, The SVM performs classification, regression and outline detection. The classification of linear SVM is done by drawing a straight line between the two classes. Consider a symptom or risk factor for the classification with T training data <inline-formula id="ieqn-1"><mml:math id="mml-ieqn-1"><mml:mo fence="false" stretchy="false">{</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>&#x03B1;</mml:mi></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mi>&#x03B2;</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mo fence="false" stretchy="false">}</mml:mo></mml:math></inline-formula>, where &#x03B1; &#x003D; 1&#x2026;r, for every input is considered as symptom x&#x03B1; has one attributes and in others of two classes as y&#x03B2; <inline-formula id="ieqn-2"><mml:math id="mml-ieqn-2"><mml:mo>&#x2208;</mml:mo><mml:mo fence="false" stretchy="false">{</mml:mo><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo fence="false" stretchy="false">}</mml:mo></mml:math></inline-formula>. &#x2212;1 denotes negative hyperplane, &#x002B;&#x2009;1 denotes positive hyperplane.</p>
<fig id="fig-3"><label>Figure 3</label><caption><title>Structure of SVM</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_21582-fig-3.png"/>
</fig>
<p>The symptoms or risk factor (training data) in the form:
<disp-formula id="eqn-1"><label>(1)</label><mml:math id="mml-eqn-1" display="block"><mml:mrow><mml:mrow><mml:mo>{</mml:mo> <mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>&#x03B1;</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mi>&#x03B2;</mml:mi></mml:msub></mml:mrow> <mml:mo>}</mml:mo></mml:mrow><mml:mo>&#x00A0;</mml:mo><mml:mi>w</mml:mi><mml:mi>h</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mtext>&#x00A0;</mml:mtext><mml:mi>&#x03B1;</mml:mi><mml:mtext>&#x00A0;</mml:mtext><mml:mo>=</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:mn>1</mml:mn><mml:mo>&#x2026;</mml:mo><mml:mi>r</mml:mi><mml:mo>,</mml:mo><mml:mtext>&#x2009;</mml:mtext><mml:msub><mml:mi>y</mml:mi><mml:mi>&#x03B1;</mml:mi></mml:msub><mml:mo>&#x2208;</mml:mo><mml:mrow><mml:mo>{</mml:mo> <mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn></mml:mrow> <mml:mo>}</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mi>&#x03B1;</mml:mi></mml:msub><mml:mo>&#x2208;</mml:mo><mml:msup><mml:mi>R</mml:mi><mml:mi>D</mml:mi></mml:msup></mml:mrow></mml:math></disp-formula>
The hyperplane has been described as
<disp-formula id="eqn-2"><label>(2)</label><mml:math id="mml-eqn-2" display="block"><mml:mo fence="false" stretchy="false">&#x27E8;</mml:mo><mml:mrow><mml:mi>w</mml:mi><mml:mo>,</mml:mo><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>&#x03B1;</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mo fence="false" stretchy="false">&#x27E9;</mml:mo><mml:mo>+</mml:mo><mml:mi>h</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:math></disp-formula>
where w is the hyperplane and perpendicular distance from the hyperplane to the origin is <inline-formula id="ieqn-3"><mml:math id="mml-ieqn-3"><mml:mfrac><mml:mi>b</mml:mi><mml:mrow><mml:mrow><mml:mo stretchy="false">|</mml:mo></mml:mrow><mml:mrow><mml:mrow><mml:mo stretchy="false">|</mml:mo></mml:mrow><mml:mi>w</mml:mi><mml:mrow><mml:mo stretchy="false">|</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mo stretchy="false">|</mml:mo></mml:mrow></mml:mrow></mml:mfrac></mml:math></inline-formula>.</p>
