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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">16957</article-id>
<article-id pub-id-type="doi">10.32604/cmc.2021.016957</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Article</subject>
</subj-group>
</article-categories>
<title-group>
<article-title>An Approach Using Fuzzy Sets and Boosting Techniques to Predict Liver Disease</article-title>
<alt-title alt-title-type="left-running-head">An Approach Using Fuzzy Sets and Boosting Techniques to Predict Liver Disease</alt-title>
<alt-title alt-title-type="right-running-head">An Approach Using Fuzzy Sets and Boosting Techniques to Predict Liver Disease</alt-title>
</title-group>
<contrib-group content-type="authors">
<contrib id="author-1" contrib-type="author" corresp="yes">
<name name-style="western">
<surname>Kumar</surname>
<given-names>Pushpendra</given-names>
</name>
<xref ref-type="aff" rid="aff-1">1</xref><xref ref-type="aff" rid="aff-2">2</xref>
<email>pushpendra7589@gmail.com</email>
</contrib>
<contrib id="author-2" contrib-type="author">
<name name-style="western">
<surname>Thakur</surname>
<given-names>Ramjeevan Singh</given-names>
</name>
<xref ref-type="aff" rid="aff-3">3</xref></contrib>
<aff id="aff-1"><label>1</label><institution>Maulana Azad National Institute of Technology</institution>, <addr-line>Bhopal</addr-line>, <country>India</country></aff>
<aff id="aff-2"><label>2</label><institution>Central University of Jharkhand</institution>, <addr-line>Ranchi</addr-line>, <country>India</country></aff>
<aff id="aff-3"><label>3</label><institution>Maulana Azad National Institute of Technology</institution>, <addr-line>Bhopal</addr-line>, <country>India</country></aff>
</contrib-group>
<author-notes><corresp id="cor1">&#x002A;Corresponding Author: Pushpendra Kumar. Email: <email>pushpendra7589@gmail.com</email></corresp></author-notes>
<pub-date pub-type="epub" date-type="pub" iso-8601-date="2021-03-23"><day>23</day><month>03</month><year>2021</year>
</pub-date>
<volume>68</volume>
<issue>3</issue>
<fpage>3513</fpage>
<lpage>3529</lpage>
<history>
<date date-type="received"><day>16</day><month>01</month><year>2021</year></date>
<date date-type="accepted"><day>04</day><month>03</month><year>2021</year></date>
</history>
<permissions>
<copyright-statement>&#x00A9; 2021 Kumar and Thakur</copyright-statement>
<copyright-year>2021</copyright-year>
<copyright-holder>Kumar and Thakur</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_16957.pdf"></self-uri>
<abstract>
<p>The aim of this research is to develop a mechanism to help medical practitioners predict and diagnose liver disease. Several systems have been proposed to help medical experts by diminishing error and increasing accuracy in diagnosing and predicting diseases. Among many existing methods, a few have considered the class imbalance issues of liver disorder datasets. As all the samples of liver disorder datasets are not useful, they do not contribute to learning about classifiers. A few samples might be redundant, which can increase the computational cost and affect the performance of the classifier. In this paper, a model has been proposed that combines noise filter, fuzzy sets, and boosting techniques (NFFBTs) for liver disease prediction. Firstly, the noise filter (NF) eliminates the outliers from the minority class and removes the outlier and redundant pair from the majority class. Secondly, the fuzzy set concept is applied to handle uncertainty in datasets. Thirdly, the AdaBoost boosting algorithm is trained with several learners viz, random forest (RF), support vector machine (SVM), logistic regression (LR), and naive Bayes (NB). The proposed NFFBT prediction system was applied to two datasets (i.e., ILPD and MPRLPD) and found that AdaBoost with RF yielded 90.65% and 98.95% accuracy and F1 scores of 92.09% and 99.24% over ILPD and MPRLPD datasets, respectively.</p>
</abstract>
<kwd-group kwd-group-type="author">
<kwd>Fuzzy set</kwd>
<kwd>imbalanced data</kwd>
<kwd>liver disease prediction</kwd>
<kwd>machine learning</kwd>
<kwd>noise filter</kwd>
</kwd-group>
</article-meta>
</front>
<body>
<sec id="s1">
<label>1</label>
<title>Introduction</title>
<p>Liver diseases are the leading cause of death in India and across the world. Approximately two million people die annually because of liver disease throughout the world. In India alone, 216,865 people died from liver disease in 2014, representing 2.44% of all deaths in the country. In 2017, the number of deaths increased to 259,749, representing 2.95% of all deaths [<xref ref-type="bibr" rid="ref-1">1</xref>].</p>
<p>Diagnosing liver disease in its early stages is a complicated task, as the liver continues to perform normally until it is severely damaged [<xref ref-type="bibr" rid="ref-2">2</xref>]. The diagnosis and treatment of liver disease are performed by medical experts. However, inappropriate treatment sometimes wastes time and money and causes the loss of life. Consequently, the development of an efficient and automatic liver disease prediction system is necessary for efficient and early diagnosis. Automated liver prediction systems take advantage of the data generated from the liver function test (LFT). This system can support the medical practitioner in diagnosing liver disease with less effort and more accuracy. The classification technique of a machine learning algorithm is applied when developing automated disease prediction systems [<xref ref-type="bibr" rid="ref-3">3</xref>,<xref ref-type="bibr" rid="ref-4">4</xref>]. The purpose of the classification algorithm is to predict the class label of an unknown instance [<xref ref-type="bibr" rid="ref-5">5</xref>] and work adequately when the instances of the dataset are uniformly distributed among all the classes (balanced) [<xref ref-type="bibr" rid="ref-6">6</xref>]. Most healthcare datasets, such as those for breast cancer [<xref ref-type="bibr" rid="ref-7">7</xref>,<xref ref-type="bibr" rid="ref-8">8</xref>], heartbeat [<xref ref-type="bibr" rid="ref-9">9</xref>], diabetes [<xref ref-type="bibr" rid="ref-10">10</xref>&#x2013;<xref ref-type="bibr" rid="ref-13">13</xref>], kidney [<xref ref-type="bibr" rid="ref-14">14</xref>], and liver disorders [<xref ref-type="bibr" rid="ref-15">15</xref>&#x2013;<xref ref-type="bibr" rid="ref-17">17</xref>], involve class imbalance. The standard classification performs poorly when a dataset is not uniformly distributed among all the classes (imbalanced) because minority class data are classified as majority class data [<xref ref-type="bibr" rid="ref-18">18</xref>&#x2013;<xref ref-type="bibr" rid="ref-20">20</xref>].</p>
<p>Four procedures have been proposed to mitigate the issues related to class imbalance. These are (a) algorithm modifications, (b) a sampling-based technique, (c) a cost-sensitive approach, and (d) ensemble learning techniques.</p>
<p><bold><italic>Algorithm modifications:</italic></bold> This procedure adjusts the conventional algorithm by biasing the learning to find a solution to the imbalance problem [<xref ref-type="bibr" rid="ref-21">21</xref>]. This strategy does not disturb the original pattern of the data, whereas this methodology requires an awareness of the corresponding classifier and application [<xref ref-type="bibr" rid="ref-21">21</xref>,<xref ref-type="bibr" rid="ref-22">22</xref>].</p>
<p><bold><italic>Sampling-based technique (SBT)</italic></bold> <bold><italic>[<xref ref-type="bibr" rid="ref-23">23</xref>&#x2013;<xref ref-type="bibr" rid="ref-26">26</xref>]:</italic></bold> Sampling can be accomplished either by oversampling or undersampling. Oversampling adds new or duplicate records to the minority class until the desired class proportion is obtained, whereas undersampling removes records from the majority class until the desired class ratio is achieved. The disadvantage of undersampling is that information may be lost if significant data are removed, while its advantage is that it decreases learning times by reducing the learning data size. Oversampling suffers from overfitting and increased model learning times.</p>
<p><bold><italic>Cost-sensitive approach:</italic></bold> This approach utilizes the variable cost matrix for instances that are misclassified by the model. The cost of misclassification needs to be defined in this approach, which is not usually given in datasets [<xref ref-type="bibr" rid="ref-24">24</xref>,<xref ref-type="bibr" rid="ref-25">25</xref>,<xref ref-type="bibr" rid="ref-27">27</xref>,<xref ref-type="bibr" rid="ref-28">28</xref>].</p>
<p><bold><italic>Ensemble learning techniques (ELT):</italic></bold> Reference [<xref ref-type="bibr" rid="ref-29">29</xref>] Ensemble learning (EL) uses multiple learning algorithms to accomplish the same task. ETL has a better classification and generalization ability than machine learners that use a single learner. In recent times, an EL that combines ELT and SBT gained recognition for its ability to solve class imbalance issues.</p>
<p>The objective of this work is to develop a noise filter, fuzzy sets, and boosting technique (NFFBT) approach to predict liver disorder. The proposed NFFBT approach aids medical practitioners in interpreting the consequences of LFT. Existing liver disorder detection techniques mostly apply the boosting technique to handle imbalanced issues of LFT datasets only. Meanwhile, the proposed NFFBT approach applies a noise filter to eliminate all noise from the majority and minority classes. This preserves the dataset&#x2019;s characteristics and reduces the model&#x2019;s training time. Then, the fuzzification system&#x2014;which eliminates the uncertainty in the relationship among the features of datasets&#x2014;and the AdaBoost boosting algorithm are applied with different classifiers to handle issues of class imbalance. The architecture of the noise filter is shown in <xref ref-type="fig" rid="fig-1">Fig. 1</xref>.</p>
<p>The rest of this paper is arranged as follows. Section 2 discusses related works and the authors&#x2019; vested motivation for this research work. A description of the proposed methodology for NFFBT development is presented in Section 3. The results and discussion are presented in Section 4. Finally, a summary of the findings and the conclusions of this research work are given in Section 5.</p>
<fig id="fig-1">
<label>Figure 1</label>
<caption>
<title>Architecture of noise filter</title>
</caption><graphic mimetype="image" mime-subtype="png" xlink:href="fig-1.png"/>
</fig>
</sec>
<sec id="s2">
<label>2</label>
<title>Related Works</title>
<p>In the last few years, a lot of studies have been performed on liver disorder predictions using classification techniques. In these studies, the decisions made by the prediction systems and input data from patients impacted liver disease diagnoses. Literature reviews concerned with the proposed methodology are summarized in <xref ref-type="table" rid="table-1">Tab. 1</xref>.</p>
<table-wrap id="table-1">
<label>Table 1</label>
<caption>
<title>Summary of literature reviews concerned with the proposed methodology</title>
</caption>
<!---->
<table>
<colgroup>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th>Sl. No.</th>
<th>Author and year</th>
<th>Technique used</th>
<th>Dataset</th>
<th>Finding</th>
<th>Issues</th>
<th></th>
</tr>
</thead>
<tbody>
<tr>
<td>1</td>
<td>Kang et al. (2017) [<xref ref-type="bibr" rid="ref-24">24</xref>]</td>
<td>Noise-filtered</td>
<td>Sixteen different datasets</td>
<td>The proposed method improves the results over original undersampling-based methods.</td>
<td>Eliminates noise from minority class data only.</td>
<td/>
</tr>
<tr>
<td>2</td>
<td>Abdar et al. (2018) [<xref ref-type="bibr" rid="ref-30">30</xref>]</td>
<td>MLPNN and boosted DT</td>
<td>ILPD dataset</td>
<td>B-C5.0 and MLPNNB-C5.0 produce the highest accuracies (92.61% and 94.12%, respectively).</td>
<td>Performs implementations on only one dataset.</td>
<td/>
</tr>
<tr>
<td>3</td>
<td>Lin et al. (2010) [<xref ref-type="bibr" rid="ref-31">31</xref>]</td>
<td>ANN, AHP, and CBR methods</td>
<td>Data from 510 liver patients from a medical center in Taiwan</td>
<td>ANN assists the physician in recognizing the existence of disease; CBR with AHP assists in classifying different types of liver disease.</td>
<td>Performs implementations on few data.</td>
<td/>
</tr>
<tr>
<td>4</td>
<td>Tan (2005) [<xref ref-type="bibr" rid="ref-32">32</xref>]</td>
<td>NWKNN method</td>
<td>Reuter and TDT2 text dataset</td>
<td>NWKNN provides better performance for unbalanced text document classification than KNN.</td>
<td>Performs classifications of unbalanced text documents.</td>
<td/>
</tr>
<tr>
<td>5</td>
<td>Jiang et al. (2019) [<xref ref-type="bibr" rid="ref-9">9</xref>]</td>
<td>Proposed MMNNS for classification of imbalance heartbeats of ECG signals</td>
<td>MIT-BIH arrhythmia, European ST-T, and MIT-BIH ST change database</td>
<td>The proposed method produced 97.3% accuracy.</td>
<td>Performance can be improved by using other types of neural networks.</td>
<td/>
</tr>
<tr>
<td>6</td>
<td>Nahato et al. (2016) [<xref ref-type="bibr" rid="ref-33">33</xref>]</td>
<td>Fuzzy sets and ELM for classifying clinical datasets</td>
<td>CHD, SHD, and PID dataset</td>
<td>Achieved the highest accuracy (94.44%) for a CHD dataset with five class labels.</td>
<td>Nature-inspired optimization techniques can be applied to improve the FELM results.</td>
<td/>
</tr>
<tr>
<td>7</td>
<td>Auxilia [<xref ref-type="bibr" rid="ref-34">34</xref>]</td>
<td>DT, NB, RF, SVM, and ANN</td>
<td>ILPD dataset</td>
<td>Analyzed the various classification algorithm and found DT work best.</td>
<td>Performed performance analysis of existing algorithm on only one dataset.</td>
<td/>
</tr>
<tr>
<td>8</td>
<td>Vats et al. [<xref ref-type="bibr" rid="ref-35">35</xref>]</td>
<td>DBSCAN, K-means, and affinity propagation</td>
<td>Liver disease data</td>
<td>Performance is measured based on adjusted mutual information, V measure, completeness, homogeneity, adjusted Rand index, and silhouette coefficient; K-mean is better than that of other techniques.</td>
<td>Unclear which dataset was used and how liver disease can be predicted.</td>
<td/>
</tr>
<tr>
<td>9</td>
<td>Lin et al. (2010) [<xref ref-type="bibr" rid="ref-31">31</xref>]</td>
