LEADER 05071nam 22008055 450 001 9910682554503321 005 20240313114930.0 010 $a981-19-6553-6 024 7 $a10.1007/978-981-19-6553-1 035 $a(CKB)5580000000525715 035 $a(DE-He213)978-981-19-6553-1 035 $a(EXLCZ)995580000000525715 100 $a20230318d2023 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aLearning with Fractional Orthogonal Kernel Classifiers in Support Vector Machines$b[electronic resource] $eTheory, Algorithms and Applications /$fedited by Jamal Amani Rad, Kourosh Parand, Snehashish Chakraverty 205 $a1st ed. 2023. 210 1$aSingapore :$cSpringer Nature Singapore :$cImprint: Springer,$d2023. 215 $a1 online resource (XIV, 305 p. 83 illus., 58 illus. in color.) 225 1 $aIndustrial and Applied Mathematics,$x2364-6845 311 $a981-19-6552-8 327 $aIntroduction 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. 330 $aThis book contains select chapters on support vector algorithms from different perspectives, including mathematical background, properties of various kernel functions, and several applications. The main focus of this book is on orthogonal kernel functions, and the properties of the classical kernel functions?Chebyshev, Legendre, Gegenbauer, and Jacobi?are reviewed in some chapters. Moreover, the fractional form of these kernel functions is introduced in the same chapters, and for ease of use for these kernel functions, a tutorial on a Python package named ORSVM is presented. The book also exhibits a variety of applications for support vector algorithms, and in addition to the classification, these algorithms along with the introduced kernel functions are utilized for solving ordinary, partial, integro, and fractional differential equations. On the other hand, nowadays, the real-time and big data applications of support vector algorithms are growing. Consequently, the Compute Unified Device Architecture (CUDA) parallelizing the procedure of support vector algorithms based on orthogonal kernel functions is presented. The book sheds light on how to use support vector algorithms based on orthogonal kernel functions in different situations and gives a significant perspective to all machine learning and scientific machine learning researchers all around the world to utilize fractional orthogonal kernel functions in their pattern recognition or scientific computing problems. 410 0$aIndustrial and Applied Mathematics,$x2364-6845 606 $aAlgebraic fields 606 $aPolynomials 606 $aMathematical optimization 606 $aQuantitative research 606 $aMachine learning 606 $aPattern recognition systems 606 $aPython (Computer program language) 606 $aField Theory and Polynomials 606 $aOptimization 606 $aData Analysis and Big Data 606 $aMachine Learning 606 $aAutomated Pattern Recognition 606 $aPython 606 $aAprenentatge automātic$2thub 606 $aAlgorismes$2thub 606 $aFuncions de Kernel$2thub 606 $aPython (Llenguatge de programaciķ) 608 $aLlibres electrōnics$2thub 615 0$aAlgebraic fields. 615 0$aPolynomials. 615 0$aMathematical optimization. 615 0$aQuantitative research. 615 0$aMachine learning. 615 0$aPattern recognition systems. 615 0$aPython (Computer program language). 615 14$aField Theory and Polynomials. 615 24$aOptimization. 615 24$aData Analysis and Big Data. 615 24$aMachine Learning. 615 24$aAutomated Pattern Recognition. 615 24$aPython. 615 7$aAprenentatge automātic 615 7$aAlgorismes 615 7$aFuncions de Kernel 615 7$aPython (Llenguatge de programaciķ) 676 $a512.3 702 $aRad$b Jamal Amani$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aParand$b Kourosh$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aChakraverty$b Snehashish$4edt$4http://id.loc.gov/vocabulary/relators/edt 906 $aBOOK 912 $a9910682554503321 996 $aLearning with Fractional Orthogonal Kernel Classifiers in Support Vector Machines$93272695 997 $aUNINA