상세정보

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 procedure of support vector algorithms based on orthogonal kernel functions is presented. Finally, a brief tutorial on Python programming for data analysis and some preliminaries of linear algebra are presented in the appendices, and the readers who are not familiar with the basics of Python programming or linear algebra can refer to them. 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.

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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 procedure of support vector algorithms based on orthogonal kernel functions is presented. Finally, a brief tutorial on Python programming for data analysis and some preliminaries of linear algebra are presented in the appendices, and the readers who are not familiar with the basics of Python programming or linear algebra can refer to them. 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.

정보제공 :

Part I Basics of Support Vector Machines
1 Introduction to SVM
Hadi Veisi
2 Basics of SVM Method and Least Squares SVM
Kourosh Parand and Fatemeh Baharifard and Alireza Afzal Aghaei and Mostafa Jani
Part II Special Kernel Classifiers3 Fractional Chebyshev Kernel Functions: Theory and Application
Amir Hosein Hadian Rasanan and Sherwin Nedaei Janbesaraei and Dumitru Baleanu
4 Fractional Legendre Kernel Functions: Theory and Application
Amirreza Azmoon and Snehashish Chakraverty and Sunil Kumar
5 Fractional Gegenbauer Kernel Functions: Theory and Application Sherwin Nedaei Janbesaraei and Amirreza Azmoon and Dumitru Baleanu
6 Fractional Jacobi Kernel Functions: Theory and Application
Amir Hosein Hadian Rasanan and Jamal Amani Rad and Malihe Shaban
and Abdon Atangana
Part III Applications of orthogonal kernels
7 Solving Ordinary Differential Equations by LS-SVM
Mohsen Razzaghi and Simin Shekarpaz and Alireza Rajabi
8 Solving Partial Differential Equations by LS-SVM
Mohammad Mahdi Moayeri and Mohammad Hemami
9 Solving Integral Equations by LS-SVR
Kourosh Parand and Alireza Afzal Aghaei and Mostafa Jani and Reza
Sahleh
10 Solving Distributed-Order Fractional Equations by LS-SVR
Amir Hosein Hadian Rasanan and Arsham Gholamzadeh Khoee and
Mostafa Jani
Part IV Orthogonal kernels in action
11 GPU Acceleration of LS-SVM, Based on Fractional Orthogonal
Functions
Armin Ahmadzadeh, Mohsen Asghari, Dara Rahmati, Saeid Gorgin, and Behzad Salami
12 Classification Using Orthogonal Kernel Functions: Tutorial on ORSVM Package
Amir Hosein Hadian Rasanan and Sherwin Nedaei Janbesaraei and Amirreza Azmoon and Mohammad Akhavan and Jamal Amani Rad
Part V Appendixes
A Python Programming Prerequisite Mohammad Akhavan