<td>SVDD with GSO algorithm</td>
<td>Collected LFT data from a community hospital in Beijing</td>
<td>The proposed method produces 84.28% accuracy, 96% sensitivity, and 86.28% specificity.</td>
<td>The method is implemented on a sample of 225 records from 1000 patients&#x2019; liver function test records.</td>
<td/>
</tr>
<tr>
<td>10</td>
<td>Patel et al. (2017) [<xref ref-type="bibr" rid="ref-36">36</xref>]</td>
<td>Hybrid fuzzy weighted nearest neighbor (fuzzy NWKNN</td>
<td>Work on six imbalanced datasets</td>
<td>The fuzzy NWKNN method is an extension of the NWKNN method.</td>
<td>Assigns a weight for majority and minority class data but calculations of weight fail under some conditions.</td>
<td/>
</tr>
<tr>
<td>11</td>
<td>Kumar et al. (2019) [<xref ref-type="bibr" rid="ref-15">15</xref>]</td>
<td>SVM and K-NN with SMOTE technique for predicting liver disorders based on imbalanced liver function test data</td>
<td>ILPD and MPRLPD</td>
<td>SVM with SMOTE performs better than K-NN with SMOTE.</td>
<td>The SMOTE technique oversamples the dataset, which can extend the training time.</td>
<td/>
</tr>
</tbody>
</table>
</table-wrap>
<p>From the above studies, it is observed that there is still a need to develop an efficient and effective system for liver disease detection using a machine learning approach.</p>
<p><xref ref-type="table" rid="table-2">Tab. 2</xref> compares previous studies about liver disease prediction. From the comparison, it is observed that these studies have not considered outliers of the majority and minority classes and have neglected the class imbalance issues of LFT datasets. This paper will address these issues.</p>
<table-wrap id="table-2">
<label>Table 2</label>
<caption>
<title>Summary of literature reviews about liver disease prediction</title>
</caption>
<!---->
<table>
<colgroup>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th>Sl. No.</th>
<th>Authors and years</th>
<th>Algorithm</th>
<th>Accuracy</th>
<th>Datasets/remarks</th>
<th></th>
</tr>
</thead>
<tbody>
<tr>
<td>1</td>
<td>Alfisahrin et al. (2013) [<xref ref-type="bibr" rid="ref-37">37</xref>]</td>
<td>NBTree</td>
<td>67.01%</td>
<td>ILPD</td>
<td/>
</tr>
<tr>
<td>2</td>
<td>Jin et al. (2014) [<xref ref-type="bibr" rid="ref-38">38</xref>]</td>
<td>LR</td>
<td>72.70%</td>
<td>ILPD</td>
<td/>
</tr>
<tr>
<td>3</td>
<td>Abdar (2015) [<xref ref-type="bibr" rid="ref-39">39</xref>]</td>
<td>C5.0</td>
<td>87.91%</td>
<td>ILPD</td>
<td/>
</tr>
<tr>
<td>4</td>
<td>Ramkumar et al. (2017) [<xref ref-type="bibr" rid="ref-40">40</xref>]</td>
<td>Bayes theorem</td>
<td>50.00%</td>
<td>Sample of 20 patients of BUPA dataset</td>
<td/>
</tr>
<tr>
<td>5</td>
<td>Hamid et al. (2017) [<xref ref-type="bibr" rid="ref-11">11</xref>]</td>
<td>Stochastic gradients</td>
<td><inline-formula id="ieqn-1"><!--<alternatives><inline-graphic xlink:href="ieqn-1.png"/><tex-math id="tex-ieqn-1"><![CDATA[$\text{AUC-ROC}= 89.5$]]></tex-math>--><mml:math id="mml-ieqn-1"><mml:mstyle class="text"><mml:mtext>AUC-ROC</mml:mtext></mml:mstyle><mml:mo>=</mml:mo><mml:mn>89</mml:mn><mml:mo>.</mml:mo><mml:mn>5</mml:mn></mml:math><!--</alternatives>--></inline-formula>%</td>
<td>This model has been examined on only 99 liver ultrasound images.</td>
<td/>
</tr>
<tr>
<td>6</td>
<td>Hashem et al. (2018) [<xref ref-type="bibr" rid="ref-41">41</xref>]</td>
<td>Alternative decision tree (ADT)</td>
<td>84.40%</td>
<td>&#x2013;</td>
<td/>
</tr>
<tr>
<td>7</td>
<td>Abdar et al. (2017) [<xref ref-type="bibr" rid="ref-42">42</xref>]</td>
<td>Boosted C5.0</td>
<td>93.75%</td>
<td>ILPD</td>
<td/>
</tr>
<tr>
<td>8</td>
<td>Abdar et al. (2018) [<xref ref-type="bibr" rid="ref-30">30</xref>]</td>
<td>MLPNNB-C5.0</td>
<td>94.12%</td>
<td>ILPD</td>
<td/>
</tr>
<tr>
<td>9</td>
<td>Lin et al. (2010) [<xref ref-type="bibr" rid="ref-31">31</xref>]</td>
<td>SVDD and GSO</td>
<td>84.28%</td>
<td>Sample of 225 patient records from 1000 LFT records.</td>
<td/>
</tr>
<tr>
<td>10</td>
<td>Auxilia [<xref ref-type="bibr" rid="ref-34">34</xref>]</td>
<td>DT</td>
<td>81%</td>
<td>ILPD</td>
<td/>
</tr>
<tr>
<td>11</td>
<td>Kumar et al. (2020) [<xref ref-type="bibr" rid="ref-17">17</xref>]</td>
<td>Variable-NWFKNN</td>
<td>78.46%, 78.46% and 95.79%</td>
<td>BUPA, ILPD, and MPRLPD datasets.</td>
<td/>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
<sec id="s3">
<label>3</label>
<title>Proposed Methodology</title>
<p>The proposed method consists of three stages: noise filtering, fuzzification, and the application of the AdaBoost boosting algorithm with different classifiers.</p>
<sec id="s3_1">
<label>3.1</label>
<title>Noise Removal</title>
<p>The noise filter mechanism eliminates outliers from the dataset. It is an essential technique for noise removal, as real-world datasets are often noisy (LFT datasets are no exception). KNN filter and redundancy-driven Tomek-linked-based undersampling techniques are used to remove noise from minority and majority classes.</p>
<sec id="s3_1_1">
<label>3.1.1</label>
<title>KNN Filter</title>
<p>The KNN filter [<xref ref-type="bibr" rid="ref-21">21</xref>] eliminates outliers from the minority class. It categorizes minority instances into highly desirable samples, moderately desirable samples, and outliers. A sample from the minority class is labeled highly desirable if all the nearest neighbors of that instance belong to the minority class. A sample from the minority class is labeled moderately desirable if all the nearest neighbors of that instance belong to both the minority and majority class. A sample from the minority class is labeled an outlier (or noise) if all the nearest neighbors of that instance belong to the majority class. The procedure of the KNN filter is given in Algorithm 1.</p>
<p>For dataset <italic>D</italic>, <inline-formula id="ieqn-2"><!--<alternatives><inline-graphic xlink:href="ieqn-2.png"/><tex-math id="tex-ieqn-2"><![CDATA[$D_{m}\subset D$]]></tex-math>--><mml:math id="mml-ieqn-2"><mml:msub><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2282;</mml:mo><mml:mi>D</mml:mi></mml:math><!--</alternatives>--></inline-formula> and <inline-formula id="ieqn-3"><!--<alternatives><inline-graphic xlink:href="ieqn-3.png"/><tex-math id="tex-ieqn-3"><![CDATA[$D_{M}\subset D$]]></tex-math>--><mml:math id="mml-ieqn-3"><mml:msub><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mi>M</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2282;</mml:mo><mml:mi>D</mml:mi></mml:math><!--</alternatives>--></inline-formula>. <italic>D<sub>m</sub></italic> and <italic>D<sub>M</sub></italic> are the minority and majority class sample, respectively, in <italic>D</italic>.</p>
<fig id="fig-4">
<graphic mimetype="image" mime-subtype="png" xlink:href="fig-4.png"/>
</fig>
</sec>
<sec id="s3_1_2">
<label>3.1.2</label>
<title>Redundancy-Driven Tomek-Linked Based Under Sampling (R_TLU)</title>
<p>R_TLU [<xref ref-type="bibr" rid="ref-23">23</xref>,<xref ref-type="bibr" rid="ref-43">43</xref>] eliminates Tomek-linked pairs and redundancy from the majority class. A pair of the pattern <italic>p<sub>m</sub></italic> and <italic>p<sub>n</sub></italic> are called a <bold><italic>Tomek-link pair</italic></bold> if <inline-formula id="ieqn-6"><!--<alternatives><inline-graphic xlink:href="ieqn-6.png"/><tex-math id="tex-ieqn-6"><![CDATA[$\neg \exists p_{k}\colon d \left(p_{m}, p_{k}\right)< d \left(p_{m}, p_{n}\right)$]]></tex-math>--><mml:math id="mml-ieqn-6"><mml:mo>&#x00AC;</mml:mo><mml:mo>&#x2203;</mml:mo><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo>:</mml:mo><mml:mi>d</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x003C;</mml:mo><mml:mi>d</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math><!--</alternatives>--></inline-formula>, where <inline-formula id="ieqn-7"><!--<alternatives><inline-graphic xlink:href="ieqn-7.png"/><tex-math id="tex-ieqn-7"><![CDATA[$\mathit{class} \left(p_{m}\right)\neq \mathit{class} \left(p_{n}\right)$]]></tex-math>--><mml:math id="mml-ieqn-7"><mml:mstyle mathvariant="italic"><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:mstyle><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2260;</mml:mo><mml:mstyle mathvariant="italic"><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:mstyle><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math><!--</alternatives>--></inline-formula>. Basically, <italic>p<sub>m</sub></italic> and <italic>p<sub>n</sub></italic> are called boundary instances that promote misclassification. An instance is <bold><italic>redundant</italic></bold> if there exists another instance with an equal ability to perform the same classification task. Redundant pairs are detected based on a similarity measure and can be defined as follows: <inline-formula id="ieqn-8"><!--<alternatives><inline-graphic xlink:href="ieqn-8.png"/><tex-math id="tex-ieqn-8"><![CDATA[$R_{pair}= \left\{ \left(p_{i}, p_{j}\right) \mid \forall p_{i}, p_{j}\in D_{M}\right.$]]></tex-math>--><mml:math id="mml-ieqn-8"><mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi><mml:mi>a</mml:mi><mml:mi>i</mml:mi><mml:mi>r</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2223;</mml:mo><mml:mo>&#x2200;</mml:mo><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2208;</mml:mo><mml:msub><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mi>M</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo></mml:mo></mml:mrow></mml:math><!--</alternatives>--></inline-formula> and similarity <inline-formula id="ieqn-9"><!--<alternatives><inline-graphic xlink:href="ieqn-9.png"/><tex-math id="tex-ieqn-9"><![CDATA[$ \left. \left(p_{i}, p_{j}\right)=\max \right\}$]]></tex-math>--><mml:math id="mml-ieqn-9"><mml:mrow><mml:mo></mml:mo><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mo class="qopname"> max</mml:mo></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:math><!--</alternatives>--></inline-formula>. Based on the contribution factor (<italic>Contr<sub>p</sub></italic>), a redundant majority pattern can be eliminated from a majority redundant pair <inline-formula id="ieqn-10"><!--<alternatives><inline-graphic xlink:href="ieqn-10.png"/><tex-math id="tex-ieqn-10"><![CDATA[$ \left(p_{i}, p_{j}\right)$]]></tex-math>--><mml:math id="mml-ieqn-10"><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math><!--</alternatives>--></inline-formula>, which is defined as follows: <inline-formula id="ieqn-11"><!--<alternatives><inline-graphic xlink:href="ieqn-11.png"/><tex-math id="tex-ieqn-11"><![CDATA[$Contr_{p}=\displaystyle\frac{1}{N}\times \left\{ \left(\displaystyle\sum_{a=1}^{n}\displaystyle\sum_{b=}^{m}\ln f \left(p_{ab}\mid C_{1}\right)\right.\right\}$]]></tex-math>--><mml:math id="mml-ieqn-11"><mml:mi>C</mml:mi><mml:mi>o</mml:mi><mml:mi>n</mml:mi><mml:mi>t</mml:mi><mml:msub><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:mfrac><mml:mo>&#x00D7;</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msubsup><mml:mrow><mml:mo>&#x2211;</mml:mo> </mml:mrow><mml:mrow><mml:mi>a</mml:mi><mml:mo lspace='0pt' rspace='0pt'>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msubsup><mml:msubsup><mml:mrow><mml:mo>&#x2211;</mml:mo> </mml:mrow><mml:mrow><mml:mi>b</mml:mi><mml:mo lspace='0pt' rspace='0pt'>=</mml:mo></mml:mrow><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msubsup><mml:mo class="qopname"> ln</mml:mo><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>a</mml:mi><mml:mi>b</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2223;</mml:mo><mml:msub><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo></mml:mo></mml:mrow></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:math><!--</alternatives>--></inline-formula>, where n is the number of instances, m is the number of attributes of each instance, <inline-formula id="ieqn-12"><!--<alternatives><inline-graphic xlink:href="ieqn-12.png"/><tex-math id="tex-ieqn-12"><![CDATA[$\ln f$]]></tex-math>--><mml:math id="mml-ieqn-12"><mml:mo class="qopname">ln</mml:mo><mml:mi>f</mml:mi></mml:math><!--</alternatives>--></inline-formula> is log likelihood function, and <italic>C</italic><sub>1</sub> is the class label of the majority class. Instances with many redundancies and a low contribution factor are eliminated as defined in <xref ref-type="disp-formula" rid="eqn-1">Eq. (1)</xref>.</p>
<p><disp-formula id="eqn-1">
<label>(1)</label>
<!--<alternatives><graphic mimetype="image" mime-subtype="png" xlink:href="eqn-1.png"/>
<tex-math id="tex-eqn-1"><![CDATA[$$\begin{equation}
Eli_{ \left(p_{i}~ or~ p_{j}\right)}=\max \left(\frac{\text{s}\text{i}\text{m}\text{i}\text{l}\text{arity} \left(p_{i},\,p_{j}\right)}{Contr_{{p_{i}}}},\,
\frac{\text{s}\text{i}\text{m}\text{i}\text{l}\text{arity} \left(p_{i},\,p_{j}\right)}{Contr_{{p_{j}}}}\right),\quad \text{w}\text{h}\text{e}\text{r}\text{e}~ p_{i},\,p_{j}\in R_{pair} \label{eqn-1}
\end{equation}$$]]></tex-math>-->
<mml:math id="mml-eqn-1" display="block"><mml:mi>E</mml:mi><mml:mi>l</mml:mi><mml:msub><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mspace width=".3em" /><mml:mi>o</mml:mi><mml:mi>r</mml:mi><mml:mspace width=".3em" /><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mo> max</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mfrac><mml:mrow><mml:mstyle><mml:mtext>s</mml:mtext></mml:mstyle><mml:mstyle><mml:mtext>i</mml:mtext></mml:mstyle><mml:mstyle><mml:mtext>m</mml:mtext></mml:mstyle><mml:mstyle><mml:mtext>i</mml:mtext></mml:mstyle><mml:mstyle><mml:mtext>l</mml:mtext></mml:mstyle><mml:mstyle><mml:mtext>arity</mml:mtext></mml:mstyle><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mspace width="0.3em"/><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mi>C</mml:mi><mml:mi>o</mml:mi><mml:mi>n</mml:mi><mml:mi>t</mml:mi><mml:msub><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:mfrac><mml:mo>,</mml:mo><mml:mspace width="0.3em"/><mml:mfrac><mml:mrow><mml:mstyle><mml:mtext>s</mml:mtext></mml:mstyle><mml:mstyle><mml:mtext>i</mml:mtext></mml:mstyle><mml:mstyle><mml:mtext>m</mml:mtext></mml:mstyle><mml:mstyle><mml:mtext>i</mml:mtext></mml:mstyle><mml:mstyle><mml:mtext>l</mml:mtext></mml:mstyle><mml:mstyle><mml:mtext>arity</mml:mtext></mml:mstyle><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mspace width="0.3em"/><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mi>C</mml:mi><mml:mi>o</mml:mi><mml:mi>n</mml:mi><mml:mi>t</mml:mi><mml:msub><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mspace width="1em"/><mml:mstyle><mml:mtext>w</mml:mtext></mml:mstyle><mml:mstyle><mml:mtext>h</mml:mtext></mml:mstyle><mml:mstyle><mml:mtext>e</mml:mtext></mml:mstyle><mml:mstyle><mml:mtext>r</mml:mtext></mml:mstyle><mml:mstyle><mml:mtext>e</mml:mtext></mml:mstyle><mml:mspace width=".3em" /><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mspace width="0.3em"/><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2208;</mml:mo><mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi><mml:mi>a</mml:mi><mml:mi>i</mml:mi><mml:mi>r</mml:mi></mml:mrow></mml:msub></mml:math><!--</alternatives>--></disp-formula></p>
