1
Philipps University Marburg, MSc in Data Science, Germany
(Alshikho@students.uni-marburg.de)
2
Faculty member, Damascus University, Faculty of Science, Syria
(maissam.jdid66@damascusuniversity.edu.sy)
3
Laboratory of Information Processing, Faculty of Science Ben M’Sik, University Hassan II, B.P 7955, Morocco
(broumisaid78@gmail.com)
Abstract :
The decision-making process is greatly affected by the data collection stage. If the data collection process is not well controlled, i.e. there is some data lost due to the poor quality of the devices used or the lack of accuracy in the data entry process...etc., this will affect the work of the SVM algorithm, which is considered one of the best. Most of the workbooks suffer from the problems of missing and anomalous data. In this paper, we propose a method to treat the missing and anomalous data by reshaping the data set defined by the classical method into the neutrosophical data set by calculating the amount of true T, false F, and neutrality I in the neutrosophical set using inverse Lagrangian interpolation. We noticed the superiority of our proposed method for processing missing data over the method of [21], then we trained a support vector machine algorithm with orthogonal legender kernel on a breast cancer dataset taken from the Statistics Department of Al-Bayrouni Hospital in Damascus, where the proposed algorithm achieved a classification accuracy of 97%. The reason we chose a support vector machine classifier with an orthogonal legender kernel has two goals: the first is to eliminate the repetition of support vectors in the feature space. The second is to solve the problem of non-linear data distribution.
Keywords :
Neutrosophic logic , Support Vector Machine , Orthogonal legend Kernel , Neutrosophic Group , Inverse Lagrangian Interpolation.
References :
[1] Kirkos, Efstathios & Spathis, Charalambos & Manolopoulos, Yannis. (2007). Data mining techniques
for the detection of fraudulent financial statements. Expert Systems with Applications, 32(4), 995-1003.
Expert Systems with Applications. 32. 995-1003. 10.1016/j.eswa.2006.02.016..
[2] ALGORE.M,2021, MACHINE LEARNING The complete Math Guide to Master Data Science with
Python and Developing Artificial Intelligence ,
[3] Quinto, Butch. (2020). Next-Generation Machine Learning with Spark: Covers XGBoost, LightGBM,
Spark NLP, Distributed Deep Learning with Keras, and More. 10.1007/978-1-4842-5669-5.
[4] Hamel, Lutz. (2009). Knowledge Discovery with Support Vector Machines. 231-235.
10.1002/9780470503065.refs.
[5] JAFARZADEH. SZ, AMINIAN. M, EFATTI. S, 2013- A Set of New Kernel Function For Support
Vector Machines: An Approach Based On Chebyshev Polynomials. ICCKE 2013, 412-416.
[6] MOGHADDAM. VH, HAMIDZADEH. J, 2016- New Hermite Orthogonal Polynomial Kernel And
Combined Kernel In Support Vector Machine Classifier. Pattern Recognition, 60 ,921-935.
[7] Z. -B. Pan, H. Chen and X. -H. You, "Support vector machine with orthogonal Legendre kernel," 2012
International Conference on Wavelet Analysis and Pattern Recognition, 2012, pp. 125-130, doi:
10.1109/ICWAPR.2012.6294766.
[8] Broumi S. and Smarandache, F., Correlation coefficient of interval neutrosophic set, Appl. Mech.
Mater., 436:511–517, 2013.
[9] Broumi, S.; Smarandache, F.; Talea, M.; Bakali, A. Operations on Interval Valued Neutrosophic
Graphs; Infinite Study; Modern Science Publisher: New York, NY, USA, 2016.
[10] ] Abdel-Basst, M., Mohamed, R., Elhoseny, M., " A model for the effective COVID-19 identification in
uncertainty environment using primary symptoms and CT scans." Health Informatics Journal, 2020.
[11] Smarandache, F., Khalid, H., "Neutrosophic Precalculus and Neutrosophic Calculus (second enlarged
edition) ", Pons Publishing House / Pons asbl, pp.20-22, 2018.
[12] Jdid .M, Alhabib.R ,and Salama.A.A, The static model of inventory management without a deficit
with Neutrosophic logic, International Journal of Neutrosophic Science (IJNS), Volume 16, Issue 1,
PP: 42-48, 2021.
[13] Jdid .M, Salama.A.A , Alhabib.R ,Khalid .H, and Alsuleiman .F, Neutrosophic Treatment of the static
model of inventory management with deficit , International Journal of Neutrosophic Science (IJNS),
Volume 18, Issue 1, PP: 20-29, 2022.
[14] Jdid .M, Alhabib.R ,Bahbouh .O , Salama.A.A and Khalid .H, The Neutrosophic Treatment for
multiple storage problem of finite materials and volumes, International Journal of Neutrosophic
Science (IJNS), Volume 18, Issue 1, PP: 42-56, 2022.
[15] Jdid .M, Alhabib.R and Salama.A.A, Fundamentals of Neutrosophical Simulation for Generating
Random Numbers Associated with Uniform Probability Distribution, Neutrosophic Sets and Systems,
49, 2022
[16] Jdid .M, Alhabib.R ,Khalid .H, and Salama.A.A, the Neutrosophic Treatment of the static model for
the inventory management with safety reserve , International Journal of Neutrosophic Science (IJNS),
Volume 18, Issue 2, PP: 262-271, 2022.
[17] Jdid .M, Salama.A.A and Khalid .H, Neutrosophic handling of the simplex direct algorithm to define
the optimal solution in linear programming , International Journal of Neutrosophic Science (IJNS),
Volume 18, Issue 1, PP: 30-41, 2022.
