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Adaptive Arctan kernel: a generalized kernel for support vector machine

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Abstract

Support Vector Machines (SVMs) can learn from high-dimensional and small amounts of training data, thanks to effective optimization methods and a diverse set of kernel functions (KFs). The adaptability of SVM to numerous real-world problems has increased interest in the SVM method, and studies conducted with this method carry significant weight in various fields. The fixed parameter “AtanK” for KFs must be specified before the SVM model training process. Therefore, determining the appropriate kernel parameter values can be timE−consuming and may lead to slow convergence of the SVM model. On the other hand, the method provides faster and more robust convergence due to the adaptive parameter in the SVM model. In this study, a new Adaptive Arctan (AA) KF, tailored to the characteristics of different datasets, is proposed as an enhancement to the AtanK KF for the SVM algorithm. The proposed AA KF is compared with experimental results on 30 public KEEL and UCI datasets, alongside AtanK, adaptive Gaussian, Radial Basis Function, linear, and polynomial KFs. The results demonstrate that the proposed AA KF outperforms the other KFs, and it exhibits superior learning ability.

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Data availability

The datasets generated during and/or analyzed during the current study are available in the [UCI and KEEL] repository.

References

  1. Cortes C and Vapnik V 1995 Support vector machine. Mach. Learn. 20(3): 273–297

    Article  Google Scholar 

  2. Kilicarslan S, Adem K and Celik M 2020 Diagnosis and classification of cancer using hybrid model based on ReliefF and convolutional neural network. Med. Hypotheses 137: 109577

    Article  Google Scholar 

  3. Cetin O and Temurtas F 2021 A comparative study on classification of magnetoencephalography signals using probabilistic neural network and multilayer neural network. Soft Comput. 25: 2267–2275

    Article  Google Scholar 

  4. Ozguven M, Yilmaz G, Adem K and Kozkurt C 2019 Use of support vector machines and artificial neural network methods in variety ımprovement studies: potato example. Curr. Investig. Agric. Curr. Res. 6(1): 706–712

    Google Scholar 

  5. Melenk J and Babuška I 1996 The partition of unity finite element method: basic theory and applications. Comput. Methods Appl. Mech. Eng. 139(1–4): 289–314

    Article  MathSciNet  Google Scholar 

  6. Baş S and Körpinar T 2019 Modified roller coaster surface in space. Mathematics 7(2): 195

    Article  Google Scholar 

  7. An-na W, Yue Z, Yun-tao H and Yun-lu L 2010 A novel construction of SVM compound kernel function. In: 2010 International Conference on Logistics Systems and Intelligent Management (ICLSIM) vol. 3, pp. 1462–1465

  8. Lin H and Lin C 2003 A study on sigmoid kernels for SVM and the training of non-PSD kernels by SMO-type methods. Neural Comput. 3(1–32): 16

    Google Scholar 

  9. Müller K, Mika S, Tsuda K and Schölkopf K 2018 An introduction to kernel-based learning algorithms. In: Handbook of Neural Network Signal Processing. pp. 4–1

  10. Fan L and Sung K 2003 Model-based varying pose face detection and facial feature registration in colour images. Pattern Recognit. Lett. 24(1–3): 237–249

    Article  Google Scholar 

  11. Deng N and Tian Y 2004 Support Vector Machines: A New Method in Data Mining. Science Press

  12. Chapelle O, Vapnik V, Bousquet O and Mukherjee S 2002 Choosing multiple parameters for support vector machines. Mach. Learn. 46: 131–159

    Article  Google Scholar 

  13. Elen A, Baş S and Közkurt C 2022 An adaptive Gaussian kernel for support vector machine. Arab. J. Sci. Eng. 47(8): 10579–10588

    Article  Google Scholar 

  14. Batuwita R and Palade V 2013 Class imbalance learning methods for support vector machines. In: Imbalanced Learning: Foundations, Algorithms, and Applications. pp. 83–99

  15. Hofmann T, Schölkopf B and Smola A 2008 Kernel methods in machine learning. Ann. Stat. 36(3): 1171–1220

    Article  MathSciNet  Google Scholar 

  16. Ding X, Liu J, Yang F and Cao J 2021 Random radial basis function kernel-based support vector machine. J. Frankl. Inst. 358(18): 10121–10140

    Article  MathSciNet  Google Scholar 

  17. Negri R, Da Silva E and Casaca W 2018 Inducing contextual classifications with kernel functions into support vector machines. IEEE Geosci. Remote Sens. Lett. 15(6): 962–966

    Article  Google Scholar 

  18. Tian M and Li H 2021 AtanK-A new SVM kernel for classification. Appl. Math. Nonlinear Sci. 8(1): 135–146

    Article  Google Scholar 

  19. Khan I, Fattah H A and Shill P C 2021 A hybrid kernel support vector machine for predicting protein structure. In: 2021 International Conference on Automation, Control and Mechatronics for Industry 4.0 (ACMI). pp. 1–5

  20. Liu X and He W 2022 Adaptive kernel scaling support vector machine with application to a prostate cancer image study. J. Appl. Stat. 49(6): 1465–1484

    Article  MathSciNet  Google Scholar 

  21. Ba W, Lu Z and Li Q 2021 Prediction of product quality based on multiple kernel learning least square support vector machine regression. In: 2021 China Automation Congress (CAC). pp. 3197–3201

  22. Kiliçarslan S and Celik M 2022 KAF+ RSigELU: a nonlinear and kernel-based activation function for deep neural networks. Neural Comput. Appl. 34(16): 13909–21392

    Article  Google Scholar 

  23. Kilicarslan S, Celik M and Sahin Ş 2021 Hybrid models based on genetic algorithm and deep learning algorithms for nutritional Anemia disease classification. Biomed. Signal Process. Control 63: 102231

    Article  Google Scholar 

  24. Kiliçarslan S and Celik M 2021 RSigELU: a nonlinear activation function for deep neural networks. Expert Syst. Appl. 174: 114805

    Article  Google Scholar 

  25. Pacal I and Kilicarslan S 2023 Deep learning-based approaches for robust classification of cervical cancer. Neural Comput. Appl. 35(25): 18813–21882

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Accounting and Tax, Bandirma Vocational School, Bandirma Onyedi Eylul University, Bandirma, Balıkesir, Turkey

    Selçuk Baş

  2. Department of Software Engineering, Faculty of Engineering and Natural Sciences, Bandirma Onyedi Eylul University, Bandirma, Balıkesir, Turkey

    Serhat Kiliçarslan & Abdullah Elen

  3. Department of Computer Engineering, Faculty of Engineering and Natural Sciences, Bandirma Onyedi Eylul University, Bandirma, Balıkesir, Turkey

    Cemil Közkurt

Authors
  1. Selçuk Baş
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  2. Serhat Kiliçarslan
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  3. Abdullah Elen
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  4. Cemil Közkurt
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Correspondence to Serhat Kiliçarslan.

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Baş, S., Kiliçarslan, S., Elen, A. et al. Adaptive Arctan kernel: a generalized kernel for support vector machine. Sādhanā 49, 120 (2024). https://doi.org/10.1007/s12046-023-02358-y

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  • DOI: https://doi.org/10.1007/s12046-023-02358-y

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