The Development of Symbolic Expressions for the Detection of Hepatitis C Patients and the Disease Progression from Blood Parameters Using Genetic Programming-Symbolic Classification Algorithm
Hepatitis C is an infectious disease which is caused by the Hepatitis C virus (HCV) and the virus primarily affects the liver. Based on the publicly available dataset used in this paper the idea is to develop a mathematical equation that could be used to detect HCV patients with high accuracy based...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-12-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/13/1/574 |
| _version_ | 1797626165021638656 |
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| author | Nikola Anđelić Ivan Lorencin Sandi Baressi Šegota Zlatan Car |
| author_facet | Nikola Anđelić Ivan Lorencin Sandi Baressi Šegota Zlatan Car |
| author_sort | Nikola Anđelić |
| collection | DOAJ |
| description | Hepatitis C is an infectious disease which is caused by the Hepatitis C virus (HCV) and the virus primarily affects the liver. Based on the publicly available dataset used in this paper the idea is to develop a mathematical equation that could be used to detect HCV patients with high accuracy based on the enzymes, proteins, and biomarker values contained in a patient’s blood sample using genetic programming symbolic classification (GPSC) algorithm. Not only that, but the idea was also to obtain a mathematical equation that could detect the progress of the disease i.e., Hepatitis C, Fibrosis, and Cirrhosis using the GPSC algorithm. Since the original dataset was imbalanced (a large number of healthy patients versus a small number of Hepatitis C/Fibrosis/Cirrhosis patients) the dataset was balanced using random oversampling, SMOTE, ADSYN, and Borderline SMOTE methods. The symbolic expressions (mathematical equations) were obtained using the GPSC algorithm using a rigorous process of 5-fold cross-validation with a random hyperparameter search method which had to be developed for this problem. To evaluate each symbolic expression generated with GPSC the mean and standard deviation values of accuracy (ACC), the area under the receiver operating characteristic curve (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mi>U</mi><mi>C</mi></mrow></semantics></math></inline-formula>), precision, recall, and F1-score were obtained. In a simple binary case (healthy vs. Hepatitis C patients) the best case was achieved with a dataset balanced with the Borderline SMOTE method. The results are <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover><mrow><mi>A</mi><mi>C</mi><mi>C</mi></mrow><mo>¯</mo></mover><mo>±</mo><mi>S</mi><mi>D</mi><mrow><mo>(</mo><mi>A</mi><mi>C</mi><mi>C</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover><mrow><mi>A</mi><mi>U</mi><mi>C</mi></mrow><mo>¯</mo></mover><mo>±</mo><mi>S</mi><mi>D</mi><mrow><mo>(</mo><mi>A</mi><mi>U</mi><mi>C</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover><mrow><mi>P</mi><mi>r</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>s</mi><mi>i</mi><mi>o</mi><mi>n</mi></mrow><mo>¯</mo></mover><mo>±</mo><mi>S</mi><mi>D</mi><mrow><mo>(</mo><mi>P</mi><mi>r</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>s</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover><mrow><mi>R</mi><mi>e</mi><mi>c</mi><mi>a</mi><mi>l</mi><mi>l</mi></mrow><mo>¯</mo></mover><mo>±</mo><mi>S</mi><mi>D</mi><mrow><mo>(</mo><mi>R</mi><mi>e</mi><mi>c</mi><mi>a</mi><mi>l</mi><mi>l</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover><mrow><mi>F</mi><mn>1</mn><mo>−</mo><mi>s</mi><mi>c</mi><mi>o</mi><mi>r</mi><mi>e</mi></mrow><mo>¯</mo></mover><mo>±</mo><mi>S</mi><mi>D</mi><mrow><mo>(</mo><mi>F</mi><mn>1</mn><mo>−</mo><mi>s</mi><mi>c</mi><mi>o</mi><mi>r</mi><mi>e</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> equal to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.99</mn><mo>±</mo><mn>5.8</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.99</mn><mo>±</mo><mn>5.4</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.998</mn><mo>±</mo><mn>1.3</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.98</mn><mo>±</mo><mn>1.19</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.99</mn><mo>±</mo><mn>5.39</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></semantics></math></inline-formula>, respectively. For