Learning with fractional orthogonal kernel classifiers in support vector machines : theory, algorithms and applications / Jamal Amani Rad, Kourosh Parand, Snehashish Chakraverty, editors.

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Learning with fractional orthogonal kernel classifiers in support vector machines : theory, algorithms and applications / Jamal Amani Rad, Kourosh Parand, Snehashish Chakraverty, editors.

9789811965531 (electronic bk.)
9811965536 (electronic bk.)
9789811965524
9811965528

Singapore : Springer, 2022.

English

1 online resource.

10.1007/978-981-19-6553-1 doi

Q325.785

006.3/1

This book contains select chapters on support vector algorithms from different perspectives, including mathematical background, properties of various kernel functions, and several applications. The main focus of this book is on orthogonal kernel functions, and the properties of the classical kernel functionsChebyshev, Legendre, Gegenbauer, and Jacobiare reviewed in some chapters. Moreover, the fractional form of these kernel functions is introduced in the same chapters, and for ease of use for these kernel functions, a tutorial on a Python package named ORSVM is presented. The book also exhibits a variety of applications for support vector algorithms, and in addition to the classification, these algorithms along with the introduced kernel functions are utilized for solving ordinary, partial, integro, and fractional differential equations. On the other hand, nowadays, the real-time and big data applications of support vector algorithms are growing. Consequently, the Compute Unified Device Architecture (CUDA) parallelizing the procedure of support vector algorithms based on orthogonal kernel functions is presented. The book sheds light on how to use support vector algorithms based on orthogonal kernel functions in different situations and gives a significant perspective to all machine learning and scientific machine learning researchers all around the world to utilize fractional orthogonal kernel functions in their pattern recognition or scientific computing problems.

References -- 4 Fractional Legendre Kernel Functions: Theory and Application -- 4.1 Introduction -- 4.2 Preliminaries -- 4.2.1 Properties of Legendre Polynomials -- 4.2.2 Properties of Fractional Legendre Functions -- 4.3 Legendre Kernel Functions -- 4.3.1 Ordinary Legendre Kernel Function -- 4.3.2 Other Legendre Kernel Functions -- 4.3.3 Fractional Legendre Kernel -- 4.4 Application of Legendre Kernel Functions on Real Datasets -- 4.4.1 Spiral Dataset -- 4.4.2 Three Monks' Dataset -- 4.5 Conclusion -- References -- 5 Fractional Gegenbauer Kernel Functions: Theory and Application

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Industrial and applied mathematics.

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