# Learning with Fractional Orthogonal Kernel Classifiers in Support Vector Machines

Theory, Algorithms and Applications
(Sprache: Englisch)

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,...

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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 functions-Chebyshev, Legendre, Gegenbauer, and Jacobi-are 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.

Inhaltsverzeichnis zu „Learning with Fractional Orthogonal Kernel Classifiers in Support Vector Machines “

Introduction to SVM.- Basics of SVM Method and Least Squares SVM.- Fractional Chebyshev Kernel Functions: Theory and Application.- Fractional Legendre Kernel Functions: Theory and Application.- Fractional Gegenbauer Kernel Functions: Theory and Application.- Fractional Jacobi Kernel Functions: Theory and Application.- Solving Ordinary Differential Equations by LS-SVM.- Solving Partial Differential Equations by LS-SVM.- Solving Integral Equations by LS-SVR.- Solving Distributed-Order Fractional Equations by LS-SVR.- GPU Acceleration of LS-SVM, Based on Fractional Orthogonal Functions.- Classification Using Orthogonal Kernel Functions: Tutorial on ORSVM Package.
Autoren-Porträt

JAMAL AMANI RAD is assistant professor at the Department of Cognitive Modeling, Institute for Cognitive and Brain Sciences, Shahid Beheshti University (SBU), Evin, Tehran, Iran. He received his Ph.D. in numerical analysis (scientific computing) from SBU in 2015. Following his Ph.D., he started a one-year post-doctoral fellowship at SBU in May 2016. He is currently focused on the development of mathematical models for cognitive processes in mathematical psychology, especially in risky or perceptual decision making. With H-index 18, he has published 64 research papers with 1032 citations. He also has contributed a chapter to the book, Mathematical Methods in Interdisciplinary Sciences, as well as published two books in Persian. He has supervised 11 M.Sc. theses and 3 Ph.D. theses. He has so far developed a good scientific collaboration with leading international researchers in mathematical modeling: E. Larsson and L. Sydow at Uppsala University, L.V. Ballestra at the University of Bologna, and E. Scalas at the University of Sussex. He is a reviewer of a few reputed journals as well as has organized quite a few international level conferences and workshops on deep learning and neural network.KOUROSH PARAND is professor at the Department of Statistics and Actuarial Science, University of Waterloo, Canada. He received his Ph.D. in numerical analysis from the Amirkabir University of Technology, Iran, in 2007. Professor Parand has published more than 220 research papers in reputed journals and conferences and has more than 3400 citations. His fields of interest include partial differential equations, ordinary differential equations, fractional calculus, spectral methods, numerical methods, and mathematical physics. Currently, he is working on machine learning techniques such as least squares support vector regression and deep learning for some engineering and neuroscience problems. He also collaborates, as a reviewer, with different prestigious international

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SNEHASHISH CHAKRAVERTY is professor at the Department of Mathematics (Applied Mathematics Group), National Institute of Technology Rourkela, Odisha, as a senior (higher administrative grade) professor and dean of Student Welfare. Earlier, he worked with the CSIR-Central Building Research Institute, Roorkee, India. He had been visiting professor at Concordia University and McGill University, Canada, during 1997-1999, and the University of Johannesburg, South Africa, during 2011-2014. After completing his graduation from St. Columba's College (now Ranchi University, Jharkhand, India), he did his M.Sc. (Mathematics), M.Phil. (Computer Applications), and Ph.D. from the University of Roorkee (now, the Indian Institute of Technology Roorkee), securing the first position in 1992. Thereafter, he did his post-doctoral research at the Institute of Sound and Vibration Research (ISVR), University of Southampton, UK, and at the Faculty of Engineering and Computer Science, Concordia University, Canada.

Professor Chakraverty is a recipient of several prestigious awards: Indian National Science Academy (INSA) nomination under International Collaboration/Bilateral Exchange Program (with the Czech Republic), Platinum Jubilee ISCA Lecture Award (2014), CSIR Young Scientist Award (1997), BOYSCAST Fellow (DST), UCOST Young Scientist Award (2007, 2008), Golden Jubilee Director's (CBRI) Award (2001), INSA International Bilateral Exchange Award (2015), Roorkee University Gold Medals (1987, 1988) for securing the first positions in M.Sc. and M.Phil. (Computer Applications). His present research area includes differential equations (ordinary, partial, and fractional), numerical analysis and computational methods, structural dynamics (FGM, nano) and fluid dynamics, mathematical and uncertainty modeling, soft computing and machine intelligence (artificial neural network, fuzzy, interval and affine computations).

With more than 30 years of experience as a researc

SNEHASHISH CHAKRAVERTY is professor at the Department of Mathematics (Applied Mathematics Group), National Institute of Technology Rourkela, Odisha, as a senior (higher administrative grade) professor and dean of Student Welfare. Earlier, he worked with the CSIR-Central Building Research Institute, Roorkee, India. He had been visiting professor at Concordia University and McGill University, Canada, during 1997-1999, and the University of Johannesburg, South Africa, during 2011-2014. After completing his graduation from St. Columba's College (now Ranchi University, Jharkhand, India), he did his M.Sc. (Mathematics), M.Phil. (Computer Applications), and Ph.D. from the University of Roorkee (now, the Indian Institute of Technology Roorkee), securing the first position in 1992. Thereafter, he did his post-doctoral research at the Institute of Sound and Vibration Research (ISVR), University of Southampton, UK, and at the Faculty of Engineering and Computer Science, Concordia University, Canada.

Professor Chakraverty is a recipient of several prestigious awards: Indian National Science Academy (INSA) nomination under International Collaboration/Bilateral Exchange Program (with the Czech Republic), Platinum Jubilee ISCA Lecture Award (2014), CSIR Young Scientist Award (1997), BOYSCAST Fellow (DST), UCOST Young Scientist Award (2007, 2008), Golden Jubilee Director's (CBRI) Award (2001), INSA International Bilateral Exchange Award (2015), Roorkee University Gold Medals (1987, 1988) for securing the first positions in M.Sc. and M.Phil. (Computer Applications). His present research area includes differential equations (ordinary, partial, and fractional), numerical analysis and computational methods, structural dynamics (FGM, nano) and fluid dynamics, mathematical and uncertainty modeling, soft computing and machine intelligence (artificial neural network, fuzzy, interval and affine computations).

With more than 30 years of experience as a researc

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Bibliographische Angaben

- 2024, 2023, XIV, 305 Seiten, 58 farbige Abbildungen, Maße: 15,5 x 23,5 cm, Kartoniert (TB), Englisch
- Herausgegeben: Jamal Amani Rad, Kourosh Parand, Snehashish Chakraverty
- Verlag: Springer, Berlin
- ISBN-10: 9811965552
- ISBN-13: 9789811965555

Sprache:

Englisch

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