</sec>
</sec>
<sec id="s3_2">
<label>3.2</label>
<title>Fuzzification Subsystem</title>
<p>In 1965, Zadeh [<xref ref-type="bibr" rid="ref-44">44</xref>] introduced the concept of the fuzzy set, which deals with uncertainty arising due to the strength of the relationships among the elements of a set [<xref ref-type="bibr" rid="ref-37">37</xref>]. Let <inline-formula id="ieqn-13"><!--<alternatives><inline-graphic xlink:href="ieqn-13.png"/><tex-math id="tex-ieqn-13"><![CDATA[$\overline{U}$]]></tex-math>--><mml:math id="mml-ieqn-13"><mml:mover accent="false" class="mml-overline"><mml:mrow><mml:mi>U</mml:mi></mml:mrow><mml:mo accent="true">&#x00AF;</mml:mo></mml:mover></mml:math><!--</alternatives>--></inline-formula> be a universal set, and let a fuzzy set (<inline-formula id="ieqn-14"><!--<alternatives><inline-graphic xlink:href="ieqn-14.png"/><tex-math id="tex-ieqn-14"><![CDATA[$\overline{X}$]]></tex-math>--><mml:math id="mml-ieqn-14"><mml:mover accent="false" class="mml-overline"><mml:mrow><mml:mi>X</mml:mi></mml:mrow><mml:mo accent="true">&#x00AF;</mml:mo></mml:mover></mml:math><!--</alternatives>--></inline-formula> over <inline-formula id="ieqn-15"><!--<alternatives><inline-graphic xlink:href="ieqn-15.png"/><tex-math id="tex-ieqn-15"><![CDATA[$\overline{U}$]]></tex-math>--><mml:math id="mml-ieqn-15"><mml:mover accent="false" class="mml-overline"><mml:mrow><mml:mi>U</mml:mi></mml:mrow><mml:mo accent="true">&#x00AF;</mml:mo></mml:mover></mml:math><!--</alternatives>--></inline-formula>) be represented as <inline-formula id="ieqn-16"><!--<alternatives><inline-graphic xlink:href="ieqn-16.png"/><tex-math id="tex-ieqn-16"><![CDATA[$\overline{X}= \left\{y, \mu \left(y\right) \mid y \in \overline{U}, \mu \left(y\right)\in \left[0, 1\right]\right\}$]]></tex-math>--><mml:math id="mml-ieqn-16"><mml:mover accent="false" class="mml-overline"><mml:mrow><mml:mi>X</mml:mi></mml:mrow><mml:mo accent="true">&#x00AF;</mml:mo></mml:mover><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mi>y</mml:mi><mml:mo>,</mml:mo><mml:mi>&#x03BC;</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>y</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2223;</mml:mo><mml:mi>y</mml:mi><mml:mo>&#x2208;</mml:mo><mml:mover accent="false" class="mml-overline"><mml:mrow><mml:mi>U</mml:mi></mml:mrow><mml:mo accent="true">&#x00AF;</mml:mo></mml:mover><mml:mo>,</mml:mo><mml:mi>&#x03BC;</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>y</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2208;</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:math><!--</alternatives>--></inline-formula>, where <inline-formula id="ieqn-17"><!--<alternatives><inline-graphic xlink:href="ieqn-17.png"/><tex-math id="tex-ieqn-17"><![CDATA[$\mu \left(y\right)$]]></tex-math>--><mml:math id="mml-ieqn-17"><mml:mi>&#x03BC;</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>y</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math><!--</alternatives>--></inline-formula> represents the degree of membership of <italic>y</italic>. The attribute of liver disorder datasets is transformed into a fuzzy set with a specific membership value using a trapezoidal membership function [<xref ref-type="bibr" rid="ref-33">33</xref>].</p>
<p><disp-formula id="eqn-2">
<label>(2)</label>
<!--<alternatives><graphic mimetype="image" mime-subtype="png" xlink:href="eqn-2.png"/>
<tex-math id="tex-eqn-2"><![CDATA[$$\begin{equation}
f \left(A,\,n_{1},\,n_{2},\,n_{3},\,n_{4}\right)= \left\{\begin{array}{l@{\quad}l@{\quad}l}0 & A < n_{1},~ A> n_{4} \\[8pt]
\displaystyle\frac{ \left(A-n_{1}\right)}{ \left(n_{2}-n_{1}\right)}& n_{1} \leq A \leq n_{2} \\[16pt]
1 & n_{2} \leq A \leq n_{3} \\[8pt]
\displaystyle\frac{ \left(n_{4}-A\right)}{ \left(n_{4}-n_{3}\right)}& n_{3} \leq A \leq n_{4}\end{array}\right. \label{eqn-2}
\end{equation}$$]]></tex-math>-->
<mml:math id="mml-eqn-2" display="block"><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>A</mml:mi><mml:mo>,</mml:mo><mml:mspace width="0.3em"/><mml:msub><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mspace width="0.3em"/><mml:msub><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mspace width="0.3em"/><mml:msub><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mspace width="0.3em"/><mml:msub><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mtable equalrows="false" columnlines="none none" equalcolumns="false"><mml:mtr><mml:mtd columnalign="left"><mml:mn>0</mml:mn><mml:mspace width="1em"/></mml:mtd><mml:mtd columnalign="left"><mml:mi>A</mml:mi><mml:mo>&#x003C;</mml:mo><mml:msub><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mspace width=".3em" /><mml:mi>A</mml:mi><mml:mo>&#x003E;</mml:mo><mml:msub><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub><mml:mspace width="1em"/></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign="left"><mml:mfrac><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>A</mml:mi><mml:mo>-</mml:mo><mml:msub><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mfrac><mml:mspace width="1em"/></mml:mtd><mml:mtd columnalign="left"><mml:msub><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>&#x2264;</mml:mo><mml:mi>A</mml:mi><mml:mo>&#x2264;</mml:mo><mml:msub><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mspace width="1em"/></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign="left"><mml:mn>1</mml:mn><mml:mspace width="1em"/></mml:mtd><mml:mtd columnalign="left"><mml:msub><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>&#x2264;</mml:mo><mml:mi>A</mml:mi><mml:mo>&#x2264;</mml:mo><mml:msub><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub><mml:mspace width="1em"/></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign="left"><mml:mfrac><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mfrac><mml:mspace width="1em"/></mml:mtd><mml:mtd columnalign="left"><mml:msub><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub><mml:mo>&#x2264;</mml:mo><mml:mi>A</mml:mi><mml:mo>&#x2264;</mml:mo><mml:msub><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub><mml:mspace width="1em"/></mml:mtd></mml:mtr> </mml:mtable></mml:mrow><mml:mo></mml:mo></mml:mrow></mml:math><!--</alternatives>--></disp-formula></p>
<p>Here, <inline-formula id="ieqn-18"><!--<alternatives><inline-graphic xlink:href="ieqn-18.png"/><tex-math id="tex-ieqn-18"><![CDATA[$n_{1}, n_{2}, n_{3}$]]></tex-math>--><mml:math id="mml-ieqn-18"><mml:msub><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:math><!--</alternatives>--></inline-formula> and <italic>n</italic><sub>4</sub> are applied to determine the membership values of the attribute value <italic>A</italic>.</p>
</sec>
<sec id="s3_3">
<label>3.3</label>
<title>Description and Fuzzification of Datasets</title>
<p>Numerous studies were performed using machine learning techniques. However, liver disease predictions remain underexplored. So, the ILPD and MPRLPD datasets are used in the evaluation of this study. The ILPD dataset consists of 583 records obtained from two classes of liver patients (416 patients suffering from a liver disorder and 167 suffering from non-liver disorders). This dataset was collected from the UCI repository [<xref ref-type="bibr" rid="ref-45">45</xref>], and it has 10 features. The MPRLPD dataset consists of 7865 liver patient records. Of these patients, 6282 had some kind of liver disease, and the other 1583 were healthy. This dataset consists of 12 features and was collected from Madhya Pradesh in the Bhopal region of India. The dataset&#x2019;s statistics (after eliminating noise, or outliers, from the minority and majority classes) are shown in <xref ref-type="table" rid="table-3">Tab. 3</xref>.</p>
<table-wrap id="table-3">
<label>Table 3</label>
<caption>
<title>Datasets&#x2019; statistics</title>
</caption>
<!---->
<table>
<colgroup>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th>Dataset</th>
<th>#Instances</th>
<th>#Attributes</th>
<th colspan="3">Before outlier elimination</th>
<th colspan="3">After outlier elimination</th>
</tr>
<tr>
<th></th>
<th></th>
<th></th>
<th>#Minority instances</th>
<th>#Majority instances</th>
<th>Imbalance ratio (IR)</th>
<th>#Minority instances</th>
<th>#Majority instances</th>
<th>Imbalance ratio (IR)</th>
</tr>
</thead>
<tbody>
<tr>
<td>ILPD</td>
<td>583</td>
<td>10</td>
<td>167</td>
<td>416</td>
<td>2.5</td>
<td>151</td>
<td>202</td>
<td>1.34</td>
</tr>
<tr>
<td>MPRLPD</td>
<td>7865</td>
<td>12</td>
<td>1583</td>
<td>6282</td>
<td>3.97</td>
<td>1441</td>
<td>2923</td>
<td>2.03</td>
</tr>
</tbody>
</table>
</table-wrap>
<fig id="fig-2">
<label>Figure 2</label>
<caption>
<title>Fuzzification of the numerical features of ILPD datasets 
</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="fig-2a.png"/>
<graphic mimetype="image" mime-subtype="png" xlink:href="fig-2b.png"/>
</fig>
<sec id="s3_3_1">
<label>3.3.1</label>
<title>Fuzzification of the ILPD Dataset</title>
<p>ILPD [<xref ref-type="bibr" rid="ref-45">45</xref>] dataset has nine attributes with the numerical datatype. During fuzzification, six features, namely age, AlkPhos, SGPT, SGOT, TP, and albumin, are represented by three fuzzy variables. Total bilirubin (TB) and direct bilirubin (DB) are represented by four variables. The remaining attribute (A/G ratio) is represented by two variables. <xref ref-type="fig" rid="fig-2">Fig. 2</xref> illustrates the fuzzification of the ILPD dataset using the membership function mentioned in <xref ref-type="disp-formula" rid="eqn-2">Eq. (2)</xref>.</p>
</sec>
<sec id="s3_3_2">
<label>3.3.2</label>
<title>Fuzzification of the MPRLPD Dataset</title>
<p>The MPRLPD dataset has 11 attributes with a numerical datatype. During fuzzification, seven attributes, namely age, TB, IB, SGPT, SGOT, TP, and A/G ratio, are represented by three variables, whereas AlkPhos is represented by three and four variables for children and adults, respectively. The remaining attributes (DB and albumin) are represented by four and two variables, respectively.</p>
</sec>
</sec>
<sec id="s3_4">
<label>3.4</label>
<title>Classification Subsystem</title>
<p>The classification subsystem implements the boosting technique to improve the performance of the classifier for imbalanced datasets. The boosting technique builds a strong classifier from several weak classifiers. Weak classifiers are algorithms whose error rate is less than random guessing (50%). In the proposed work, classification is done using the AdaBoost boosting algorithm [<xref ref-type="bibr" rid="ref-46">46</xref>,<xref ref-type="bibr" rid="ref-47">47</xref>]. The steps used in the AdaBoost algorithm are given below.</p>
<p><bold><italic>Initialization step:</italic></bold> <inline-formula id="ieqn-19"><!--<alternatives><inline-graphic xlink:href="ieqn-19.png"/><tex-math id="tex-ieqn-19"><![CDATA[$\forall p\in D$]]></tex-math>--><mml:math id="mml-ieqn-19"><mml:mo>&#x2200;</mml:mo><mml:mi>p</mml:mi><mml:mo>&#x2208;</mml:mo><mml:mi>D</mml:mi></mml:math><!--</alternatives>--></inline-formula>, set
<disp-formula id="eqn-3">
<!--<alternatives><graphic mimetype="image" mime-subtype="png" xlink:href="eqn-3.png"/>-->
<mml:math id="mml-eqn-3" display="block"><mml:mrow><mml:mi>&#x03C9;</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>P</mml:mi></mml:mrow></mml:mfrac><mml:mo>,</mml:mo><mml:mspace width="1em"/><mml:mstyle><mml:mtext>where&#x00A0;</mml:mtext><mml:mi>P</mml:mi><mml:mtext>&#x00A0;is&#x00A0;the&#x00A0;total&#x00A0;number&#x00A0;of&#x00A0;patterns.</mml:mtext></mml:mstyle></mml:mrow></mml:math>
<!--</alternatives>--></disp-formula>
</p>
<p><bold><italic>Iteration step</italic></bold>: for <inline-formula id="ieqn-20"><!--<alternatives><inline-graphic xlink:href="ieqn-20.png"/><tex-math id="tex-ieqn-20"><![CDATA[$\ttextit{k}= 1$]]></tex-math>--><mml:math id="mml-ieqn-20"><mml:mstyle class="text"><mml:mtext class="textit" mathvariant="italic">k</mml:mtext></mml:mstyle><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:math><!--</alternatives>--></inline-formula> to <italic>K</italic></p>
<p>1) Based on the weight <inline-formula id="ieqn-21"><!--<alternatives><inline-graphic xlink:href="ieqn-21.png"/><tex-math id="tex-ieqn-21"><![CDATA[$\omega \left(p\right)$]]></tex-math>--><mml:math id="mml-ieqn-21"><mml:mi>&#x03C9;</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math><!--</alternatives>--></inline-formula>, find the best weak classifier <inline-formula id="ieqn-22"><!--<alternatives><inline-graphic xlink:href="ieqn-22.png"/><tex-math id="tex-ieqn-22"><![CDATA[$h_{k} \left(p\right)$]]></tex-math>--><mml:math id="mml-ieqn-22"><mml:msub><mml:mrow><mml:mi>h</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math><!--</alternatives>--></inline-formula></p>
<p>2) Compute total error as <inline-formula id="ieqn-23"><!--<alternatives><inline-graphic xlink:href="ieqn-23.png"/><tex-math id="tex-ieqn-23"><![CDATA[$Total_{\mathit{error}}$]]></tex-math>--><mml:math id="mml-ieqn-23"><mml:mi>T</mml:mi><mml:mi>o</mml:mi><mml:mi>t</mml:mi><mml:mi>a</mml:mi><mml:msub><mml:mrow><mml:mi>l</mml:mi></mml:mrow><mml:mrow><mml:mstyle mathvariant="italic"><mml:mi>e</mml:mi><mml:mi>r</mml:mi><mml:mi>r</mml:mi><mml:mi>o</mml:mi><mml:mi>r</mml:mi></mml:mstyle></mml:mrow></mml:msub></mml:math><!--</alternatives>--></inline-formula>
<disp-formula id="eqn-4">
<!--<alternatives><graphic mimetype="image" mime-subtype="png" xlink:href="eqn-4.png"/>
<tex-math id="tex-eqn-4"><![CDATA[$$\begin{eqnarray*}
Total_{\mathit{error}}=\sum_{i=1}^{P}\omega \left(p^{i}\right).1 \left\{\begin{array}{l@{\quad}l}
1 & if~ \left[y^{i}\neq h_{k} \left(p^{i}\right)\right] \\[10pt]
0 & \mathit{otherwise}\end{array}\right.
