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.

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