Titlebook: Learning with Fractional Orthogonal Kernel Classifiers in Support Vector Machines; Theory, Algorithms a Jamal Amani Rad,Kourosh Parand,Sneh

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Fractional Chebyshev Kernel Functions: Theory and Applicationd 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.

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Fractional Legendre Kernel Functions: Theory and Application some basic features of Legendre and fractional Legendre functions are introduced and reviewed, and then the kernels of these functions are introduced and validated. Finally, the performance of these functions in solving two problems (two sample datasets) is measured.

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Fractional Gegenbauer Kernel Functions: Theory and Applicationl 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.

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Classification Using Orthogonal Kernel Functions: Tutorial on ORSVM Packagech effort to implement. To make it easy for anyone who needs to try and use these kernels, a Python package is provided here. In this chapter, the ORSVM package is introduced as an SVM classification package with orthogonal kernel functions.

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Solving Ordinary Differential Equations by LS-SVM Finally, by presenting some numerical examples, the results of the current method are compared with other methods. The comparison shows that the proposed method is fast and highly accurate with exponential convergence.

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Basics of SVM Method and Least Squares SVM a unique solution and also satisfies the Karush–Kuhn–Tucker conditions, it can be solved very efficiently. In this chapter, the formulation of optimization problems which have arisen in the various forms of support vector machine algorithms is discussed.

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Fractional Chebyshev Kernel Functions: Theory and Applicationgonal 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 an