\end{eqnarray*}$$]]></tex-math>-->
<mml:math id="mml-eqn-4" display="block"><mml:mrow><mml:mi>T</mml:mi><mml:mi>o</mml:mi><mml:mi>t</mml:mi><mml:mi>a</mml:mi><mml:msub><mml:mrow><mml:mi>l</mml:mi></mml:mrow><mml:mrow><mml:mstyle mathvariant="italic"><mml:mi>e</mml:mi><mml:mi>r</mml:mi><mml:mi>r</mml:mi><mml:mi>o</mml:mi><mml:mi>r</mml:mi></mml:mstyle></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle='true'><mml:mstyle displaystyle='true'><mml:munderover><mml:mrow><mml:mo>&#x2211;</mml:mo> </mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo lspace='0pt' rspace='0pt'>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>P</mml:mi></mml:mrow></mml:munderover></mml:mstyle></mml:mstyle><mml:mi>&#x03C9;</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msup><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msup></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>.</mml:mo><mml:mn>1</mml:mn><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mtable equalrows="false" columnlines="none" equalcolumns="false"><mml:mtr><mml:mtd columnalign="left"><mml:mn>1</mml:mn><mml:mspace width="1em"/></mml:mtd><mml:mtd columnalign="left"><mml:mi>i</mml:mi><mml:mi>f</mml:mi><mml:mspace width=".3em" /><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:msup><mml:mrow><mml:mi>y</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msup><mml:mo>&#x2260;</mml:mo><mml:msub><mml:mrow><mml:mi>h</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msup><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign="left"><mml:mn>0</mml:mn><mml:mspace width="1em"/></mml:mtd><mml:mtd columnalign="left"><mml:mstyle mathvariant="italic"><mml:mi>o</mml:mi><mml:mi>t</mml:mi><mml:mi>h</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi><mml:mi>w</mml:mi><mml:mi>i</mml:mi><mml:mi>s</mml:mi><mml:mi>e</mml:mi></mml:mstyle></mml:mtd></mml:mtr> </mml:mtable></mml:mrow><mml:mo></mml:mo></mml:mrow></mml:mrow></mml:math><!--</alternatives>--></disp-formula>
</p>
<p>3) Compute weight <inline-formula id="ieqn-24"><!--<alternatives><inline-graphic xlink:href="ieqn-24.png"/><tex-math id="tex-ieqn-24"><![CDATA[$\alpha _{k}$]]></tex-math>--><mml:math id="mml-ieqn-24"><mml:msub><mml:mrow><mml:mi>&#x03B1;</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:math><!--</alternatives>--></inline-formula>
<disp-formula id="eqn-5">
<!--<alternatives><graphic mimetype="image" mime-subtype="png" xlink:href="eqn-5.png"/>
<tex-math id="tex-eqn-5"><![CDATA[$$\begin{eqnarray*}
\alpha _{k}=\frac{1}{2}\log \left(\frac{1-Total_{\mathit{error}}}{Total_{\mathit{error}}}\right)
\end{eqnarray*}$$]]></tex-math>-->
<mml:math id="mml-eqn-5" display="block"><mml:mrow><mml:msub><mml:mrow><mml:mi>&#x03B1;</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:mfrac><mml:mo>log</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mfrac><mml:mrow><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:mi>T</mml:mi><mml:mi>o</mml:mi><mml:mi>t</mml:mi><mml:mi>a</mml:mi><mml:msub><mml:mrow><mml:mi>l</mml:mi></mml:mrow><mml:mrow><mml:mstyle mathvariant="italic"><mml:mi>e</mml:mi><mml:mi>r</mml:mi><mml:mi>r</mml:mi><mml:mi>o</mml:mi><mml:mi>r</mml:mi></mml:mstyle></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi>T</mml:mi><mml:mi>o</mml:mi><mml:mi>t</mml:mi><mml:mi>a</mml:mi><mml:msub><mml:mrow><mml:mi>l</mml:mi></mml:mrow><mml:mrow><mml:mstyle mathvariant="italic"><mml:mi>e</mml:mi><mml:mi>r</mml:mi><mml:mi>r</mml:mi><mml:mi>o</mml:mi><mml:mi>r</mml:mi></mml:mstyle></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math><!--</alternatives>--></disp-formula>
</p>
<p>4) Update the weight for misclassified patterns
<disp-formula id="eqn-6">
<!--<alternatives><graphic mimetype="image" mime-subtype="png" xlink:href="eqn-6.png"/>
<tex-math id="tex-eqn-6"><![CDATA[$$\begin{eqnarray*}
\omega \left(p\right)=\omega \left(p\right).e^{{a_{k}}}
\end{eqnarray*}$$]]></tex-math>-->
<mml:math id="mml-eqn-6" display="block"><mml:mrow><mml:mi>&#x03C9;</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>&#x03C9;</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>.</mml:mo><mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:msup></mml:mrow></mml:math><!--</alternatives>--></disp-formula>
</p>
<p>5) Normalize the weight so that <inline-formula id="ieqn-25"><!--<alternatives><inline-graphic xlink:href="ieqn-25.png"/><tex-math id="tex-ieqn-25"><![CDATA[$\displaystyle\sum_{i=1}^{P}\omega \left(p^{i}\right)=1$]]></tex-math>--><mml:math id="mml-ieqn-25"><mml:munderover><mml:mrow><mml:mo>&#x2211;</mml:mo></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo lspace='0pt' rspace='0pt'>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>P</mml:mi></mml:mrow></mml:munderover><mml:mi>&#x03C9;</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msup><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msup></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:math><!--</alternatives>--></inline-formula></p>
<p>6) Output of the final classifier
<disp-formula id="eqn-7">
<!--<alternatives><graphic mimetype="image" mime-subtype="png" xlink:href="eqn-7.png"/>
<tex-math id="tex-eqn-7"><![CDATA[$$\begin{eqnarray*}
F_{\mathit{output}} \left(p\right)=sign \left(\sum_{k=1}^{K}\alpha _{k}h_{k} \left(p\right)\right)
\end{eqnarray*}$$]]></tex-math>-->
<mml:math id="mml-eqn-7" display="block"><mml:mrow><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mstyle mathvariant="italic"><mml:mi>o</mml:mi><mml:mi>u</mml:mi><mml:mi>t</mml:mi><mml:mi>p</mml:mi><mml:mi>u</mml:mi><mml:mi>t</mml:mi></mml:mstyle></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><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:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mstyle displaystyle='true'><mml:mstyle displaystyle='true'><mml:munderover><mml:mrow><mml:mo>&#x2211;</mml:mo> </mml:mrow><mml:mrow><mml:mi>k</mml:mi><mml:mo lspace='0pt' rspace='0pt'>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>K</mml:mi></mml:mrow></mml:munderover></mml:mstyle></mml:mstyle><mml:msub><mml:mrow><mml:mi>&#x03B1;</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>h</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math><!--</alternatives>--></disp-formula>
</p>
</sec>
</sec>
<sec id="s4">
<label>4</label>
<title>Results and Discussion</title>
<p>This section presents the evaluation of the NFFBT approach&#x2019;s performance. The proposed approach is evaluated based on two datasets. One dataset is a benchmark dataset collected from the UCI repository, and the other is collected from a local hospital in Bhopal, India. Both datasets have two classes. RF [<xref ref-type="bibr" rid="ref-47">47</xref>], SVM [<xref ref-type="bibr" rid="ref-48">48</xref>], LR [<xref ref-type="bibr" rid="ref-49">49</xref>], and NB [<xref ref-type="bibr" rid="ref-6">6</xref>] machine learning algorithms are applied with a boosting technique on data prepared using the NFFBT approach (outlier-free datasets), as well as on original datasets. MATLAB R 2014a and Python are used to conduct the experiment. The NFFBT approach is implemented using MATLAB R 2014a, and classifications are performed using Python.</p>
<p>The performance of the proposed model is validated according to measures that are calculated based on the values of the confusion matrix. The confusion matrix [<xref ref-type="bibr" rid="ref-50">50</xref>] summarizes the predicted results of a classifier (<xref ref-type="table" rid="table-4">Tab. 4</xref>). The performance measures&#x2014;namely accuracy (Accu), specificity (Spec), sensitivity (Sens), precision (Prec), false positive rate (<inline-formula id="ieqn-26"><!--<alternatives><inline-graphic xlink:href="ieqn-26.png"/><tex-math id="tex-ieqn-26"><![CDATA[$\text{F}\text{P}_{\text{r}\text{a}\text{t}\text{e}}$]]></tex-math>--><mml:math id="mml-ieqn-26"><mml:mstyle class="text"><mml:mtext>F</mml:mtext></mml:mstyle><mml:msub><mml:mrow><mml:mstyle class="text"><mml:mtext>P</mml:mtext></mml:mstyle></mml:mrow><mml:mrow><mml:mstyle class="text"><mml:mtext>r</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>t</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>e</mml:mtext></mml:mstyle></mml:mrow></mml:msub></mml:math><!--</alternatives>--></inline-formula>), false negative rate (<inline-formula id="ieqn-27"><!--<alternatives><inline-graphic xlink:href="ieqn-27.png"/><tex-math id="tex-ieqn-27"><![CDATA[$\text{F}\text{N}_{\text{r}\text{a}\text{t}\text{e}}$]]></tex-math>--><mml:math id="mml-ieqn-27"><mml:mstyle class="text"><mml:mtext>F</mml:mtext></mml:mstyle><mml:msub><mml:mrow><mml:mstyle class="text"><mml:mtext>N</mml:mtext></mml:mstyle></mml:mrow><mml:mrow><mml:mstyle class="text"><mml:mtext>r</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>t</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>e</mml:mtext></mml:mstyle></mml:mrow></mml:msub></mml:math><!--</alternatives>--></inline-formula>), F1-score, G-mean, and area under the curve (AUC)&#x2014;are used to appraise the developed model, (<xref ref-type="table" rid="table-5">Tab. 5</xref>). The results are evaluated using a 10-fold cross-validation technique over the mentioned measures.</p>
<table-wrap id="table-4">
<label>Table 4</label>
<caption>
<title>Confusion matrix (CM)</title>
</caption>
<!---->
<table>
<colgroup>
<col/>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th>Actual class</th>
<th>Predicted class</th>
<th>Outcome</th>
</tr>
</thead>
<tbody>
<tr>
<td>Disease (unhealthy)</td>
<td>Disease</td>
<td>True positive (TP)</td>
</tr>
<tr>
<td>Disease (unhealthy)</td>
<td>No disease</td>
<td>False positive (FP)</td>
</tr>
<tr>
<td>No disease (healthy)</td>
<td>No disease</td>
<td>True negative (TN)</td>
</tr>
<tr>
<td>No disease (healthy)</td>
<td>Disease</td>
<td>False negative (FN)</td>
</tr>
</tbody>
</table>
</table-wrap>
<p><xref ref-type="table" rid="table-6">Tabs. 6</xref> and <xref ref-type="table" rid="table-8">8</xref> show the results of original datasets, whereas <xref ref-type="table" rid="table-7">Tabs. 7</xref> and <xref ref-type="table" rid="table-9">9</xref> show the results on outlier-free datasets. <xref ref-type="table" rid="table-6">Tab. 6</xref> contains the results of the original ILPD dataset. For this dataset, Accu (78.39%), Spec (64.34%), Prec (87.74%), <inline-formula id="ieqn-28"><!--<alternatives><inline-graphic xlink:href="ieqn-28.png"/><tex-math id="tex-ieqn-28"><![CDATA[$\text{F}\text{P}_{\text{r}\text{a}\text{t}\text{e}}$]]></tex-math>--><mml:math id="mml-ieqn-28"><mml:mstyle class="text"><mml:mtext>F</mml:mtext></mml:mstyle><mml:msub><mml:mrow><mml:mstyle class="text"><mml:mtext>P</mml:mtext></mml:mstyle></mml:mrow><mml:mrow><mml:mstyle class="text"><mml:mtext>r</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>t</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>e</mml:mtext></mml:mstyle></mml:mrow></mml:msub></mml:math><!--</alternatives>--></inline-formula> (35.66%), F1-score (85.28%), G-mean (73.05%), and AUC. (73.65%) are better obtained using AdaBoost with RF. Meanwhile, Sens. (96.38%) and <inline-formula id="ieqn-29"><!--<alternatives><inline-graphic xlink:href="ieqn-29.png"/><tex-math id="tex-ieqn-29"><![CDATA[$\text{F}\text{N}_{\text{r}\text{a}\text{t}\text{e}}$]]></tex-math>--><mml:math id="mml-ieqn-29"><mml:mstyle class="text"><mml:mtext>F</mml:mtext></mml:mstyle><mml:msub><mml:mrow><mml:mstyle class="text"><mml:mtext>N</mml:mtext></mml:mstyle></mml:mrow><mml:mrow><mml:mstyle class="text"><mml:mtext>r</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>t</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>e</mml:mtext></mml:mstyle></mml:mrow></mml:msub></mml:math><!--</alternatives>--></inline-formula> (3.62%) are better obtained using AdaBoost with NB.</p>
<table-wrap id="table-5">
<label>Table 5</label>
<caption>
<title>Performance measures</title>
</caption>
<!---->
<table>
<colgroup>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th>Measures</th>
<th>Formula</th>
</tr>
</thead>
<tbody>
<tr>
<td>Accu</td>
<td><inline-formula id="ieqn-30"><!--<alternatives><inline-graphic xlink:href="ieqn-30.png"/><tex-math id="tex-ieqn-30"><![CDATA[$\displaystyle\frac{TP+TN}{TP+FP+TN+FN}$]]></tex-math>--><mml:math id="mml-ieqn-30"><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><!--</alternatives>--></inline-formula></td>
</tr>
<tr>
<td>Spec (<inline-formula id="ieqn-31"><!--<alternatives><inline-graphic xlink:href="ieqn-31.png"/><tex-math id="tex-ieqn-31"><![CDATA[$\text{T}\text{N}_{\text{r}\text{a}\text{t}\text{e}}$]]></tex-math>--><mml:math id="mml-ieqn-31"><mml:mstyle class="text"><mml:mtext>T</mml:mtext></mml:mstyle><mml:msub><mml:mrow><mml:mstyle class="text"><mml:mtext>N</mml:mtext></mml:mstyle></mml:mrow><mml:mrow><mml:mstyle class="text"><mml:mtext>r</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>t</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>e</mml:mtext></mml:mstyle></mml:mrow></mml:msub></mml:math><!--</alternatives>--></inline-formula>)</td>
<td><inline-formula id="ieqn-32"><!--<alternatives><inline-graphic xlink:href="ieqn-32.png"/><tex-math id="tex-ieqn-32"><![CDATA[$\displaystyle\frac{TN}{TN+FP}$]]></tex-math>--><mml:math id="mml-ieqn-32"><mml:mfrac><mml:mrow><mml:mi>T</mml:mi><mml:mi>N</mml:mi></mml:mrow><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:mfrac></mml:math><!--</alternatives>--></inline-formula></td>