<p>Solving the optimization problem is equal to finding the optimal hyperplane
<disp-formula id="eqn-3"><label>(3)</label><mml:math id="mml-eqn-3" display="block"><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac><mml:mrow><mml:msup><mml:mi>w</mml:mi><mml:mi>t</mml:mi></mml:msup></mml:mrow><mml:mi>w</mml:mi><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mi>&#x03B1;</mml:mi></mml:msub></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mo fence="false" stretchy="false">&#x27E8;</mml:mo><mml:mrow><mml:mi>w</mml:mi><mml:mo>.</mml:mo><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>&#x03B1;</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mo fence="false" stretchy="false">&#x27E9;</mml:mo><mml:mo>+</mml:mo><mml:mi>b</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mo>&#x2265;</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>}</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mspace width="1em" /><mml:mi>&#x03B1;</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo>&#x2026;</mml:mo><mml:mi>N</mml:mi></mml:math></disp-formula>
The problem is in the quadratic form. For constraints minimization, longing to allocate Lagrange multipliers &#x03B2; and conclude that in the dual form:
<disp-formula id="eqn-4"><label>(4)</label><mml:math id="mml-eqn-4" display="block"><mml:mrow><mml:mo>{</mml:mo><mml:mtable columnalign="left" rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:mrow><mml:mo>&#x2211;</mml:mo></mml:mrow><mml:mo>&#x2061;</mml:mo><mml:mi mathvariant="normal">&#x005F;</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>&#x03B1;</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:msup><mml:mo stretchy="false">)</mml:mo><mml:mrow><mml:mo>&#x2227;</mml:mo></mml:mrow></mml:msup><mml:mi>N</mml:mi><mml:mi>i</mml:mi><mml:mi mathvariant="normal">&#x005F;</mml:mi><mml:mi>&#x03B1;</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mn>2</mml:mn><mml:mrow><mml:mo>&#x2211;</mml:mo></mml:mrow><mml:mo>&#x2061;</mml:mo><mml:mi mathvariant="normal">&#x005F;</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>&#x03B1;</mml:mi><mml:mo>,</mml:mo><mml:mi>&#x03B2;</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mrow><mml:mspace width="thickmathspace" /></mml:mrow><mml:mi>i</mml:mi><mml:mi mathvariant="normal">&#x005F;</mml:mi><mml:mi>&#x03B1;</mml:mi><mml:mo>,</mml:mo><mml:mi>i</mml:mi><mml:mi mathvariant="normal">&#x005F;</mml:mi><mml:mi>&#x03B2;</mml:mi><mml:mo>&#x00D7;</mml:mo><mml:mi>y</mml:mi><mml:mi mathvariant="normal">&#x005F;</mml:mi><mml:mi>&#x03B1;</mml:mi><mml:mi>y</mml:mi><mml:mi mathvariant="normal">&#x005F;</mml:mi><mml:mi>&#x03B2;</mml:mi><mml:mspace width="thickmathspace" /><mml:mo fence="false" stretchy="false">&#x27E8;</mml:mo><mml:mrow><mml:mi>x</mml:mi><mml:mi mathvariant="normal">&#x005F;</mml:mi><mml:mi>&#x03B1;</mml:mi><mml:mo>,</mml:mo><mml:mi>x</mml:mi><mml:mi mathvariant="normal">&#x005F;</mml:mi><mml:mi>&#x03B2;</mml:mi></mml:mrow><mml:mo fence="false" stretchy="false">&#x27E9;</mml:mo><mml:mspace width="thickmathspace" /><mml:mi>i</mml:mi><mml:mi mathvariant="normal">&#x005F;</mml:mi><mml:mi>&#x03B1;</mml:mi><mml:mo>&#x2265;</mml:mo><mml:mn>0</mml:mn></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mo>&#x2211;</mml:mo></mml:mrow><mml:mo>&#x2061;</mml:mo><mml:mi