Learning with Fractional Orthogonal Kernel Classifiers in Support Vector Machines: Theory, Algorithms and Applications
Rad, Jamal Amani, Parand, Kourosh, Chakraverty, Snehashish
- 出版商: Springer
- 出版日期: 2024-03-20
- 售價: $5,710
- 貴賓價: 9.5 折 $5,425
- 語言: 英文
- 頁數: 305
- 裝訂: Quality Paper - also called trade paper
- ISBN: 9811965552
- ISBN-13: 9789811965555
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相關分類:
Algorithms-data-structures
海外代購書籍(需單獨結帳)
相關主題
商品描述
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.
商品描述(中文翻譯)
本書包含了關於支持向量算法的選定章節，從不同的角度探討，包括數學背景、各種核函數的特性以及幾個應用。本書的主要焦點是正交核函數，並在某些章節中回顧了經典核函數的特性——切比雪夫（Chebyshev）、勒讓德（Legendre）、根根堡（Gegenbauer）和雅可比（Jacobi）。此外，這些核函數的分數形式也在同一章節中介紹，並為了方便使用這些核函數，提供了一個名為ORSVM的Python套件的教學。本書還展示了支持向量算法的多種應用，除了分類外，這些算法連同所介紹的核函數也被用於解決常微分方程、偏微分方程、積分方程和分數微分方程。
另一方面，現今支持向量算法的即時和大數據應用正在增長。因此，基於正交核函數的支持向量算法程序的計算統一設備架構（CUDA）平行化方法被提出。本書闡明了如何在不同情況下使用基於正交核函數的支持向量算法，並為全球所有機器學習和科學機器學習研究人員提供了一個重要的視角，以便在他們的模式識別或科學計算問題中利用分數正交核函數。
作者簡介
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 journals.
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.
作者簡介(中文翻譯)
JAMAL AMANI RAD 是伊朗德黑蘭Shahid Beheshti大學（SBU）認知與腦科學研究所認知建模系的助理教授。他於2015年獲得SBU的數值分析（科學計算）博士學位。獲得博士學位後，他於2016年5月開始在SBU進行為期一年的博士後研究。他目前專注於數學心理學中認知過程的數學模型開發，特別是在風險或感知決策方面。擁有H指數18，他已發表64篇研究論文，引用次數達1032次。他還為《跨學科科學中的數學方法》一書撰寫了一章，並出版了兩本波斯語書籍。他指導了11篇碩士論文和3篇博士論文。至今，他與數學建模領域的國際領先研究者建立了良好的科學合作關係，包括瑞典烏普薩拉大學的E. Larsson和L. Sydow、意大利博洛尼亞大學的L.V. Ballestra，以及英國薩塞克斯大學的E. Scalas。他是幾本知名期刊的審稿人，並組織了多場國際級的深度學習和神經網絡會議及研討會。
KOUROSH PARAND 是加拿大滑鐵盧大學統計與精算科學系的教授。他於2007年在伊朗阿米爾卡比爾科技大學獲得數值分析博士學位。Parand教授在知名期刊和會議上發表了超過220篇研究論文，引用次數超過3400次。他的研究興趣包括偏微分方程、常微分方程、分數微積分、譜方法、數值方法和數學物理。目前，他正在研究機器學習技術，如最小二乘支持向量回歸和深度學習，應用於一些工程和神經科學問題。他還作為審稿人與不同的國際知名期刊合作。
SNEHASHISH CHAKRAVERTY 是印度奧迪沙州國立技術研究所（National Institute of Technology Rourkela）數學系（應用數學組）的教授，擔任高級教授及學生福利院長。此前，他曾在印度魯爾基的CSIR中央建築研究所工作。他在1997年至1999年間曾擔任加拿大康考迪亞大學和麥吉爾大學的訪問教授，以及在2011年至2014年間擔任南非約翰尼斯堡大學的訪問教授。在從聖科倫巴學院（現為印度賴恰大學）畢業後，他在魯爾基大學（現為印度魯爾基科技大學）獲得數學碩士、計算機應用碩士及博士學位，並於1992年獲得第一名。隨後，他在英國南安普敦大學聲音與振動研究所（ISVR）和加拿大康考迪亞大學工程與計算機科學學院進行博士後研究。
Chakraverty教授獲得了多項著名獎項，包括印度國家科學院（INSA）在國際合作/雙邊交流計劃下的提名（與捷克共和國合作）、2014年白金禧年ISCA演講獎、1997年CSIR青年科學家獎、BOYSCAST獎（DST）、2007年和2008年UCOST青年科學家獎、2001年金禧年主任獎（CBRI）、2015年INSA國際雙邊交流獎，以及1987年和1988年魯爾基大學金獎（M.Sc.和計算機應用碩士第一名）。他目前的研究領域包括微分方程（常微分、偏微分和分數）、數值分析和計算方法、結構動力學（FGM、納米）和流體動力學、數學和不確定性建模、軟計算和機器智能（人工神經網絡、模糊、區間和仿射計算）。
擁有超過30年的研究經驗。