</tr>
<tr>
<td>Sens (<inline-formula id="ieqn-33"><!--<alternatives><inline-graphic xlink:href="ieqn-33.png"/><tex-math id="tex-ieqn-33"><![CDATA[$\text{T}\text{P}_{\text{r}\text{a}\text{t}\text{e}}$]]></tex-math>--><mml:math id="mml-ieqn-33"><mml:mstyle class="text"><mml:mtext>T</mml:mtext></mml:mstyle><mml:msub><mml:mrow><mml:mstyle class="text"><mml:mtext>P</mml:mtext></mml:mstyle></mml:mrow><mml:mrow><mml:mstyle class="text"><mml:mtext>r</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>t</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>e</mml:mtext></mml:mstyle></mml:mrow></mml:msub></mml:math><!--</alternatives>--></inline-formula>)</td>
<td><inline-formula id="ieqn-34"><!--<alternatives><inline-graphic xlink:href="ieqn-34.png"/><tex-math id="tex-ieqn-34"><![CDATA[$\displaystyle\frac{TP}{TP+FN}$]]></tex-math>--><mml:math id="mml-ieqn-34"><mml:mfrac><mml:mrow><mml:mi>T</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>N</mml:mi></mml:mrow></mml:mfrac></mml:math><!--</alternatives>--></inline-formula></td>
</tr>
<tr>
<td>Prec</td>
<td><inline-formula id="ieqn-35"><!--<alternatives><inline-graphic xlink:href="ieqn-35.png"/><tex-math id="tex-ieqn-35"><![CDATA[$\displaystyle\frac{TP}{TP+FP}$]]></tex-math>--><mml:math id="mml-ieqn-35"><mml:mfrac><mml:mrow><mml:mi>T</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:mrow></mml:mfrac></mml:math><!--</alternatives>--></inline-formula></td>
</tr>
<tr>
<td><inline-formula id="ieqn-36"><!--<alternatives><inline-graphic xlink:href="ieqn-36.png"/><tex-math id="tex-ieqn-36"><![CDATA[$\text{F}\text{P}_{\text{r}\text{a}\text{t}\text{e}}$]]></tex-math>--><mml:math id="mml-ieqn-36"><mml:mstyle class="text"><mml:mtext>F</mml:mtext></mml:mstyle><mml:msub><mml:mrow><mml:mstyle class="text"><mml:mtext>P</mml:mtext></mml:mstyle></mml:mrow><mml:mrow><mml:mstyle class="text"><mml:mtext>r</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>t</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>e</mml:mtext></mml:mstyle></mml:mrow></mml:msub></mml:math><!--</alternatives>--></inline-formula></td>
<td><inline-formula id="ieqn-37"><!--<alternatives><inline-graphic xlink:href="ieqn-37.png"/><tex-math id="tex-ieqn-37"><![CDATA[$\displaystyle\frac{FP}{TN+FP}$]]></tex-math>--><mml:math id="mml-ieqn-37"><mml:mfrac><mml:mrow><mml:mi>F</mml:mi><mml:mi>P</mml:mi></mml:mrow><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:mfrac></mml:math><!--</alternatives>--></inline-formula></td>
</tr>
<tr>
<td><inline-formula id="ieqn-38"><!--<alternatives><inline-graphic xlink:href="ieqn-38.png"/><tex-math id="tex-ieqn-38"><![CDATA[$\text{F}\text{N}_{\text{r}\text{a}\text{t}\text{e}}$]]></tex-math>--><mml:math id="mml-ieqn-38"><mml:mstyle class="text"><mml:mtext>F</mml:mtext></mml:mstyle><mml:msub><mml:mrow><mml:mstyle class="text"><mml:mtext>N</mml:mtext></mml:mstyle></mml:mrow><mml:mrow><mml:mstyle class="text"><mml:mtext>r</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>t</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>e</mml:mtext></mml:mstyle></mml:mrow></mml:msub></mml:math><!--</alternatives>--></inline-formula></td>
<td><inline-formula id="ieqn-39"><!--<alternatives><inline-graphic xlink:href="ieqn-39.png"/><tex-math id="tex-ieqn-39"><![CDATA[$\displaystyle\frac{FN}{TP+FN}$]]></tex-math>--><mml:math id="mml-ieqn-39"><mml:mfrac><mml:mrow><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>N</mml:mi></mml:mrow></mml:mfrac></mml:math><!--</alternatives>--></inline-formula></td>
</tr>
<tr>
<td>F1-score</td>
<td><inline-formula id="ieqn-40"><!--<alternatives><inline-graphic xlink:href="ieqn-40.png"/><tex-math id="tex-ieqn-40"><![CDATA[$\displaystyle\frac{2 * TP}{2 * TP+FP+FN}$]]></tex-math>--><mml:math id="mml-ieqn-40"><mml:mfrac><mml:mrow><mml:mn>2</mml:mn><mml:mo>*</mml:mo><mml:mi>T</mml:mi><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mo>*</mml:mo><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>F</mml:mi><mml:mi>N</mml:mi></mml:mrow></mml:mfrac></mml:math><!--</alternatives>--></inline-formula></td>
</tr>
<tr>
<td>G-mean</td>
<td><inline-formula id="ieqn-41"><!--<alternatives><inline-graphic xlink:href="ieqn-41.png"/><tex-math id="tex-ieqn-41"><![CDATA[$\sqrt{\text{T}\text{P}_{\text{r}\text{a}\text{t}\text{e}}\times \mathrm{TN}_{\text{r}\text{a}\text{t}\text{e}}}$]]></tex-math>--><mml:math id="mml-ieqn-41"><mml:msqrt><mml:mrow><mml:mstyle class="text"><mml:mtext>T</mml:mtext></mml:mstyle><mml:msub><mml:mrow><mml:mstyle class="text"><mml:mtext>P</mml:mtext></mml:mstyle></mml:mrow><mml:mrow><mml:mstyle class="text"><mml:mtext>r</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>t</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>e</mml:mtext></mml:mstyle></mml:mrow></mml:msub><mml:mo>&#x00D7;</mml:mo><mml:msub><mml:mrow><mml:mstyle mathvariant="normal"><mml:mi>T</mml:mi><mml:mi>N</mml:mi></mml:mstyle></mml:mrow><mml:mrow><mml:mstyle class="text"><mml:mtext>r</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>t</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>e</mml:mtext></mml:mstyle></mml:mrow></mml:msub></mml:mrow></mml:msqrt></mml:math><!--</alternatives>--></inline-formula></td>
</tr>
<tr>
<td>AUC</td>
<td><inline-formula id="ieqn-42"><!--<alternatives><inline-graphic xlink:href="ieqn-42.png"/><tex-math id="tex-ieqn-42"><![CDATA[$\displaystyle\frac{1+TP_{rate}-FP_{rate}}{2}$]]></tex-math>--><mml:math id="mml-ieqn-42"><mml:mfrac><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mi>T</mml:mi><mml:msub><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mi>e</mml:mi></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:mi>F</mml:mi><mml:msub><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mi>e</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:mfrac></mml:math><!--</alternatives>--></inline-formula></td>
</tr>
</tbody>
</table>
</table-wrap>
 
<table-wrap id="table-6">
<label>Table 6</label>
<caption>
<title>Original ILPD dataset</title>
</caption>
<!---->
<table>
<colgroup>
<col/>
<col/>
<col/>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th>Performance measures</th>
<th><inline-formula id="ieqn-43"><!--<alternatives><inline-graphic xlink:href="ieqn-43.png"/><tex-math id="tex-ieqn-43"><![CDATA[$\text{A}\text{d}\text{a}\text{B}\text{o}\text{ost}+ \text{R}\text{F}$]]></tex-math>--><mml:math id="mml-ieqn-43"><mml:mstyle class="text"><mml:mtext>A</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>d</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>B</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>o</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>ost</mml:mtext></mml:mstyle><mml:mo>+</mml:mo><mml:mstyle class="text"><mml:mtext>R</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>F</mml:mtext></mml:mstyle></mml:math><!--</alternatives>--></inline-formula></th>
<th><inline-formula id="ieqn-44"><!--<alternatives><inline-graphic xlink:href="ieqn-44.png"/><tex-math id="tex-ieqn-44"><![CDATA[$\text{A}\text{d}\text{a}\text{B}\text{o}\text{ost}+ \text{S}\text{V}\text{M}$]]></tex-math>--><mml:math id="mml-ieqn-44"><mml:mstyle class="text"><mml:mtext>A</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>d</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>B</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>o</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>ost</mml:mtext></mml:mstyle><mml:mo>+</mml:mo><mml:mstyle class="text"><mml:mtext>S</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>V</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>M</mml:mtext></mml:mstyle></mml:math><!--</alternatives>--></inline-formula></th>
<th><inline-formula id="ieqn-45"><!--<alternatives><inline-graphic xlink:href="ieqn-45.png"/><tex-math id="tex-ieqn-45"><![CDATA[$\text{A}\text{d}\text{a}\text{B}\text{o}\text{ost}+ \text{Logistic R}$]]></tex-math>--><mml:math id="mml-ieqn-45"><mml:mstyle class="text"><mml:mtext>A</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>d</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>B</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>o</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>ost</mml:mtext></mml:mstyle><mml:mo>+</mml:mo><mml:mstyle class="text"><mml:mtext>Logistic&#x00A0;R</mml:mtext></mml:mstyle></mml:math><!--</alternatives>--></inline-formula></th>
<th><inline-formula id="ieqn-46"><!--<alternatives><inline-graphic xlink:href="ieqn-46.png"/><tex-math id="tex-ieqn-46"><![CDATA[$\text{A}\text{d}\text{a}\text{B}\text{o}\text{ost}+ \text{N}\text{B}$]]></tex-math>--><mml:math id="mml-ieqn-46"><mml:mstyle class="text"><mml:mtext>A</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>d</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>B</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>o</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>ost</mml:mtext></mml:mstyle><mml:mo>+</mml:mo><mml:mstyle class="text"><mml:mtext>N</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>B</mml:mtext></mml:mstyle></mml:math><!--</alternatives>--></inline-formula></th>
</tr>
</thead>
<tbody>
<tr>
<td>Accu</td>
<td>78.39</td>
<td>73.58</td>
<td>75.64</td>
<td>63.81</td>
</tr>
<tr>
<td>Spec</td>
<td>64.34</td>
<td>55.28</td>
<td>55.36</td>
<td>43.92</td>
</tr>
<tr>
<td>Sens</td>
<td>82.95</td>
<td>78.48</td>
<td>89.14</td>
<td>96.38</td>
</tr>
<tr>
<td>Prec</td>
<td>87.74</td>
<td>86.78</td>
<td>75.00</td>
<td>51.20</td>
</tr>
<tr>
<td>FP<inline-formula id="ieqn-47"><!--<alternatives><inline-graphic xlink:href="ieqn-47.png"/><tex-math id="tex-ieqn-47"><![CDATA[$_{\text{r}\text{a}\text{t}\text{e}}$]]></tex-math>--><mml:math id="mml-ieqn-47"><mml:msub><mml:mrow></mml:mrow><mml:mrow><mml:mstyle class="text"><mml:mtext>r</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>t</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>e</mml:mtext></mml:mstyle></mml:mrow></mml:msub></mml:math><!--</alternatives>--></inline-formula></td>
<td>35.66</td>
<td>44.72</td>
<td>44.64</td>
<td>56.08</td>
</tr>
<tr>
<td>FN<inline-formula id="ieqn-48"><!--<alternatives><inline-graphic xlink:href="ieqn-48.png"/><tex-math id="tex-ieqn-48"><![CDATA[$_{\text{r}\text{a}\text{t}\text{e}}$]]></tex-math>--><mml:math id="mml-ieqn-48"><mml:msub><mml:mrow></mml:mrow><mml:mrow><mml:mstyle class="text"><mml:mtext>r</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>t</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>e</mml:mtext></mml:mstyle></mml:mrow></mml:msub></mml:math><!--</alternatives>--></inline-formula></td>
<td>17.05</td>
<td>21.52</td>
<td>10.86</td>
<td>3.62</td>
</tr>
<tr>
<td>F1-score</td>
<td>85.28</td>
<td>82.42</td>
<td>81.46</td>
<td>66.88</td>
</tr>
<tr>
<td>G-mean</td>
<td>73.05</td>
<td>65.87</td>
<td>70.25</td>
<td>65.06</td>
</tr>
<tr>
<td>AUC</td>
<td>73.65</td>
<td>66.88</td>
<td>72.25</td>
<td>70.15</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>The ILPD dataset is processed using the NFFBT technique, for which AdaBoost is used along with RF, SVM, LR, and NB for the outlier-free ILPD dataset (<xref ref-type="table" rid="table-7">Tab. 7</xref>). It is found that AdaBoost with RF produces better results than other mentioned classifiers for Accu (90.65%), Spec (92.75%), Sens (89.30), Prec (95.05%), <inline-formula id="ieqn-49"><!--<alternatives><inline-graphic xlink:href="ieqn-49.png"/><tex-math id="tex-ieqn-49"><![CDATA[$\text{F}\text{P}_{\text{r}\text{a}\text{t}\text{e}}$]]></tex-math>--><mml:math id="mml-ieqn-49"><mml:mstyle class="text"><mml:mtext>F</mml:mtext></mml:mstyle><mml:msub><mml:mrow><mml:mstyle class="text"><mml:mtext>P</mml:mtext></mml:mstyle></mml:mrow><mml:mrow><mml:mstyle class="text"><mml:mtext>r</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>t</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>e</mml:mtext></mml:mstyle></mml:mrow></mml:msub></mml:math><!--</alternatives>--></inline-formula> (7.25%), <inline-formula id="ieqn-50"><!--<alternatives><inline-graphic xlink:href="ieqn-50.png"/><tex-math id="tex-ieqn-50"><![CDATA[$\text{F}\text{N}_{\text{r}\text{a}\text{t}\text{e}}$]]></tex-math>--><mml:math id="mml-ieqn-50"><mml:mstyle class="text"><mml:mtext>F</mml:mtext></mml:mstyle><mml:msub><mml:mrow><mml:mstyle class="text"><mml:mtext>N</mml:mtext></mml:mstyle></mml:mrow><mml:mrow><mml:mstyle class="text"><mml:mtext>r</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>t</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>e</mml:mtext></mml:mstyle></mml:mrow></mml:msub></mml:math><!--</alternatives>--></inline-formula> (10.70%), F1-score (92.09%), G-mean (91.01%), and AUC (91.03%). <xref ref-type="table" rid="table-7">Tab. 7</xref> indicates better results than <xref ref-type="table" rid="table-6">Tab. 6</xref> because it contains results derived from an improved ILPD dataset.</p>
<table-wrap id="table-7">
<label>Table 7</label>
<caption>
<title>Outlier-free ILPD dataset</title>
</caption>
<!---->
<table>
<colgroup>
<col/>
<col/>
<col/>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th>Performance measures</th>