mathvariant="normal">&#x005F;</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>&#x03B1;</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:msup><mml:mo stretchy="false">)</mml:mo><mml:mrow><mml:mo>&#x2227;</mml:mo></mml:mrow></mml:msup><mml:mi>N</mml:mi><mml:mi>i</mml:mi><mml:mi mathvariant="normal">&#x005F;</mml:mi><mml:mi>&#x03B1;</mml:mi><mml:mi>y</mml:mi><mml:mi mathvariant="normal">&#x005F;</mml:mi><mml:mi>&#x03B1;</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mtd></mml:mtr></mml:mtable><mml:mo>}</mml:mo></mml:mrow></mml:math></disp-formula>
</p>
<p>By evaluating <xref ref-type="disp-formula" rid="eqn-4">Eq. (4)</xref>, Lagrange multipliers &#x03B1; is found out, and the optimal hyperplane is given below:
<disp-formula id="eqn-5"><label>(5)</label><mml:math id="mml-eqn-5" display="block"><mml:mtable columnalign="left" rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:msup><mml:mi>w</mml:mi><mml:mrow><mml:mo>&#x2227;</mml:mo></mml:mrow></mml:msup><mml:mo>&#x2217;</mml:mo><mml:mo>=</mml:mo><mml:mrow><mml:mo>&#x2211;</mml:mo></mml:mrow><mml:mo>&#x2061;</mml:mo><mml:mi mathvariant="normal">&#x005F;</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>&#x03B1;</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:msup><mml:mo stretchy="false">)</mml:mo><mml:mrow><mml:mo>&#x2227;</mml:mo></mml:mrow></mml:msup><mml:mi>N</mml:mi><mml:mi>i</mml:mi><mml:mi mathvariant="normal">&#x005F;</mml:mi><mml:mi>&#x03B1;</mml:mi><mml:mi>y</mml:mi><mml:mi mathvariant="normal">&#x005F;</mml:mi><mml:mi>&#x03B1;</mml:mi><mml:mi>x</mml:mi><mml:mi mathvariant="normal">&#x005F;</mml:mi><mml:mi>&#x03B1;</mml:mi></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:msup><mml:mi>b</mml:mi><mml:mo>&#x2217;</mml:mo></mml:msup></mml:mrow><mml:mo>=</mml:mo><mml:mo>&#x2212;</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac><mml:mo fence="false" stretchy="false">&#x27E8;</mml:mo><mml:mrow><mml:mrow><mml:msup><mml:mi>w</mml:mi><mml:mo>&#x2217;</mml:mo></mml:msup></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>r</mml:mi></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mo fence="false" stretchy="false">&#x27E9;</mml:mo></mml:mstyle></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mi>s</mml:mi><mml:mi>i</mml:mi><mml:mi>g</mml:mi><mml:mi>n</mml:mi><mml:mo fence="false" stretchy="false">&#x27E8;</mml:mo><mml:mrow><mml:mrow><mml:msup><mml:mi>w</mml:mi><mml:mo>&#x2217;</mml:mo></mml:msup></mml:mrow><mml:mo>,</mml:mo><mml:mi>x</mml:mi></mml:mrow><mml:mo fence="false" stretchy="false">&#x27E9;</mml:mo><mml:mo>+</mml:mo><mml:mrow><mml:msup><mml:mi>b</mml:mi><mml:mo>&#x2217;</mml:mo></mml:msup></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
where xr and xs are any support vectors from each class satisfying:
<disp-formula id="eqn-6"><label>(6)</label><mml:math id="mml-eqn-6" display="block"><mml:mrow><mml:msub><mml:mi>&#x03B1;</mml:mi><mml:mrow><mml:mi>r</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>&#x03B1;</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:mrow><mml:mo>.</mml:mo><mml:mo>&#x003E;</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mspace width="1em" /><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mi>r</mml:mi></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mspace width="1em" /><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:math></disp-formula>