the multiclass problem, OneVsRestClassifer was used in combination with GPSC 5-fold cross-validation and random hyperparameter search, and the best case was achieved with a dataset balanced with the Borderline SMOTE method. To evaluate symbolic expressions obtained in this case previous evaluation metric methods were used however for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mi>U</mi><mi>C</mi></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>P</mi><mi>r</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>s</mi><mi>i</mi><mi>o</mi><mi>n</mi></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>e</mi><mi>c</mi><mi>a</mi><mi>l</mi><mi>l</mi></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mn>1</mn><mo>−</mo><mi>s</mi><mi>c</mi><mi>o</mi><mi>r</mi><mi>e</mi></mrow></semantics></math></inline-formula> the macro values were computed since this method calculates metrics for each label, and find their unweighted mean value. In multiclass case the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover><mrow><mi>A</mi><mi>C</mi><mi>C</mi></mrow><mo>¯</mo></mover><mo>±</mo><mi>S</mi><mi>D</mi><mrow><mo>(</mo><mi>A</mi><mi>C</mi><mi>C</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mover><mrow><mi>A</mi><mi>U</mi><mi>C</mi></mrow><mo>¯</mo></mover><mrow><mi>m</mi><mi>a</mi><mi>c</mi><mi>r</mi><mi>o</mi></mrow></msub><mo>±</mo><mi>S</mi><mi>D</mi><mrow><mo>(</mo><mi>A</mi><mi>U</mi><mi>C</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mover><mrow><mi>P</mi><mi>r</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>s</mi><mi>i</mi><mi>o</mi><mi>n</mi></mrow><mo>¯</mo></mover><mrow><mi>m</mi><mi>a</mi><mi>c</mi><mi>r</mi><mi>o</mi></mrow></msub><mo>±</mo><mi>S</mi><mi>D</mi><mrow><mo>(</mo><mi>P</mi><mi>r</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>s</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mover><mrow><mi>R</mi><mi>e</mi><mi>c</mi><mi>a</mi><mi>l</mi><mi>l</mi></mrow><mo>¯</mo></mover><mrow><mi>m</mi><mi>a</mi><mi>c</mi><mi>r</mi><mi>o</mi></mrow></msub><mo>±</mo><mi>S</mi><mi>D</mi><mrow><mo>(</mo><mi>R</mi><mi>e</mi><mi>c</mi><mi>a</mi><mi>l</mi><mi>l</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mover><mrow><mi>F</mi><mn>1</mn><mo>−</mo><mi>s</mi><mi>c</mi><mi>o</mi><mi>r</mi><mi>e</mi></mrow><mo>¯</mo></mover><mrow><mi>m</mi><mi>a</mi><mi>c</mi><mi>r</mi><mi>o</mi></mrow></msub><mo>±</mo><mi>S</mi><mi>D</mi><mrow><mo>(</mo><mi>F</mi><mn>1</mn><mo>−</mo><mi>s</mi><mi>c</mi><mi>o</mi><mi>r</mi><mi>e</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> are equal to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.934</mn><mo>±</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.987</mn><mo>±</mo><mn>1.8</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.942</mn><mo>±</mo><mn>6.9</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.934</mn><mo>±</mo><mn>7.84</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.932</mn><mo>±</mo><mn>8.4</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></semantics></math></inline-formula>, respectively. For the best binary and multi-class cases, the symbolic expressions are shown and evaluated on the original dataset. |
| first_indexed | 2024-03-11T10:06:37Z |
| format | Article |
| id | doaj.art-278a66e494d14f7e820a91c31c88e6d5 |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-11T10:06:37Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj.art-278a66e494d14f7e820a91c31c88e6d52023-11-16T14:58:55ZengMDPI AGApplied Sciences2076-34172022-12-0113157410.3390/app13010574The Development of Symbolic Expressions for the Detection of Hepatitis C Patients and the Disease Progression from Blood Parameters Using Genetic Programming-Symbolic Classification AlgorithmNikola Anđelić0Ivan Lorencin1Sandi Baressi Šegota2Zlatan Car3Faculty of Engineering, University of Rijeka, Vukovarska 58, 51000 Rijeka, CroatiaFaculty of Engineering, University of Rijeka, Vukovarska 58, 51000 Rijeka, CroatiaFaculty of Engineering, University of Rijeka, Vukovarska 58, 51000 Rijeka, CroatiaFaculty of Engineering, University of Rijeka, Vukovarska 58, 51000 Rijeka, CroatiaHepatitis C is an infectious disease which is caused by