<th><inline-formula id="ieqn-51"><!--<alternatives><inline-graphic xlink:href="ieqn-51.png"/><tex-math id="tex-ieqn-51"><![CDATA[$\text{A}\text{d}\text{a}\text{B}\text{o}\text{ost}+ \text{R}\text{F}$]]></tex-math>--><mml:math id="mml-ieqn-51"><mml:mstyle class="text"><mml:mtext>A</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>d</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>B</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>o</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>ost</mml:mtext></mml:mstyle><mml:mo>+</mml:mo><mml:mstyle class="text"><mml:mtext>R</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>F</mml:mtext></mml:mstyle></mml:math><!--</alternatives>--></inline-formula></th>
<th><inline-formula id="ieqn-52"><!--<alternatives><inline-graphic xlink:href="ieqn-52.png"/><tex-math id="tex-ieqn-52"><![CDATA[$\text{A}\text{d}\text{a}\text{B}\text{o}\text{ost}+ \text{S}\text{V}\text{M}$]]></tex-math>--><mml:math id="mml-ieqn-52"><mml:mstyle class="text"><mml:mtext>A</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>d</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>B</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>o</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>ost</mml:mtext></mml:mstyle><mml:mo>+</mml:mo><mml:mstyle class="text"><mml:mtext>S</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>V</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>M</mml:mtext></mml:mstyle></mml:math><!--</alternatives>--></inline-formula></th>
<th><inline-formula id="ieqn-53"><!--<alternatives><inline-graphic xlink:href="ieqn-53.png"/><tex-math id="tex-ieqn-53"><![CDATA[$\text{A}\text{d}\text{a}\text{B}\text{o}\text{ost}+ \text{Logistic R}$]]></tex-math>--><mml:math id="mml-ieqn-53"><mml:mstyle class="text"><mml:mtext>A</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>d</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>B</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>o</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>ost</mml:mtext></mml:mstyle><mml:mo>+</mml:mo><mml:mstyle class="text"><mml:mtext>Logistic&#x00A0;R</mml:mtext></mml:mstyle></mml:math><!--</alternatives>--></inline-formula></th>
<th><inline-formula id="ieqn-54"><!--<alternatives><inline-graphic xlink:href="ieqn-54.png"/><tex-math id="tex-ieqn-54"><![CDATA[$\text{A}\text{d}\text{a}\text{B}\text{o}\text{ost}+ \text{N}\text{B}$]]></tex-math>--><mml:math id="mml-ieqn-54"><mml:mstyle class="text"><mml:mtext>A</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>d</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>B</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>o</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>ost</mml:mtext></mml:mstyle><mml:mo>+</mml:mo><mml:mstyle class="text"><mml:mtext>N</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>B</mml:mtext></mml:mstyle></mml:math><!--</alternatives>--></inline-formula></th>
</tr>
</thead>
<tbody>
<tr>
<td>Accu</td>
<td>90.65</td>
<td>80.74</td>
<td>83.85</td>
<td>87.54</td>
</tr>
<tr>
<td>Spec</td>
<td>92.75</td>
<td>73.45</td>
<td>77.33</td>
<td>85.43</td>
</tr>
<tr>
<td>Sens</td>
<td>89.30</td>
<td>88.07</td>
<td>90.06</td>
<td>89.11</td>
</tr>
<tr>
<td>Prec</td>
<td>95.05</td>
<td>76.73</td>
<td>80.69</td>
<td>89.11</td>
</tr>
<tr>
<td>FP<inline-formula id="ieqn-55"><!--<alternatives><inline-graphic xlink:href="ieqn-55.png"/><tex-math id="tex-ieqn-55"><![CDATA[$_{\text{r}\text{a}\text{t}\text{e}}$]]></tex-math>--><mml:math id="mml-ieqn-55"><mml:msub><mml:mrow></mml:mrow><mml:mrow><mml:mstyle class="text"><mml:mtext>r</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>t</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>e</mml:mtext></mml:mstyle></mml:mrow></mml:msub></mml:math><!--</alternatives>--></inline-formula></td>
<td>7.25</td>
<td>26.55</td>
<td>22.67</td>
<td>14.57</td>
</tr>
<tr>
<td>FN<inline-formula id="ieqn-56"><!--<alternatives><inline-graphic xlink:href="ieqn-56.png"/><tex-math id="tex-ieqn-56"><![CDATA[$_{\text{r}\text{a}\text{t}\text{e}}$]]></tex-math>--><mml:math id="mml-ieqn-56"><mml:msub><mml:mrow></mml:mrow><mml:mrow><mml:mstyle class="text"><mml:mtext>r</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>t</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>e</mml:mtext></mml:mstyle></mml:mrow></mml:msub></mml:math><!--</alternatives>--></inline-formula></td>
<td>10.70</td>
<td>11.93</td>
<td>9.94</td>
<td>10.89</td>
</tr>
<tr>
<td>F1-score</td>
<td>92.09</td>
<td>82.01</td>
<td>85.12</td>
<td>89.11</td>
</tr>
<tr>
<td>G-mean</td>
<td>91.01</td>
<td>80.43</td>
<td>83.45</td>
<td>87.25</td>
</tr>
<tr>
<td>AUC</td>
<td>91.03</td>
<td>80.76</td>
<td>83.69</td>
<td>87.27</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>Accuracy is a valid metric for the efficiency of a classifier for experiments performed using balanced datasets. In this study, both the ILPD and MPRLPD datasets are imbalanced. Therefore, in this case, the F1-score is expected to indicate balance between precision and recall. The F1-scores of <inline-formula id="ieqn-57"><!--<alternatives><inline-graphic xlink:href="ieqn-57.png"/><tex-math id="tex-ieqn-57"><![CDATA[$\text{A}\text{d}\text{a}\text{B}\text{o}\text{ost}+ \text{R}\text{F}$]]></tex-math>--><mml:math id="mml-ieqn-57"><mml:mstyle class="text"><mml:mtext>A</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>d</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>B</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>o</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>ost</mml:mtext></mml:mstyle><mml:mo>+</mml:mo><mml:mstyle class="text"><mml:mtext>R</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>F</mml:mtext></mml:mstyle></mml:math><!--</alternatives>--></inline-formula> were 92.09% and 99.21% in <xref ref-type="table" rid="table-7">Tabs. 7</xref> and <xref ref-type="table" rid="table-9">9</xref>, respectively. This confirmed that the <inline-formula id="ieqn-58"><!--<alternatives><inline-graphic xlink:href="ieqn-58.png"/><tex-math id="tex-ieqn-58"><![CDATA[$\text{A}\text{d}\text{a}\text{B}\text{o}\text{ost}+ \text{R}\text{F}$]]></tex-math>--><mml:math id="mml-ieqn-58"><mml:mstyle class="text"><mml:mtext>A</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>d</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>B</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>o</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>ost</mml:mtext></mml:mstyle><mml:mo>+</mml:mo><mml:mstyle class="text"><mml:mtext>R</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>F</mml:mtext></mml:mstyle></mml:math><!--</alternatives>--></inline-formula> technique performs better than the other three techniques for these two datasets.</p>
<p><xref ref-type="table" rid="table-8">Tab. 8</xref> shows the results of the original MPRLPD. AdaBoost with RF produced the best results for Accu (91.21%), Spec (85.28%), Prec (97.04%), <inline-formula id="ieqn-59"><!--<alternatives><inline-graphic xlink:href="ieqn-59.png"/><tex-math id="tex-ieqn-59"><![CDATA[$\text{F}\text{P}_{\text{r}\text{a}\text{t}\text{e}}$]]></tex-math>--><mml:math id="mml-ieqn-59"><mml:mstyle class="text"><mml:mtext>F</mml:mtext></mml:mstyle><mml:msub><mml:mrow><mml:mstyle class="text"><mml:mtext>P</mml:mtext></mml:mstyle></mml:mrow><mml:mrow><mml:mstyle class="text"><mml:mtext>r</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>t</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>e</mml:mtext></mml:mstyle></mml:mrow></mml:msub></mml:math><!--</alternatives>--></inline-formula> (14.72%), F1-score (94.64%), G-mean (88.75%), and AUC (88.82%), whereas AdaBoost with NB produced the best results for Sens (99.70%) and <inline-formula id="ieqn-60"><!--<alternatives><inline-graphic xlink:href="ieqn-60.png"/><tex-math id="tex-ieqn-60"><![CDATA[$\text{F}\text{N}_{\text{r}\text{a}\text{t}\text{e}}$]]></tex-math>--><mml:math id="mml-ieqn-60"><mml:mstyle class="text"><mml:mtext>F</mml:mtext></mml:mstyle><mml:msub><mml:mrow><mml:mstyle class="text"><mml:mtext>N</mml:mtext></mml:mstyle></mml:mrow><mml:mrow><mml:mstyle class="text"><mml:mtext>r</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>t</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>e</mml:mtext></mml:mstyle></mml:mrow></mml:msub></mml:math><!--</alternatives>--></inline-formula> (0.30%).</p>
<table-wrap id="table-8">
<label>Table 8</label>
<caption>
<title>Original MPRLPD dataset</title>
</caption>
<!---->
<table>
<colgroup>
<col/>
<col/>
<col/>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th>Performance measures</th>
<th><inline-formula id="ieqn-61"><!--<alternatives><inline-graphic xlink:href="ieqn-61.png"/><tex-math id="tex-ieqn-61"><![CDATA[$\text{A}\text{d}\text{a}\text{B}\text{o}\text{ost}+ \text{R}\text{F}$]]></tex-math>--><mml:math id="mml-ieqn-61"><mml:mstyle class="text"><mml:mtext>A</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>d</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>B</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>o</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>ost</mml:mtext></mml:mstyle><mml:mo>+</mml:mo><mml:mstyle class="text"><mml:mtext>R</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>F</mml:mtext></mml:mstyle></mml:math><!--</alternatives>--></inline-formula></th>
<th><inline-formula id="ieqn-62"><!--<alternatives><inline-graphic xlink:href="ieqn-62.png"/><tex-math id="tex-ieqn-62"><![CDATA[$\text{A}\text{d}\text{a}\text{B}\text{o}\text{ost}+ \text{S}\text{V}\text{M}$]]></tex-math>--><mml:math id="mml-ieqn-62"><mml:mstyle class="text"><mml:mtext>A</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>d</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>B</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>o</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>ost</mml:mtext></mml:mstyle><mml:mo>+</mml:mo><mml:mstyle class="text"><mml:mtext>S</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>V</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>M</mml:mtext></mml:mstyle></mml:math><!--</alternatives>--></inline-formula></th>
<th><inline-formula id="ieqn-63"><!--<alternatives><inline-graphic xlink:href="ieqn-63.png"/><tex-math id="tex-ieqn-63"><![CDATA[$\text{A}\text{d}\text{a}\text{B}\text{o}\text{ost}+ \text{Logistic R}$]]></tex-math>--><mml:math id="mml-ieqn-63"><mml:mstyle class="text"><mml:mtext>A</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>d</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>B</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>o</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>ost</mml:mtext></mml:mstyle><mml:mo>+</mml:mo><mml:mstyle class="text"><mml:mtext>Logistic&#x00A0;R</mml:mtext></mml:mstyle></mml:math><!--</alternatives>--></inline-formula></th>
<th><inline-formula id="ieqn-64"><!--<alternatives><inline-graphic xlink:href="ieqn-64.png"/><tex-math id="tex-ieqn-64"><![CDATA[$\text{A}\text{d}\text{a}\text{B}\text{o}\text{ost}+ \text{N}\text{B}$]]></tex-math>--><mml:math id="mml-ieqn-64"><mml:mstyle class="text"><mml:mtext>A</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>d</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>B</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>o</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>ost</mml:mtext></mml:mstyle><mml:mo>+</mml:mo><mml:mstyle class="text"><mml:mtext>N</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>B</mml:mtext></mml:mstyle></mml:math><!--</alternatives>--></inline-formula></th>
</tr>
</thead>
<tbody>
<tr>
<td>Accu</td>
<td>91.21</td>
<td>82.42</td>
<td>85.43</td>
<td>75.17</td>
</tr>
<tr>
<td>Spec</td>
<td>85.28</td>
<td>56.23</td>
<td>59.36</td>
<td>44.73</td>
</tr>
<tr>
<td>Sens</td>
<td>92.35</td>
<td>89.12</td>
<td>96.44</td>
<td>99.70</td>
</tr>
<tr>
<td>Prec</td>
<td>97.04</td>
<td>88.83</td>
<td>84.89</td>
<td>69.12</td>
</tr>
<tr>
<td>FP<inline-formula id="ieqn-65"><!--<alternatives><inline-graphic xlink:href="ieqn-65.png"/><tex-math id="tex-ieqn-65"><![CDATA[$_{\text{r}\text{a}\text{t}\text{e}}$]]></tex-math>--><mml:math id="mml-ieqn-65"><mml:msub><mml:mrow></mml:mrow><mml:mrow><mml:mstyle class="text"><mml:mtext>r</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>t</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>e</mml:mtext></mml:mstyle></mml:mrow></mml:msub></mml:math><!--</alternatives>--></inline-formula></td>
<td>14.72</td>
<td>43.77</td>
<td>40.64</td>
<td>55.27</td>
</tr>
<tr>
<td>FN<inline-formula id="ieqn-66"><!--<alternatives><inline-graphic xlink:href="ieqn-66.png"/><tex-math id="tex-ieqn-66"><![CDATA[$_{\text{r}\text{a}\text{t}\text{e}}$]]></tex-math>--><mml:math id="mml-ieqn-66"><mml:msub><mml:mrow></mml:mrow><mml:mrow><mml:mstyle class="text"><mml:mtext>r</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>t</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>e</mml:mtext></mml:mstyle></mml:mrow></mml:msub></mml:math><!--</alternatives>--></inline-formula></td>
<td>7.65</td>
<td>10.88</td>
<td>3.56</td>
<td>0.30</td>
</tr>
<tr>
<td>F1-score</td>
<td>94.64</td>
<td>88.97</td>
<td>90.30</td>
<td>81.64</td>
</tr>
<tr>
<td>G-mean</td>
<td>88.75</td>
<td>70.79</td>
<td>75.66</td>
<td>66.78</td>
</tr>
<tr>
<td>AUC</td>
<td>88.82</td>
<td>72.68</td>
<td>77.90</td>
<td>72.22</td>
</tr>
</tbody>
</table>
</table-wrap>