</p>
<p>By use of optimization quadratic Algorithms 1 the optimization problem has been solved.</p>
<fig id="fig-7">
<graphic mimetype="image" mime-subtype="png" xlink:href="CMC_21582-fig-7.png"/></fig>
</sec>
</sec>
<sec id="s4"><label>4</label><title>Results and Discussions</title>
<p>In this, SVM classification algorithm are used to analyze the health data for cardiovascular disease. For each attribute in SVM, the optimal hyperplane has been predicted. The performance metrics such as Accuracy, Specificity and Sensitivity were used to prove the efficacy of this modern approach. <?A3B2 "tbl2",5,"anchor"?><xref ref-type="table" rid="table-2">Tab. 2</xref> gives the baseline clinical characteristics of patients.</p>
<table-wrap id="table-2"><label>Table 2</label><caption><title>Baseline clinical characteristics of patients</title></caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th align="left">Variable</th>
<th align="left">Men</th>
<th align="left">Women</th>
<th align="left">Probability</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left">Age, Years</td>
<td align="left">50.02&#x2009;&#x00B1;&#x2009;4.33</td>
<td align="left">58.40&#x2009;&#x00B1;&#x2009;4.10</td>
<td align="left">&#x003C;0.001</td>
</tr>
<tr>
<td align="left">Height, m</td>
<td align="left">1.88&#x2009;&#x00B1;&#x2009;0.10</td>
<td align="left">1.71&#x2009;&#x00B1;&#x2009;0.07</td>
<td align="left">&#x003C;0.001</td>
</tr>
<tr>
<td align="left">Weight, Kg</td>
<td align="left">102.25&#x2009;&#x00B1;&#x2009;17.01</td>
<td align="left">86.20&#x2009;&#x00B1;&#x2009;14.26</td>
<td align="left">&#x003C;0.001</td>
</tr>
<tr>
<td align="left">BMI, kg/m<sup>2</sup></td>
<td align="left">33.08&#x2009;&#x00B1;&#x2009;5.36</td>
<td align="left">33.39&#x2009;&#x00B1;&#x2009;6.20</td>
<td align="left">0.285</td>
</tr>
<tr>
<td align="left">Total cholesterol</td>
<td align="left">7.76&#x2009;&#x00B1;&#x2009;2.72</td>
<td align="left">8.12&#x2009;&#x00B1;&#x2009;2.40</td>
<td align="left">&#x003C;0.001</td>
</tr>
<tr>
<td align="left">Oral glucose tolerance test, mol/L</td>
<td align="left">6.96&#x2009;&#x00B1;&#x2009;3.06</td>
<td align="left">8.12&#x2009;&#x00B1;&#x2009;3.60</td>
<td align="left">&#x003C;0.001</td>
</tr>
<tr>
<td align="left">Right CAVI</td>
<td align="left">8.96&#x2009;&#x00B1;&#x2009;1.76</td>
<td align="left">9.00&#x2009;&#x00B1;&#x2009;1.51</td>
<td align="left">0.530</td>
</tr>
<tr>
<td align="left">Left CAVI</td>
<td align="left">8.86&#x2009;&#x00B1;&#x2009;2.82</td>
<td align="left">8.92&#x2009;&#x00B1;&#x2009;2.40</td>
<td align="left">0.030</td>
</tr>
<tr>
<td align="left">Mean CAVI</td>
<td align="left">7.95&#x2009;&#x00B1;&#x2009;1.56</td>
<td align="left">8.96&#x2009;&#x00B1;&#x2009;2.35</td>
<td align="left">0.098</td>
</tr>
<tr>
<td align="left">Heart rate, bpm</td>
<td align="left">65.83&#x2009;&#x00B1;&#x2009;10.51</td>
<td align="left">66.34&#x2009;&#x00B1;&#x2009;10.16</td>
<td align="left">0.009</td>
</tr>
<tr>
<td align="left">Smoking, n (&#x0025;)</td>
<td align="left">330(45)</td>
<td align="left">190(15)</td>
<td align="left">&#x003C;0.001</td>
</tr>
<tr>
<td align="left">Family history of CLDN (&#x0025;)</td>
<td align="left">295(37)</td>
<td align="left">450(35)</td>