[18] Jdid .M, and Khalid .H, mysterious Neutrosophic linear models , International Journal of
Neutrosophic Science (IJNS), Volume 18, Issue 2, PP: 243-253, 2022.
[19] Maissam Jdid, Basel Shahin, Fatima Al Suleiman, Important Neutrosophic Rules for DecisionMaking in the Case of Uncertain Data, International Journal of Neutrosophic Science (IJNS), Volume
18, Issue3, PP: 166-176, 2022
[20] Maissam Jdid, Rafif Alhabib, Neutrosophic dynamic programming, International Journal of
Neutrosophic Science (IJNS), Volume 18, Issue3, PP: 157-165, 2022.
[21] Ju, Wen & Cheng, H.D.. (2013). A novel neutrosophic logic SVM (N-SVM) and its application to
image categorization. New Mathematics and Natural Computation. 09. 10.1142/S1793005713500038.
[22] Hemdan, E.E.-D., Shouman, M.A., Karar, M.E.: Covidx-net: a framework of deep learning
[23] classifiers to diagnose covid-19 in x-ray images (2020). arXiv preprint arXiv:2003.11055
[24] Pannu, H.S., Singh, D., Malhi, A.K.: Improved particle swarm optimization based adaptive neuro-fuzzy
inference system for benzene detection. CLEAN–Soil Air Water 46(5), 1700162 (2018)
[25] Jain, G., Mittal, D., Thakur, D., Mittal, M.K.: A deep learning approach to detect covid-19 coronavirus
with X-Ray images. Biocybernetics Biomed. Eng. 40(4), 1391–1405 (2020)
[26] Agarwal, Ravi P., and Donal O’Regan. “Legendre Polynomials and Functions.” Ordinary and Partial
Differential Equations, n.d., 47–56. doi:10.1007/978-0-387-79146-3_7.
[27] Shawe-Taylor, John & Sun, Shiliang. (2014). Kernel Methods and Support Vector Machines.
10.1016/B978-0-12-396502-8.00016-4.
[28] Djelloul, Naima & Abdessamad, Amir. (2019). Analysis of legendre polynomial kernel in support
vector machines. International Journal of Computing Science and Mathematics. 10. 580.
10.1504/IJCSM.2019.10025670.
[29] Turhan, Muhammed & Şengür, Dönüş & Karabatak, Songül & Guo, Yanhui & Smarandache, Florentin.
(2018). Neutrosophic Weighted Support Vector Machines for the Determination of School
Administrators Who Attended an Action Learning Course Based on Their Conflict-Handling Styles.
[30] Evgeniou, Theodoros & Pontil, Massimiliano. (2001). Support Vector Machines: Theory and
Applications. 2049. 249-257. 10.1007/3-540-44673-7_12.
[31] Ghosh, Debdas & Singh, Abhishek & Shukla, Kuldeep Kumar & Manchanda, Kartik. (2019). Extended
Karush-Kuhn-Tucker Condition for Constrained Interval Optimization Problems and its Application in
Support Vector Machines. Information Sciences. 504. 10.1016/j.ins.2019.07.017.
[32] Nasr Deen Eid,(2011), Numerical analysis, Directorate of University Books and Publications, Aleppo
University
[33] Mahmoud Mohamed Ahmed,Numerical Analysis1,Tishreen University,2010
| Style | # |
|---|---|
| MLA | Mohammed Alshikho, Maissam Jdid , Said Broumi. "A Study of a Support Vector Machine Algorithm with an Orthogonal Legendre Kernel According to Neutrosophic logic and Inverse Lagrangian Interpolation." Full Length Article, Vol. 5, No. 1, 2023 ,PP. 41-51 (Doi : https://doi.org/10.54216/JNFS.050105) |
| APA | Mohammed Alshikho, Maissam Jdid , Said Broumi. (2023). A Study of a Support Vector Machine Algorithm with an Orthogonal Legendre Kernel According to Neutrosophic logic and Inverse Lagrangian Interpolation. Journal of Full Length Article, 5 ( 1 ), 41-51 (Doi : https://doi.org/10.54216/JNFS.050105) |
| Chicago | Mohammed Alshikho, Maissam Jdid , Said Broumi. "A Study of a Support Vector Machine Algorithm with an Orthogonal Legendre Kernel According to Neutrosophic logic and Inverse Lagrangian Interpolation." Journal of Full Length Article, 5 no. 1 (2023): 41-51 (Doi : https://doi.org/10.54216/JNFS.050105) |
| Harvard | Mohammed Alshikho, Maissam Jdid , Said Broumi. (2023). A Study of a Support Vector Machine Algorithm with an Orthogonal Legendre Kernel According to Neutrosophic logic and Inverse Lagrangian Interpolation. Journal of Full Length Article, 5 ( 1 ), 41-51 (Doi : https://doi.org/10.54216/JNFS.050105) |
| Vancouver | Mohammed Alshikho, Maissam Jdid , Said Broumi. A Study of a Support Vector Machine Algorithm with an Orthogonal Legendre Kernel According to Neutrosophic logic and Inverse Lagrangian Interpolation. Journal of Full Length Article, (2023); 5 ( 1 ): 41-51 (Doi : https://doi.org/10.54216/JNFS.050105) |
| IEEE | Mohammed Alshikho, Maissam Jdid, Said Broumi, A Study of a Support Vector Machine Algorithm with an Orthogonal Legendre Kernel According to Neutrosophic logic and Inverse Lagrangian Interpolation, Journal of Full Length Article, Vol. 5 , No. 1 , (2023) : 41-51 (Doi : https://doi.org/10.54216/JNFS.050105) |