Learning with Fractional Orthogonal Kernel Classifiers in Support Vector Machines / Industrial and Applied Mathematics (PDF)
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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.
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
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 researcher and teacher, he has authored 23 books, published 382 research papers (till date) in journals and conferences. He is on the editorial boards of various international journals, book series, and conference proceedings. Professor Chakraverty is the chief editor of the International Journal of Fuzzy Computation and Modelling, associate editor of the journal, Computational Methods in Structural Engineering, Frontiers in Built Environment, and on the editorial board of several other book series and journals: Modeling and Optimization in Science and Technologies (Springer Nature), Coupled Systems Mechanics, Curved and Layered Structures, Journal of Composites Science, Engineering Research Express, and Applications and Applied Mathematics: An International Journal. He also is a reviewer of around 50 international journals of repute, and he was the president of the Section of Mathematical Sciences (including Statistics) of "Indian Science Congress" (2015-2016) and was the vicepresident of Orissa Mathematical Society (from 2011-2013). He has guided 18 Ph.D. students and 9 ongoing. He has undertaken around 16 research projects as principal investigator funded by international and national agencies totaling about INR 1.5 crore. He also has successfully organized a good number of international and national conferences, workshops, and training programs.
- 2023, 2023, 305 Seiten, Englisch
- Herausgegeben: Jamal Amani Rad, Kourosh Parand, Snehashish Chakraverty
- Verlag: Springer Nature Singapore
- ISBN-10: 9811965536
- ISBN-13: 9789811965531
- Erscheinungsdatum: 18.03.2023
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