<td align="left">0.921</td>
</tr>
<tr>
<td align="left">Diabetes, n (&#x0025;)</td>
<td align="left">150(20)</td>
<td align="left">250(20)</td>
<td align="left">0.962</td>
</tr>
<tr>
<td align="left">Hypertension</td>
<td align="left">109.01&#x2009;&#x00B1;&#x2009;13.06</td>
<td align="left">107.08&#x2009;&#x00B1;&#x2009;15.23</td>
<td align="left">0.045</td>
</tr>
</tbody>
</table>
</table-wrap>
<sec id="s4_1"><label>4.1</label><title>Confusion Matrix</title>
<p>Confusion matrix is defined to showcase the performance of an algorithm through visualization or to describe the performance of a classification model on a set of test data for which the true values are known. A confusion matrix is also called an error matrix shown in <?A3B2 "fig4",5,"anchor"?><xref ref-type="fig" rid="fig-4">Fig. 4</xref> that depicts the time taken for the completion of the training dataset. After the construction of confusion matrix, the sensitivity, specificity, and accuracy are calculated as,
<disp-formula id="eqn-7"><label>(7)</label><mml:math id="mml-eqn-7" display="block"><mml:mi>S</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mi>s</mml:mi><mml:mi>i</mml:mi><mml:mi>t</mml:mi><mml:mi>i</mml:mi><mml:mi>v</mml:mi><mml:mi>i</mml:mi><mml:mi>t</mml:mi><mml:mi>y</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mi>T</mml:mi><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>T</mml:mi><mml:mi>P</mml:mi><mml:mo>+</mml:mo><mml:mi>F</mml:mi><mml:mi>N</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mfrac></mml:math></disp-formula>
<disp-formula id="eqn-8"><label>(8)</label><mml:math id="mml-eqn-8" display="block"><mml:mi>S</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:mi>i</mml:mi><mml:mi>f</mml:mi><mml:mi>i</mml:mi><mml:mi>c</mml:mi><mml:mi>i</mml:mi><mml:mi>t</mml:mi><mml:mi>y</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mi>T</mml:mi><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>T</mml:mi><mml:mi>N</mml:mi><mml:mo>+</mml:mo><mml:mi>F</mml:mi><mml:mi>P</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mfrac></mml:math></disp-formula>
<disp-formula id="eqn-9"><label>(9)</label><mml:math id="mml-eqn-9" display="block"><mml:mi>A</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:mi>u</mml:mi><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>y</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>T</mml:mi><mml:mi>P</mml:mi><mml:mo>+</mml:mo><mml:mi>T</mml:mi><mml:mi>N</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>T</mml:mi><mml:mi>P</mml:mi><mml:mo>+</mml:mo><mml:mi>F</mml:mi><mml:mi>P</mml:mi><mml:mo>+</mml:mo><mml:mi>T</mml:mi><mml:mi>N</mml:mi><mml:mo>+</mml:mo><mml:mi>F</mml:mi><mml:mi>N</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mfrac></mml:math></disp-formula>
where, TP-True positive; FP-False positive; TN-True negative; FN-False-negative.</p>
<fig id="fig-4"><label>Figure 4</label><caption><title>Confusion Matrix</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_21582-fig-4.png"/></fig>
</sec>
<sec id="s4_2"><label>4.2</label><title>Kappa Statistic</title>
<p>Kappa Statistics is the measure of how closely the instances have been classified. The kappa coefficient is represented as follows