the Hepatitis C virus (HCV) and the virus primarily affects the liver. Based on the publicly available dataset used in this paper the idea is to develop a mathematical equation that could be used to detect HCV patients with high accuracy based on the enzymes, proteins, and biomarker values contained in a patient’s blood sample using genetic programming symbolic classification (GPSC) algorithm. Not only that, but the idea was also to obtain a mathematical equation that could detect the progress of the disease i.e., Hepatitis C, Fibrosis, and Cirrhosis using the GPSC algorithm. Since the original dataset was imbalanced (a large number of healthy patients versus a small number of Hepatitis C/Fibrosis/Cirrhosis patients) the dataset was balanced using random oversampling, SMOTE, ADSYN, and Borderline SMOTE methods. The symbolic expressions (mathematical equations) were obtained using the GPSC algorithm using a rigorous process of 5-fold cross-validation with a random hyperparameter search method which had to be developed for this problem. To evaluate each symbolic expression generated with GPSC the mean and standard deviation values of accuracy (ACC), the area under the receiver operating characteristic curve (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mi>U</mi><mi>C</mi></mrow></semantics></math></inline-formula>), precision, recall, and F1-score were obtained. In a simple binary case (healthy vs. Hepatitis C patients) the best case was achieved with a dataset balanced with the Borderline SMOTE method. The results are <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover><mrow><mi>A</mi><mi>C</mi><mi>C</mi></mrow><mo>¯</mo></mover><mo>±</mo><mi>S</mi><mi>D</mi><mrow><mo>(</mo><mi>A</mi><mi>C</mi><mi>C</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover><mrow><mi>A</mi><mi>U</mi><mi>C</mi></mrow><mo>¯</mo></mover><mo>±</mo><mi>S</mi><mi>D</mi><mrow><mo>(</mo><mi>A</mi><mi>U</mi><mi>C</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover><mrow><mi>P</mi><mi>r</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>s</mi><mi>i</mi><mi>o</mi><mi>n</mi></mrow><mo>¯</mo></mover><mo>±</mo><mi>S</mi><mi>D</mi><mrow><mo>(</mo><mi>P</mi><mi>r</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>s</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover><mrow><mi>R</mi><mi>e</mi><mi>c</mi><mi>a</mi><mi>l</mi><mi>l</mi></mrow><mo>¯</mo></mover><mo>±</mo><mi>S</mi><mi>D</mi><mrow><mo>(</mo><mi>R</mi><mi>e</mi><mi>c</mi><mi>a</mi><mi>l</mi><mi>l</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover><mrow><mi>F</mi><mn>1</mn><mo>−</mo><mi>s</mi><mi>c</mi><mi>o</mi><mi>r</mi><mi>e</mi></mrow><mo>¯</mo></mover><mo>±</mo><mi>S</mi><mi>D</mi><mrow><mo>(</mo><mi>F</mi><mn>1</mn><mo>−</mo><mi>s</mi><mi>c</mi><mi>o</mi><mi>r</mi><mi>e</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> equal to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.99</mn><mo>±</mo><mn>5.8</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.99</mn><mo>±</mo><mn>5.4</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.998</mn><mo>±</mo><mn>1.3</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.98</mn><mo>±</mo><mn>1.19</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.99</mn><mo>±</mo><mn>5.39</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></semantics></math></inline-formula>, respectively. For the multiclass problem, OneVsRestClassifer was used in combination with GPSC 5-fold cross-validation and random hyperparameter search, and the best case was achieved with a dataset balanced with the Borderline SMOTE method. To evaluate symbolic expressions obtained in this case previous evaluation metric methods were used however for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mi>U</mi><mi>C</mi></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>P</mi><mi>r</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>s</mi><mi>i</mi><mi>o</mi><mi>n</mi></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>e</mi><mi>c</mi><mi>a</mi><mi>l</mi><mi>l</mi></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mn>1</mn><mo>−</mo><mi>s</mi><mi>c</mi><mi>o</mi><mi>r</mi><mi>e</mi></mrow></semantics></math></inline-formula> the macro values were computed since this method calculates metrics