Browsing by Author "Nedaei Janbesaraei, S."

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Citation - Scopus: 6
Fractional Chebyshev Kernel Functions: Theory and Application
(Springer, 2023) Hadian Rasanan, A.H.; Nedaei Janbesaraei, S.; Baleanu, D.
Orthogonal functions have many useful properties and can be used for different purposes in machine learning. One of the main applications of the orthogonal functions is producing powerful kernel functions for the support vector machine algorithm. Maybe the simplest orthogonal function that can be used for producing kernel functions is the Chebyshev polynomials. In this chapter, after reviewing some essential properties of Chebyshev polynomials and fractional Chebyshev functions, various Chebyshev kernel functions are presented, and fractional Chebyshev kernel functions are introduced. Finally, the performance of the various Chebyshev kernel functions is illustrated on two sample datasets. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd 2023.
Citation - Scopus: 3
Fractional Gegenbauer Kernel Functions: Theory and Application
(Springer, 2023) Azmoon, A.; Baleanu, D.; Nedaei Janbesaraei, S.
Because of the usage of many functions as a kernel, the support vector machine method has demonstrated remarkable versatility in tackling numerous machine learning issues. Gegenbauer polynomials, like the Chebyshev and Legender polynomials which are introduced in previous chapters, are among the most commonly utilized orthogonal polynomials that have produced outstanding results in the support vector machine method. In this chapter, some essential properties of Gegenbauer and fractional Gegenbauer functions are presented and reviewed, followed by the kernels of these functions, which are introduced and validated. Finally, the performance of these functions in addressing two issues (two example datasets) is evaluated. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd 2023.