<p><xref ref-type="table" rid="table-9">Tab. 9</xref> shows the results of the improved MPRLPD dataset using the NFFBT approach. AdaBoost with RF produced the best results for Accu (98.98%), Spec (98.00%), Sens (99.42%), Prec (99.01%), <inline-formula id="ieqn-67"><!--<alternatives><inline-graphic xlink:href="ieqn-67.png"/><tex-math id="tex-ieqn-67"><![CDATA[$\text{F}\text{P}_{\text{r}\text{a}\text{t}\text{e}}$]]></tex-math>--><mml:math id="mml-ieqn-67"><mml:mstyle class="text"><mml:mtext>F</mml:mtext></mml:mstyle><mml:msub><mml:mrow><mml:mstyle class="text"><mml:mtext>P</mml:mtext></mml:mstyle></mml:mrow><mml:mrow><mml:mstyle class="text"><mml:mtext>r</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>t</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>e</mml:mtext></mml:mstyle></mml:mrow></mml:msub></mml:math><!--</alternatives>--></inline-formula> (2.00%), <inline-formula id="ieqn-68"><!--<alternatives><inline-graphic xlink:href="ieqn-68.png"/><tex-math id="tex-ieqn-68"><![CDATA[$\text{F}\text{N}_{\text{r}\text{a}\text{t}\text{e}}$]]></tex-math>--><mml:math id="mml-ieqn-68"><mml:mstyle class="text"><mml:mtext>F</mml:mtext></mml:mstyle><mml:msub><mml:mrow><mml:mstyle class="text"><mml:mtext>N</mml:mtext></mml:mstyle></mml:mrow><mml:mrow><mml:mstyle class="text"><mml:mtext>r</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>t</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>e</mml:mtext></mml:mstyle></mml:mrow></mml:msub></mml:math><!--</alternatives>--></inline-formula> (0.58%), F1-score (20.58%), G-mean (99.21%), and AUC (98.71%).</p>
<p>The Prec value of 99.01% in <xref ref-type="table" rid="table-9">Tab. 9</xref> indicates that the <inline-formula id="ieqn-69"><!--<alternatives><inline-graphic xlink:href="ieqn-69.png"/><tex-math id="tex-ieqn-69"><![CDATA[$\text{A}\text{d}\text{a}\text{B}\text{o}\text{ost}+ \text{R}\text{F}$]]></tex-math>--><mml:math id="mml-ieqn-69"><mml:mstyle class="text"><mml:mtext>A</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>d</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>B</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>o</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>ost</mml:mtext></mml:mstyle><mml:mo>+</mml:mo><mml:mstyle class="text"><mml:mtext>R</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>F</mml:mtext></mml:mstyle></mml:math><!--</alternatives>--></inline-formula> combination can predict 99 out of 100 liver patients as diseased and one liver patient as healthy. Meanwhile, <inline-formula id="ieqn-70"><!--<alternatives><inline-graphic xlink:href="ieqn-70.png"/><tex-math id="tex-ieqn-70"><![CDATA[$\text{A}\text{d}\text{a}\text{B}\text{o}\text{ost}+ \text{S}\text{V}\text{M}$]]></tex-math>--><mml:math id="mml-ieqn-70"><mml:mstyle class="text"><mml:mtext>A</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>d</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>B</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>o</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>ost</mml:mtext></mml:mstyle><mml:mo>+</mml:mo><mml:mstyle class="text"><mml:mtext>S</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>V</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>M</mml:mtext></mml:mstyle></mml:math><!--</alternatives>--></inline-formula>, <inline-formula id="ieqn-71"><!--<alternatives><inline-graphic xlink:href="ieqn-71.png"/><tex-math id="tex-ieqn-71"><![CDATA[$\text{A}\text{d}\text{a}\text{B}\text{o}\text{ost}+ \text{L}\text{o}\text{g}\text{i}\text{s}\text{tic}$]]></tex-math>--><mml:math id="mml-ieqn-71"><mml:mstyle class="text"><mml:mtext>A</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>d</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>B</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>o</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>ost</mml:mtext></mml:mstyle><mml:mo>+</mml:mo><mml:mstyle class="text"><mml:mtext>L</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>o</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>g</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>i</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>s</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>tic</mml:mtext></mml:mstyle></mml:math><!--</alternatives>--></inline-formula> R, and <inline-formula id="ieqn-72"><!--<alternatives><inline-graphic xlink:href="ieqn-72.png"/><tex-math id="tex-ieqn-72"><![CDATA[$\text{A}\text{d}\text{a}\text{B}\text{o}\text{ost}+ \text{N}\text{B}$]]></tex-math>--><mml:math id="mml-ieqn-72"><mml:mstyle class="text"><mml:mtext>A</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>d</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>B</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>o</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>ost</mml:mtext></mml:mstyle><mml:mo>+</mml:mo><mml:mstyle class="text"><mml:mtext>N</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>B</mml:mtext></mml:mstyle></mml:math><!--</alternatives>--></inline-formula> can predict 90.59%, 89.87%, and 92.23% patients having a liver disorder.</p>
<table-wrap id="table-9">
<label>Table 9</label>
<caption>
<title>Outlier-free MPRLPD dataset</title>
</caption>
<!---->
<table>
<colgroup>
<col/>
<col/>
<col/>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th>Performance measures</th>
<th><inline-formula id="ieqn-73"><!--<alternatives><inline-graphic xlink:href="ieqn-73.png"/><tex-math id="tex-ieqn-73"><![CDATA[$\text{A}\text{d}\text{a}\text{B}\text{o}\text{ost}+ \text{R}\text{F}$]]></tex-math>--><mml:math id="mml-ieqn-73"><mml:mstyle class="text"><mml:mtext>A</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>d</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>B</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>o</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>ost</mml:mtext></mml:mstyle><mml:mo>+</mml:mo><mml:mstyle class="text"><mml:mtext>R</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>F</mml:mtext></mml:mstyle></mml:math><!--</alternatives>--></inline-formula></th>
<th><inline-formula id="ieqn-74"><!--<alternatives><inline-graphic xlink:href="ieqn-74.png"/><tex-math id="tex-ieqn-74"><![CDATA[$\text{A}\text{d}\text{a}\text{B}\text{o}\text{ost}+ \text{S}\text{V}\text{M}$]]></tex-math>--><mml:math id="mml-ieqn-74"><mml:mstyle class="text"><mml:mtext>A</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>d</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>B</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>o</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>ost</mml:mtext></mml:mstyle><mml:mo>+</mml:mo><mml:mstyle class="text"><mml:mtext>S</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>V</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>M</mml:mtext></mml:mstyle></mml:math><!--</alternatives>--></inline-formula></th>
<th><inline-formula id="ieqn-75"><!--<alternatives><inline-graphic xlink:href="ieqn-75.png"/><tex-math id="tex-ieqn-75"><![CDATA[$\text{A}\text{d}\text{a}\text{B}\text{o}\text{ost}+ \text{Logistic R}$]]></tex-math>--><mml:math id="mml-ieqn-75"><mml:mstyle class="text"><mml:mtext>A</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>d</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>B</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>o</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>ost</mml:mtext></mml:mstyle><mml:mo>+</mml:mo><mml:mstyle class="text"><mml:mtext>Logistic&#x00A0;R</mml:mtext></mml:mstyle></mml:math><!--</alternatives>--></inline-formula></th>
<th><inline-formula id="ieqn-76"><!--<alternatives><inline-graphic xlink:href="ieqn-76.png"/><tex-math id="tex-ieqn-76"><![CDATA[$\text{A}\text{d}\text{a}\text{B}\text{o}\text{ost}+ \text{N}\text{B}$]]></tex-math>--><mml:math id="mml-ieqn-76"><mml:mstyle class="text"><mml:mtext>A</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>d</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>B</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>o</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>ost</mml:mtext></mml:mstyle><mml:mo>+</mml:mo><mml:mstyle class="text"><mml:mtext>N</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>B</mml:mtext></mml:mstyle></mml:math><!--</alternatives>--></inline-formula></th>
</tr>
</thead>
<tbody>
<tr>
<td>Accu</td>
<td>98.95</td>
<td>87.05</td>
<td>88.93</td>
<td>89.30</td>
</tr>
<tr>
<td>Spec</td>
<td>98.00</td>
<td>80.72</td>
<td>80.90</td>
<td>84.10</td>
</tr>
<tr>
<td>Sens</td>
<td>99.42</td>
<td>90.13</td>
<td>93.35</td>
<td>91.83</td>
</tr>
<tr>
<td>Prec</td>
<td>99.01</td>
<td>90.59</td>
<td>89.87</td>
<td>92.23</td>
</tr>
<tr>
<td>FP<inline-formula id="ieqn-77"><!--<alternatives><inline-graphic xlink:href="ieqn-77.png"/><tex-math id="tex-ieqn-77"><![CDATA[$_{\text{r}\text{a}\text{t}\text{e}}$]]></tex-math>--><mml:math id="mml-ieqn-77"><mml:msub><mml:mrow></mml:mrow><mml:mrow><mml:mstyle class="text"><mml:mtext>r</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>t</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>e</mml:mtext></mml:mstyle></mml:mrow></mml:msub></mml:math><!--</alternatives>--></inline-formula></td>
<td>2.00</td>
<td>19.28</td>
<td>19.10</td>
<td>15.90</td>
</tr>
<tr>
<td>FN<inline-formula id="ieqn-78"><!--<alternatives><inline-graphic xlink:href="ieqn-78.png"/><tex-math id="tex-ieqn-78"><![CDATA[$_{\text{r}\text{a}\text{t}\text{e}}$]]></tex-math>--><mml:math id="mml-ieqn-78"><mml:msub><mml:mrow></mml:mrow><mml:mrow><mml:mstyle class="text"><mml:mtext>r</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>t</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>e</mml:mtext></mml:mstyle></mml:mrow></mml:msub></mml:math><!--</alternatives>--></inline-formula></td>
<td>0.58</td>
<td>9.87</td>
<td>6.65</td>
<td>8.17</td>
</tr>
<tr>
<td>F1-score</td>
<td>99.21</td>
<td>90.36</td>
<td>91.58</td>
<td>92.03</td>
</tr>
<tr>
<td>G-mean</td>
<td>98.71</td>
<td>85.29</td>
<td>86.91</td>
<td>87.88</td>
</tr>
<tr>
<td>AUC</td>
<td>98.71</td>
<td>85.42</td>
<td>87.13</td>
<td>87.96</td>
</tr>
</tbody>
</table>
</table-wrap>
<fig id="fig-3">
<label>Figure 3</label>
<caption>
<title>(a &#x0026; b) The ROC curve for the ILPD dataset; (c &#x0026; d) the ROC curve for the MPRLPD dataset</title>
</caption><graphic mimetype="image" mime-subtype="png" xlink:href="fig-3.png"/>
</fig>
<p>Because liver disease is a significant cause of death in India and globally, patients need to be diagnosed accurately. If a liver patient is diagnosed as false positive, then that patient&#x2019;s healthy status would be at risk. Hence, in cases with a high percentage of false positives, Spec is the best evaluation metric. In <xref ref-type="table" rid="table-9">Tab. 9</xref>, the Spec value for <inline-formula id="ieqn-79"><!--<alternatives><inline-graphic xlink:href="ieqn-79.png"/><tex-math id="tex-ieqn-79"><![CDATA[$\text{A}\text{d}\text{a}\text{b}\text{o}\text{ost}+ \text{R}\text{F}$]]></tex-math>--><mml:math id="mml-ieqn-79"><mml:mstyle class="text"><mml:mtext>A</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>d</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>b</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>o</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>ost</mml:mtext></mml:mstyle><mml:mo>+</mml:mo><mml:mstyle class="text"><mml:mtext>R</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>F</mml:mtext></mml:mstyle></mml:math><!--</alternatives>--></inline-formula> was 98%, meaning that false positives are rare (2%).</p>