for each label, and find their unweighted mean value. In multiclass case the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover><mrow><mi>A</mi><mi>C</mi><mi>C</mi></mrow><mo>¯</mo></mover><mo>±</mo><mi>S</mi><mi>D</mi><mrow><mo>(</mo><mi>A</mi><mi>C</mi><mi>C</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mover><mrow><mi>A</mi><mi>U</mi><mi>C</mi></mrow><mo>¯</mo></mover><mrow><mi>m</mi><mi>a</mi><mi>c</mi><mi>r</mi><mi>o</mi></mrow></msub><mo>±</mo><mi>S</mi><mi>D</mi><mrow><mo>(</mo><mi>A</mi><mi>U</mi><mi>C</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mover><mrow><mi>P</mi><mi>r</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>s</mi><mi>i</mi><mi>o</mi><mi>n</mi></mrow><mo>¯</mo></mover><mrow><mi>m</mi><mi>a</mi><mi>c</mi><mi>r</mi><mi>o</mi></mrow></msub><mo>±</mo><mi>S</mi><mi>D</mi><mrow><mo>(</mo><mi>P</mi><mi>r</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>s</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mover><mrow><mi>R</mi><mi>e</mi><mi>c</mi><mi>a</mi><mi>l</mi><mi>l</mi></mrow><mo>¯</mo></mover><mrow><mi>m</mi><mi>a</mi><mi>c</mi><mi>r</mi><mi>o</mi></mrow></msub><mo>±</mo><mi>S</mi><mi>D</mi><mrow><mo>(</mo><mi>R</mi><mi>e</mi><mi>c</mi><mi>a</mi><mi>l</mi><mi>l</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mover><mrow><mi>F</mi><mn>1</mn><mo>−</mo><mi>s</mi><mi>c</mi><mi>o</mi><mi>r</mi><mi>e</mi></mrow><mo>¯</mo></mover><mrow><mi>m</mi><mi>a</mi><mi>c</mi><mi>r</mi><mi>o</mi></mrow></msub><mo>±</mo><mi>S</mi><mi>D</mi><mrow><mo>(</mo><mi>F</mi><mn>1</mn><mo>−</mo><mi>s</mi><mi>c</mi><mi>o</mi><mi>r</mi><mi>e</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> are equal to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.934</mn><mo>±</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.987</mn><mo>±</mo><mn>1.8</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.942</mn><mo>±</mo><mn>6.9</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.934</mn><mo>±</mo><mn>7.84</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.932</mn><mo>±</mo><mn>8.4</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></semantics></math></inline-formula>, respectively. For the best binary and multi-class cases, the symbolic expressions are shown and evaluated on the original dataset.https://www.mdpi.com/2076-3417/13/1/574ADASYNborderline SMOTEgenetic programming-symbolic classifierHepatitis Cfibrosiscirrhosis |
| spellingShingle | Nikola Anđelić Ivan Lorencin Sandi Baressi Šegota Zlatan Car The Development of Symbolic Expressions for the Detection of Hepatitis C Patients and the Disease Progression from Blood Parameters Using Genetic Programming-Symbolic Classification Algorithm Applied Sciences ADASYN borderline SMOTE genetic programming-symbolic classifier Hepatitis C fibrosis cirrhosis |
| title | The Development of Symbolic Expressions for the Detection of Hepatitis C Patients and the Disease Progression from Blood Parameters Using Genetic Programming-Symbolic Classification Algorithm |
| title_full | The Development of Symbolic Expressions for the Detection of Hepatitis C Patients and the Disease Progression from Blood Parameters Using Genetic Programming-Symbolic Classification Algorithm |
| title_fullStr | The Development of Symbolic Expressions for the Detection of Hepatitis C Patients and the Disease Progression from Blood Parameters Using Genetic Programming-Symbolic Classification Algorithm |
| title_full_unstemmed | The Development of Symbolic Expressions for the Detection of Hepatitis C Patients and the Disease Progression from Blood Parameters Using Genetic Programming-Symbolic Classification Algorithm |
| title_short | The Development of Symbolic Expressions for the Detection of Hepatitis C Patients and the Disease Progression from Blood Parameters Using Genetic Programming-Symbolic Classification Algorithm |
| title_sort | development of symbolic expressions for the detection of hepatitis c patients and the disease progression from blood parameters using genetic programming symbolic classification algorithm |
| topic | ADASYN borderline SMOTE genetic programming-symbolic classifier Hepatitis C fibrosis cirrhosis |
| url | https://www.mdpi.com/2076-3417/13/1/574 |
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