<disp-formula id="eqn-10"><label>(10)</label><mml:math id="mml-eqn-10" display="block"><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mi>e</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mi>e</mml:mi></mml:msub></mml:mrow></mml:mrow></mml:mfrac></mml:math></disp-formula>
where k is kappa value, p0 denotes the probability of observed agreement and pe denotes the probability of hypothetical agreement. With the help of confusion matrix, p0 and pe is computed followed by p<sub>class1</sub> and p<sub>class2.</sub>
<disp-formula id="eqn-11"><label>(11)</label><mml:math id="mml-eqn-11" display="block"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mi>T</mml:mi><mml:mi>P</mml:mi><mml:mo>+</mml:mo><mml:mi>T</mml:mi><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mi>T</mml:mi><mml:mi>P</mml:mi><mml:mo>+</mml:mo><mml:mi>F</mml:mi><mml:mi>P</mml:mi><mml:mo>+</mml:mo><mml:mi>T</mml:mi><mml:mi>N</mml:mi><mml:mo>+</mml:mo><mml:mi>F</mml:mi><mml:mi>N</mml:mi></mml:mrow></mml:mfrac></mml:math></disp-formula>
</p>
<p>p0&#x003D;pclass1 &#x002B; pclass2,</p>
<p>where pclass1 and pclass2 is computed as follows
<disp-formula id="eqn-12"><label>(12)</label><mml:math id="mml-eqn-12" display="block"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mi>l</mml:mi><mml:mi>a</mml:mi><mml:mi>s</mml:mi><mml:mi>s</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mi>T</mml:mi><mml:mi>P</mml:mi><mml:mo>+</mml:mo><mml:mi>F</mml:mi><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>T</mml:mi><mml:mi>P</mml:mi><mml:mo>+</mml:mo><mml:mi>F</mml:mi><mml:mi>P</mml:mi><mml:mo>+</mml:mo><mml:mi>T</mml:mi><mml:mi>N</mml:mi><mml:mo>+</mml:mo><mml:mi>F</mml:mi><mml:mi>N</mml:mi></mml:mrow></mml:mfrac><mml:mo>&#x00D7;</mml:mo><mml:mfrac><mml:mrow><mml:mi>T</mml:mi><mml:mi>P</mml:mi><mml:mo>+</mml:mo><mml:mi>F</mml:mi><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mi>T</mml:mi><mml:mi>P</mml:mi><mml:mo>+</mml:mo><mml:mi>F</mml:mi><mml:mi>P</mml:mi><mml:mo>+</mml:mo><mml:mi>T</mml:mi><mml:mi>N</mml:mi><mml:mo>+</mml:mo><mml:mi>F</mml:mi><mml:mi>N</mml:mi></mml:mrow></mml:mfrac></mml:math></disp-formula>
<disp-formula id="eqn-13"><label>(13)</label><mml:math id="mml-eqn-13" display="block"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mi>l</mml:mi><mml:mi>a</mml:mi><mml:mi>s</mml:mi><mml:mi>s</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mi>F</mml:mi><mml:mi>N</mml:mi><mml:mo>+</mml:mo><mml:mi>T</mml:mi><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mi>T</mml:mi><mml:mi>P</mml:mi><mml:mo>+</mml:mo><mml:mi>F</mml:mi><mml:mi>P</mml:mi><mml:mo>+</mml:mo><mml:mi>T</mml:mi><mml:mi>N</mml:mi><mml:mo>+</mml:mo><mml:mi>F</mml:mi><mml:mi>N</mml:mi></mml:mrow></mml:mfrac><mml:mo>&#x00D7;</mml:mo><mml:mfrac><mml:mrow><mml:mi>F</mml:mi><mml:mi>P</mml:mi><mml:mo>+</mml:mo><mml:mi>T</mml:mi><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mi>T</mml:mi><mml:mi>P</mml:mi><mml:mo>+</mml:mo><mml:mi>F</mml:mi><mml:mi>P</mml:mi><mml:mo>+</mml:mo><mml:mi>T</mml:mi><mml:mi>N</mml:mi><mml:mo>+</mml:mo><mml:mi>F</mml:mi><mml:mi>N</mml:mi></mml:mrow></mml:mfrac></mml:math></disp-formula>
</p>
</sec>
<sec id="s4_3"><label>4.3</label><title>Mean Absolute Error</title>
<p>The average difference between predicted and actual value in all test cases called average prediction error which otherwise refers to the mean of the absolute values of each prediction error on all instances of the given test data set.
