Learning With Fractional Orthogonal Kernel Classifiers In Support Vector Machines
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Learning with Fractional Orthogonal Kernel Classifiers in Support Vector Machines
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.
Dimensionality Reduction in Machine Learning
Dimensionality Reduction in Machine Learning covers both the mathematical and programming sides of dimension reduction algorithms, comparing them in various aspects. Part One provides an introduction to Machine Learning and the Data Life Cycle, with chapters covering the basic concepts of Machine Learning, essential mathematics for Machine Learning, and the methods and concepts of Feature Selection. Part Two covers Linear Methods for Dimension Reduction, with chapters on Principal Component Analysis and Linear Discriminant Analysis. Part Three covers Non-Linear Methods for Dimension Reduction, with chapters on Linear Local Embedding, Multi-dimensional Scaling, and t-distributed Stochastic Neighbor Embedding.Finally, Part Four covers Deep Learning Methods for Dimension Reduction, with chapters on Feature Extraction and Deep Learning, Autoencoders, and Dimensionality reduction in deep learning through group actions. With this stepwise structure and the applied code examples, readers become able to apply dimension reduction algorithms to different types of data, including tabular, text, and image data. - Provides readers with a comprehensive overview of various dimension reduction algorithms, including linear methods, non-linear methods, and deep learning methods - Covers the implementation aspects of algorithms supported by numerous code examples - Compares different algorithms so the reader can understand which algorithm is suitable for their purpose - Includes algorithm examples that are supported by a Github repository which consists of full notebooks for the programming code
Recent Developments in Fractional Calculus: Theory, Applications, and Numerical Simulations
This book discusses recent developments in fractional calculus and fractional differential equations in a very elaborative manner and is of interest to research scholars, academicians and scientists who want to enhance the knowledge in the context of new insights and mathematical ideas in fractional calculus and its emerging applications in various fields. It focuses on strengthening the existing results along with identifying the practical challenges encountered. The purpose of this collection is to provide comprehension of articles that reflect recent mathematical results as well as some results in applied sciences untouched by the tools and techniques of fractional calculus along with their modelling and computation having applications in diverse arenas.