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.

A comprehensive introduction to Support Vector Machines and related kernel methods. In the 1990s, a new type of learning algorithm was developed, based on results from statistical learning theory: the Support Vector Machine (SVM). This gave rise to a new class of theoretically elegant learning machines that use a central concept of SVMs—-kernels—for a number of learning tasks. Kernel machines provide a modular framework that can be adapted to different tasks and domains by the choice of the kernel function and the base algorithm. They are replacing neural networks in a variety of fields, including engineering, information retrieval, and bioinformatics. Learning with Kernels provides an introduction to SVMs and related kernel methods. Although the book begins with the basics, it also includes the latest research. It provides all of the concepts necessary to enable a reader equipped with some basic mathematical knowledge to enter the world of machine learning using theoretically well-founded yet easy-to-use kernel algorithms and to understand and apply the powerful algorithms that have been developed over the last few years.

An overview of the theory and application of kernel classification methods. Linear classifiers in kernel spaces have emerged as a major topic within the field of machine learning. The kernel technique takes the linear classifier—a limited, but well-established and comprehensively studied model—and extends its applicability to a wide range of nonlinear pattern-recognition tasks such as natural language processing, machine vision, and biological sequence analysis. This book provides the first comprehensive overview of both the theory and algorithms of kernel classifiers, including the most recent developments. It begins by describing the major algorithmic advances: kernel perceptron learning, kernel Fisher discriminants, support vector machines, relevance vector machines, Gaussian processes, and Bayes point machines. Then follows a detailed introduction to learning theory, including VC and PAC-Bayesian theory, data-dependent structural risk minimization, and compression bounds. Throughout, the book emphasizes the interaction between theory and algorithms: how learning algorithms work and why. The book includes many examples, complete pseudo code of the algorithms presented, and an extensive source code library.

Covering the fundamentals of kernel-based learning theory, this is an essential resource for graduate students and professionals in computer science.

Support Vectors Machines have become a well established tool within machine learning. They work well in practice and have now been used across a wide range of applications from recognizing hand-written digits, to face identification, text categorisation, bioinformatics, and database marketing. In this book we give an introductory overview of this subject. We start with a simple Support Vector Machine for performing binary classification before considering multi-class classification and learning in the presence of noise. We show that this framework can be extended to many other scenarios such as prediction with real-valued outputs, novelty detection and the handling of complex output structures such as parse trees. Finally, we give an overview of the main types of kernels which are used in practice and how to learn and make predictions from multiple types of input data. Table of Contents: Support Vector Machines for Classification / Kernel-based Models / Learning with Kernels

What Is Support Vector Machine In the field of machine learning, support vector machines are supervised learning models that examine data for classification and regression analysis. These models come with related learning algorithms. Vladimir Vapnik and his coworkers at AT&T Bell Laboratories were responsible for its creation. Because they are founded on statistical learning frameworks or the VC theory, which was developed by Vapnik and Chervonenkis (1974), support vector machines (SVMs) are among the most accurate prediction systems. A non-probabilistic binary linear classifier is what results when an SVM training algorithm is given a series of training examples, each of which is marked as belonging to one of two categories. The algorithm then develops a model that assigns subsequent examples to either one of the two categories or neither of them. The support vector machine (SVM) allocates training examples to points in space in such a way as to maximize the difference in size between the two categories. After that, new examples are mapped into that same space, and depending on which side of the gap they fall on, a prediction is made as to which category they belong to. How You Will Benefit (I) Insights, and validations about the following topics: Chapter 1: Support vector machine Chapter 2: Linear classifier Chapter 3: Perceptron Chapter 4: Projection (linear algebra) Chapter 5: Linear separability Chapter 6: Kernel method Chapter 7: Sequential minimal optimization Chapter 8: Least-squares support vector machine Chapter 9: Hinge loss Chapter 10: Polynomial kernel (II) Answering the public top questions about support vector machine. (III) Real world examples for the usage of support vector machine in many fields. (IV) 17 appendices to explain, briefly, 266 emerging technologies in each industry to have 360-degree full understanding of support vector machine' technologies. Who This Book Is For Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of support vector machine.

This is a comprehensive introduction to Support Vector Machines, a generation learning system based on advances in statistical learning theory.

An overview of the theory and application of kernel classification methods.