<disp-formula id="eqn-14"><label>(14)</label><mml:math id="mml-eqn-14" display="block"><mml:mi>M</mml:mi><mml:mi>A</mml:mi><mml:mi>E</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mi>n</mml:mi><mml:mrow><mml:mspace width="thickmathspace" /></mml:mrow><mml:mrow><mml:mo>&#x2211;</mml:mo></mml:mrow><mml:mo>&#x2061;</mml:mo><mml:mi mathvariant="normal">&#x005F;</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:msup><mml:mo stretchy="false">)</mml:mo><mml:mrow><mml:mo>&#x2227;</mml:mo></mml:mrow></mml:msup><mml:mi>n</mml:mi><mml:mrow><mml:mo stretchy="false">|</mml:mo></mml:mrow><mml:mrow><mml:mi>e</mml:mi><mml:mi mathvariant="normal">&#x005F;</mml:mi><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">|</mml:mo></mml:mrow></mml:math></disp-formula>
</p>
</sec>
<sec id="s4_4"><label>4.4</label><title>Standard Deviation</title>
<p>Standard deviation measures the spread of the data about the mean value.
<disp-formula id="eqn-15"><label>(15)</label><mml:math id="mml-eqn-15" display="block"><mml:mi>&#x03C3;</mml:mi><mml:mo>=</mml:mo><mml:mo stretchy="false">&#x221A;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mo>&#x2211;</mml:mo></mml:mrow><mml:mo>&#x2061;</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>x</mml:mi><mml:mi mathvariant="normal">&#x005F;</mml:mi><mml:mi>i</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>&#x03BC;</mml:mi></mml:mrow><mml:msup><mml:mo stretchy="false">)</mml:mo><mml:mrow><mml:mo>&#x2227;</mml:mo></mml:mrow></mml:msup><mml:mn>2</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula>
</p>
</sec>
<sec id="s4_5"><label>4.5</label><title>Median</title>
<p>The median is the middle number sorted in ascending, or descending list of numbers and can be more descriptive data set than the average.
<disp-formula id="eqn-16"><label>(16)</label><mml:math id="mml-eqn-16" display="block"><mml:mfrac><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mn>2</mml:mn></mml:mfrac></mml:math></disp-formula>
</p>
<p><?A3B2 "tbl3",5,"anchor"?><xref ref-type="table" rid="table-3">Tab. 3</xref> shows by using validation data set, the detailed prediction has been done in the form of confusion matrices and error rate obtained using SVM.</p>
<table-wrap id="table-3"><label>Table 3</label><caption><title>Confusion matrix and error rate obtained using SVM</title></caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th align="left">Confusion matrix</th>
<th></th>
<th></th>
<th align="left">Error rate</th>
</tr>
<tr>
   <th></th>
   <th></th>
   <th></th>
<th>0.5913</th>
</tr>
<tr>
<th></th>
<th align="left">Normal</th>
<th>Abnormal</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left">Normal</td>
<td align="left">200</td>
<td>180</td>
</tr>
<tr>
<td align="left">Abnormal</td>
<td align="left">195</td>
<td>170</td>
</tr>
</tbody>
</table>
</table-wrap>
<p><?A3B2 "tbl4",5,"anchor"?><xref ref-type="table" rid="table-4">Tab. 4</xref> shows the performance metrics and the results obtained by the proposed method where each metric is calculated accordingly.</p>
<table-wrap id="table-4"><label>Table 4</label><caption><title>Performance metrices of KNN, SVM and Naive Bayes</title></caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th align="left">Performance Metrics</th>
<th align="left">SVM</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left">Time</td>
<td align="left">0.04</td>
</tr>
<tr>
<td align="left">Kappa statistics</td>
<td align="left">0.6233</td>
</tr>
<tr>
<td align="left">Standard deviation</td>
<td align="left">0.3108</td>
</tr>
<tr>
<td align="left">Mean absolute error</td>
<td align="left">0.5377</td>
</tr>
<tr>
<td align="left">Median</td>
<td align="left">0.5515</td>
</tr>
<tr>
<td align="left">Accuracy (&#x0025;)</td>
<td align="left">81.2187</td>
</tr>
<tr>
<td align="left">Sensitivity (&#x0025;)</td>
<td align="left">93.2031</td>
</tr>
<tr>
<td align="left">Specificity (&#x0025;)</td>
<td align="left">89.8655</td>
</tr>
</tbody>
</table>
</table-wrap>