<p>The ROC curve is framed by plotting <inline-formula id="ieqn-80"><!--<alternatives><inline-graphic xlink:href="ieqn-80.png"/><tex-math id="tex-ieqn-80"><![CDATA[$\text{T}\text{P}_{\text{r}\text{a}\text{t}\text{e}}$]]></tex-math>--><mml:math id="mml-ieqn-80"><mml:mstyle class="text"><mml:mtext>T</mml:mtext></mml:mstyle><mml:msub><mml:mrow><mml:mstyle class="text"><mml:mtext>P</mml:mtext></mml:mstyle></mml:mrow><mml:mrow><mml:mstyle class="text"><mml:mtext>r</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>t</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>e</mml:mtext></mml:mstyle></mml:mrow></mml:msub></mml:math><!--</alternatives>--></inline-formula> against <inline-formula id="ieqn-81"><!--<alternatives><inline-graphic xlink:href="ieqn-81.png"/><tex-math id="tex-ieqn-81"><![CDATA[$\text{F}\text{P}_{\text{r}\text{a}\text{t}\text{e}}$]]></tex-math>--><mml:math id="mml-ieqn-81"><mml:mstyle class="text"><mml:mtext>F</mml:mtext></mml:mstyle><mml:msub><mml:mrow><mml:mstyle class="text"><mml:mtext>P</mml:mtext></mml:mstyle></mml:mrow><mml:mrow><mml:mstyle class="text"><mml:mtext>r</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>t</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>e</mml:mtext></mml:mstyle></mml:mrow></mml:msub></mml:math><!--</alternatives>--></inline-formula> at various threshold levels. It gives a visual portrayal of the relative tradeoffs between the <inline-formula id="ieqn-82"><!--<alternatives><inline-graphic xlink:href="ieqn-82.png"/><tex-math id="tex-ieqn-82"><![CDATA[$\text{T}\text{P}_{\text{r}\text{a}\text{t}\text{e}}$]]></tex-math>--><mml:math id="mml-ieqn-82"><mml:mstyle class="text"><mml:mtext>T</mml:mtext></mml:mstyle><mml:msub><mml:mrow><mml:mstyle class="text"><mml:mtext>P</mml:mtext></mml:mstyle></mml:mrow><mml:mrow><mml:mstyle class="text"><mml:mtext>r</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>t</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>e</mml:mtext></mml:mstyle></mml:mrow></mml:msub></mml:math><!--</alternatives>--></inline-formula> (Sens) and <inline-formula id="ieqn-83"><!--<alternatives><inline-graphic xlink:href="ieqn-83.png"/><tex-math id="tex-ieqn-83"><![CDATA[$\text{F}\text{P}_{\text{r}\text{a}\text{t}\text{e}}$]]></tex-math>--><mml:math id="mml-ieqn-83"><mml:mstyle class="text"><mml:mtext>F</mml:mtext></mml:mstyle><mml:msub><mml:mrow><mml:mstyle class="text"><mml:mtext>P</mml:mtext></mml:mstyle></mml:mrow><mml:mrow><mml:mstyle class="text"><mml:mtext>r</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>t</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>e</mml:mtext></mml:mstyle></mml:mrow></mml:msub></mml:math><!--</alternatives>--></inline-formula> (1-Spec) of classifications with respect to data distributions (<inline-formula id="ieqn-84"><!--<alternatives><inline-graphic xlink:href="ieqn-84.png"/><tex-math id="tex-ieqn-84"><![CDATA[$\text{F}\text{P}_{\text{r}\text{a}\text{t}\text{e}}$]]></tex-math>--><mml:math id="mml-ieqn-84"><mml:mstyle class="text"><mml:mtext>F</mml:mtext></mml:mstyle><mml:msub><mml:mrow><mml:mstyle class="text"><mml:mtext>P</mml:mtext></mml:mstyle></mml:mrow><mml:mrow><mml:mstyle class="text"><mml:mtext>r</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>t</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>e</mml:mtext></mml:mstyle></mml:mrow></mml:msub></mml:math><!--</alternatives>--></inline-formula> is on the x-axis, and <inline-formula id="ieqn-85"><!--<alternatives><inline-graphic xlink:href="ieqn-85.png"/><tex-math id="tex-ieqn-85"><![CDATA[$\text{T}\text{P}_{\text{r}\text{a}\text{t}\text{e}}$]]></tex-math>--><mml:math id="mml-ieqn-85"><mml:mstyle class="text"><mml:mtext>T</mml:mtext></mml:mstyle><mml:msub><mml:mrow><mml:mstyle class="text"><mml:mtext>P</mml:mtext></mml:mstyle></mml:mrow><mml:mrow><mml:mstyle class="text"><mml:mtext>r</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>t</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>e</mml:mtext></mml:mstyle></mml:mrow></mml:msub></mml:math><!--</alternatives>--></inline-formula> is on the y-axis).</p>
<p>AUC is a measure of the separation capability of classifiers in a particular dataset. The ROC curve is drawn from the results of the proposed NFFBT in the ILPD and MPRLPD datasets. A comparison of <xref ref-type="fig" rid="fig-3">Fig. 3a</xref> and <xref ref-type="fig" rid="fig-3">3b</xref> shows that all the four techniques (i.e., <inline-formula id="ieqn-86"><!--<alternatives><inline-graphic xlink:href="ieqn-86.png"/><tex-math id="tex-ieqn-86"><![CDATA[$\text{A}\text{d}\text{a}\text{B}\text{o}\text{ost}+ \text{R}\text{F}$]]></tex-math>--><mml:math id="mml-ieqn-86"><mml:mstyle class="text"><mml:mtext>A</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>d</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>B</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>o</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>ost</mml:mtext></mml:mstyle><mml:mo>+</mml:mo><mml:mstyle class="text"><mml:mtext>R</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>F</mml:mtext></mml:mstyle></mml:math><!--</alternatives>--></inline-formula>, <inline-formula id="ieqn-87"><!--<alternatives><inline-graphic xlink:href="ieqn-87.png"/><tex-math id="tex-ieqn-87"><![CDATA[$\text{A}\text{d}\text{a}\text{B}\text{o}\text{ost}+ \text{S}\text{V}\text{M}$]]></tex-math>--><mml:math id="mml-ieqn-87"><mml:mstyle class="text"><mml:mtext>A</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>d</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>B</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>o</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>ost</mml:mtext></mml:mstyle><mml:mo>+</mml:mo><mml:mstyle class="text"><mml:mtext>S</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>V</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>M</mml:mtext></mml:mstyle></mml:math><!--</alternatives>--></inline-formula>, <inline-formula id="ieqn-88"><!--<alternatives><inline-graphic xlink:href="ieqn-88.png"/><tex-math id="tex-ieqn-88"><![CDATA[$\text{A}\text{d}\text{a}\text{b}\text{o}\text{ost}+ \text{L}\text{R}$]]></tex-math>--><mml:math id="mml-ieqn-88"><mml:mstyle class="text"><mml:mtext>A</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>d</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>b</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>o</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>ost</mml:mtext></mml:mstyle><mml:mo>+</mml:mo><mml:mstyle class="text"><mml:mtext>L</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>R</mml:mtext></mml:mstyle></mml:math><!--</alternatives>--></inline-formula>, and <inline-formula id="ieqn-89"><!--<alternatives><inline-graphic xlink:href="ieqn-89.png"/><tex-math id="tex-ieqn-89"><![CDATA[$\text{A}\text{d}\text{a}\text{B}\text{o}\text{ost}+ \text{N}\text{B}$]]></tex-math>--><mml:math id="mml-ieqn-89"><mml:mstyle class="text"><mml:mtext>A</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>d</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>B</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>o</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>ost</mml:mtext></mml:mstyle><mml:mo>+</mml:mo><mml:mstyle class="text"><mml:mtext>N</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>B</mml:mtext></mml:mstyle></mml:math><!--</alternatives>--></inline-formula>) presented comparatively better separability between classes of diseased and healthy people for the outlier-free ILPD dataset than the original ILPD dataset. Specifically, <inline-formula id="ieqn-90"><!--<alternatives><inline-graphic xlink:href="ieqn-90.png"/><tex-math id="tex-ieqn-90"><![CDATA[$\text{A}\text{d}\text{a}\text{B}\text{o}\text{ost}+ \text{R}\text{F}$]]></tex-math>--><mml:math id="mml-ieqn-90"><mml:mstyle class="text"><mml:mtext>A</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>d</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>B</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>o</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>ost</mml:mtext></mml:mstyle><mml:mo>+</mml:mo><mml:mstyle class="text"><mml:mtext>R</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>F</mml:mtext></mml:mstyle></mml:math><!--</alternatives>--></inline-formula> produced the best disease predictions, and <inline-formula id="ieqn-91"><!--<alternatives><inline-graphic xlink:href="ieqn-91.png"/><tex-math id="tex-ieqn-91"><![CDATA[$\text{A}\text{d}\text{a}\text{B}\text{o}\text{ost}+ \text{S}\text{V}\text{M}$]]></tex-math>--><mml:math id="mml-ieqn-91"><mml:mstyle class="text"><mml:mtext>A</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>d</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>B</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>o</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>ost</mml:mtext></mml:mstyle><mml:mo>+</mml:mo><mml:mstyle class="text"><mml:mtext>S</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>V</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>M</mml:mtext></mml:mstyle></mml:math><!--</alternatives>--></inline-formula> was the poorest performer. Similarly, these four techniques also showed more promising results in the outlier free MPRLPD dataset (<xref ref-type="fig" rid="fig-3">Fig. 3d</xref>) than in the original MPRLPD dataset (<xref ref-type="fig" rid="fig-3">Fig. 3c</xref>). Specifically, <inline-formula id="ieqn-92"><!--<alternatives><inline-graphic xlink:href="ieqn-92.png"/><tex-math id="tex-ieqn-92"><![CDATA[$\text{A}\text{d}\text{a}\text{B}\text{o}\text{ost}+ \text{R}\text{F}$]]></tex-math>--><mml:math id="mml-ieqn-92"><mml:mstyle class="text"><mml:mtext>A</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>d</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>B</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>o</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>ost</mml:mtext></mml:mstyle><mml:mo>+</mml:mo><mml:mstyle class="text"><mml:mtext>R</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>F</mml:mtext></mml:mstyle></mml:math><!--</alternatives>--></inline-formula> performed the best regarding the separation of healthy patients and those with liver disease, indicated by the fact that the AUC was close to 1.</p>
</sec>
<sec id="s5">
<label>5</label>
<title>Conclusion</title>
<p>In this paper, an NFFBT approach is proposed. This approach works in two main phases. First noise is eliminated using KNN filter and R_TLU techniques. The KNN filter eliminates outliers from the minority class, and R_TLU eliminates outliers from the majority class. After that, datasets are fuzzified so that uncertainty can be handled. In the second phase, the fuzzified datasets are classified using AdaBoost with RF, SVM, LR, and NB.</p>
<p>ILPD and MPRLPD datasets have been used in experiments to evaluate the performance of the NFFBT approach. These datasets are imbalanced, and so the AdaBoost algorithm is applied to the dataset because it can classify the imbalanced datasets. The AdaBoost boosting algorithm is applied with different classifiers, both without outlier removal (original dataset) and after removing noise from and fuzzifying (NFFBT) the datasets.</p>
<p>The results show improvements in Accu (12.26%), Spec (28.41%), Sens (6.35%), Prec (7.31%), <inline-formula id="ieqn-93"><!--<alternatives><inline-graphic xlink:href="ieqn-93.png"/><tex-math id="tex-ieqn-93"><![CDATA[$\text{F}\text{P}_{\text{r}\text{a}\text{t}\text{e}}$]]></tex-math>--><mml:math id="mml-ieqn-93"><mml:mstyle class="text"><mml:mtext>F</mml:mtext></mml:mstyle><mml:msub><mml:mrow><mml:mstyle class="text"><mml:mtext>P</mml:mtext></mml:mstyle></mml:mrow><mml:mrow><mml:mstyle class="text"><mml:mtext>r</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>t</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>e</mml:mtext></mml:mstyle></mml:mrow></mml:msub></mml:math><!--</alternatives>--></inline-formula> (28.41%), <inline-formula id="ieqn-94"><!--<alternatives><inline-graphic xlink:href="ieqn-94.png"/><tex-math id="tex-ieqn-94"><![CDATA[$\text{F}\text{N}_{\text{r}\text{a}\text{t}\text{e}}$]]></tex-math>--><mml:math id="mml-ieqn-94"><mml:mstyle class="text"><mml:mtext>F</mml:mtext></mml:mstyle><mml:msub><mml:mrow><mml:mstyle class="text"><mml:mtext>N</mml:mtext></mml:mstyle></mml:mrow><mml:mrow><mml:mstyle class="text"><mml:mtext>r</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>t</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>e</mml:mtext></mml:mstyle></mml:mrow></mml:msub></mml:math><!--</alternatives>--></inline-formula> (6.35%), F1-score (6.81%), G-mean (17.96%), and AUC (17.38%) using the NFFBT approach when compared to the original ILPD dataset. Meanwhile, improvements in Accu (7.74%), Spec (12.72%), Sens (7.07%), Prec (1.97%), <inline-formula id="ieqn-95"><!--<alternatives><inline-graphic xlink:href="ieqn-95.png"/><tex-math id="tex-ieqn-95"><![CDATA[$\text{F}\text{P}_{\text{r}\text{a}\text{t}\text{e}}$]]></tex-math>--><mml:math id="mml-ieqn-95"><mml:mstyle class="text"><mml:mtext>F</mml:mtext></mml:mstyle><mml:msub><mml:mrow><mml:mstyle class="text"><mml:mtext>P</mml:mtext></mml:mstyle></mml:mrow><mml:mrow><mml:mstyle class="text"><mml:mtext>r</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>t</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>e</mml:mtext></mml:mstyle></mml:mrow></mml:msub></mml:math><!--</alternatives>--></inline-formula> (12.72), <inline-formula id="ieqn-96"><!--<alternatives><inline-graphic xlink:href="ieqn-96.png"/><tex-math id="tex-ieqn-96"><![CDATA[$\text{F}\text{N}_{\text{r}\text{a}\text{t}\text{e}}$]]></tex-math>--><mml:math id="mml-ieqn-96"><mml:mstyle class="text"><mml:mtext>F</mml:mtext></mml:mstyle><mml:msub><mml:mrow><mml:mstyle class="text"><mml:mtext>N</mml:mtext></mml:mstyle></mml:mrow><mml:mrow><mml:mstyle class="text"><mml:mtext>r</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>a</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>t</mml:mtext></mml:mstyle><mml:mstyle class="text"><mml:mtext>e</mml:mtext></mml:mstyle></mml:mrow></mml:msub></mml:math><!--</alternatives>--></inline-formula> (7.07%), F1-score (4.57%, G-mean (9.96%), and AUC (9.89%) were achieved using NFFBT approach when compared with the original MPRLPD dataset.</p>
<p>These results confirm the advantageous performance of the proposed NFFBT approach when compared to AdaBoost with RF. Based on the results, we argue that the NFFBT can be used by healthcare organizations and liver research institutes to classify imbalanced LFT data. It can also be utilized as a screening tool by doctors to predict and diagnose liver disease.</p>
<p>In the future, similar experiments can be done for imbalanced datasets in other domains like finance, cyber forensics, and athlete doping tests, among many others.</p>
</sec>
</body>
<back>
<fn-group><fn fn-type="other"><p><bold>Funding Statement:</bold> The authors received no specific funding for this study.</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>
<ref-list content-type="authoryear">
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