<p><?A3B2 "fig5",5,"anchor"?><xref ref-type="fig" rid="fig-5">Fig. 5</xref> gives the chart model evaluation using SVM and it proves the performance of classification accuracy 81.2187&#x0025;, Sensitivity 93.2031&#x0025; and Specificity 89.8655&#x0025;. <?A3B2 "tbl5",5,"anchor"?><xref ref-type="table" rid="table-5">Tab. 5</xref>, it shows the comparison of existing systems and proposed systems for predicting cardiovascular disease.</p>
<fig id="fig-5"><label>Figure 5</label><caption><title>Performance of the support vector machine</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_21582-fig-5.png"/>
</fig>
<table-wrap id="table-5"><label>Table 5</label><caption><title>Comparison of existing and proposed system</title></caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left" charoff="12"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th align="left">S.no.</th>
<th align="left">Authors</th>
<th align="left">Methodology</th>
<th align="left">Accuracy (&#x0025;) </th>
</tr>
</thead>
<tbody>
<tr>
<td align="left">1.</td>
<td align="left">Islam et al. [<xref ref-type="bibr" rid="ref-29">29</xref>]</td>
<td align="left">Na&#x00EF;ve Bayes, Logistic regression</td>
<td align="left">80</td>
</tr>
<tr>
<td align="left">2.</td>
<td align="left">Haq et al. [<xref ref-type="bibr" rid="ref-31">31</xref>]</td>
<td align="left">KNN, ANN, Na&#x00EF;ve Bayes, Decision tree</td>
<td align="left">89</td>
</tr>
<tr>
<td align="left">3.</td>
<td align="left">Dinesh et al. [<xref ref-type="bibr" rid="ref-40">40</xref>]</td>
<td align="left">Gradient boosting, random forest, Na&#x00EF;ve Bayes, Logistic regression</td>
<td align="left">88</td>
</tr>
<tr>
<td align="left">4.</td>
<td align="left">Bhardwaj et al. [<xref ref-type="bibr" rid="ref-38">38</xref>]</td>
<td align="left">Genetically Optimized Neural Network</td>
<td align="left">93.24</td>
</tr>
<tr>
<td align="left">5.</td>
<td align="left">Proposed system</td>
<td align="left">SVM</td>
<td align="left">95</td>
</tr>
</tbody>
</table>
</table-wrap>
<p><?A3B2 "fig6",5,"anchor"?><xref ref-type="fig" rid="fig-6">Fig. 6</xref> is a graphical representation of a comparison of existing system with the proposed method for predicting cardiovascular disease in the early stage with more accuracy when compared to other machine learning techniques.</p>
<fig id="fig-6"><label>Figure 6</label><caption><title>Comparison of existing and proposed system</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_21582-fig-6.png"/>
</fig>
</sec>
</sec>
<sec id="s5"><label>5</label><title>Conclusion and Future Scope</title>
<p>In this study the occurrence of CVD is more in humans because of genetic disorder when compared to other health issues. Therefore, medical practioner are in need of suitable technique or model to predict primarily. Nowadays, machine learning techniques are adapted in medical science for such decision-making situations. The proposed system designed under supervised learning using SVM plays efficiently in decision appealing and retrieving proficiency from an enormous amount of data thereby delivering better patient care and productivity. This system proves as an excellent model in addressing the classification problems and go-to method for any type of prediction problem. In this research paper, the classification techniques used for identifying cardiovascular in patients gives more prediction accuracy compare to other technical approaches. Future research is required to validate the algorithm for a huge population in taking many risk parameters into consideration.</p>
</sec>
</body>
<back>
<fn-group>
<fn fn-type="other"><p><bold>Funding Statement:</bold> Thanks for the Graphic Era Hill University and authors thanks to Saudi Electronic University for the financial support.</p></fn>
<fn fn-type="conflict"><p><bold>Conflicts of Interest:</bold> The authors declare that they have no conflicts of interest to report regarding the present study.</p></fn>
</fn-group>
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