Learning With Fractional Orthogonal Kernel Classifiers In Support Vector Machines PDF Download
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Author | : Jamal Amani Rad |
Publisher | : Springer Nature |
Total Pages | : 312 |
Release | : 2023-03-18 |
Genre | : Mathematics |
ISBN | : 9811965536 |
Download Learning with Fractional Orthogonal Kernel Classifiers in Support Vector Machines Book in PDF, ePub and Kindle
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.
Author | : Bernhard Schölkopf |
Publisher | : MIT Press |
Total Pages | : 658 |
Release | : 2002 |
Genre | : Computers |
ISBN | : 9780262194754 |
Download Learning with Kernels Book in PDF, ePub and Kindle
A comprehensive introduction to Support Vector Machines and related kernel methods.
Author | : Ralf Herbrich |
Publisher | : MIT Press |
Total Pages | : 402 |
Release | : 2001-12-07 |
Genre | : Computers |
ISBN | : 9780262263047 |
Download Learning Kernel Classifiers Book in PDF, ePub and Kindle
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.
Author | : M.N. Murty |
Publisher | : Springer |
Total Pages | : 103 |
Release | : 2016-08-16 |
Genre | : Computers |
ISBN | : 3319410636 |
Download Support Vector Machines and Perceptrons Book in PDF, ePub and Kindle
This work reviews the state of the art in SVM and perceptron classifiers. A Support Vector Machine (SVM) is easily the most popular tool for dealing with a variety of machine-learning tasks, including classification. SVMs are associated with maximizing the margin between two classes. The concerned optimization problem is a convex optimization guaranteeing a globally optimal solution. The weight vector associated with SVM is obtained by a linear combination of some of the boundary and noisy vectors. Further, when the data are not linearly separable, tuning the coefficient of the regularization term becomes crucial. Even though SVMs have popularized the kernel trick, in most of the practical applications that are high-dimensional, linear SVMs are popularly used. The text examines applications to social and information networks. The work also discusses another popular linear classifier, the perceptron, and compares its performance with that of the SVM in different application areas.>
Author | : Ralf Herbrich |
Publisher | : Mit Press |
Total Pages | : 364 |
Release | : 2002-01 |
Genre | : Computers |
ISBN | : 9780262083065 |
Download Learning Kernel Classifiers Book in PDF, ePub and Kindle
An overview of the theory and application of kernel classification methods.
Author | : Alexander J. Smola |
Publisher | : MIT Press |
Total Pages | : 436 |
Release | : 2000 |
Genre | : Computers |
ISBN | : 9780262194488 |
Download Advances in Large Margin Classifiers Book in PDF, ePub and Kindle
The book provides an overview of recent developments in large margin classifiers, examines connections with other methods (e.g., Bayesian inference), and identifies strengths and weaknesses of the method, as well as directions for future research. The concept of large margins is a unifying principle for the analysis of many different approaches to the classification of data from examples, including boosting, mathematical programming, neural networks, and support vector machines. The fact that it is the margin, or confidence level, of a classification--that is, a scale parameter--rather than a raw training error that matters has become a key tool for dealing with classifiers. This book shows how this idea applies to both the theoretical analysis and the design of algorithms. The book provides an overview of recent developments in large margin classifiers, examines connections with other methods (e.g., Bayesian inference), and identifies strengths and weaknesses of the method, as well as directions for future research. Among the contributors are Manfred Opper, Vladimir Vapnik, and Grace Wahba.
Author | : Bernhard Schölkopf |
Publisher | : MIT Press |
Total Pages | : 400 |
Release | : 1999 |
Genre | : Computers |
ISBN | : 9780262194167 |
Download Advances in Kernel Methods Book in PDF, ePub and Kindle
A young girl hears the story of her great-great-great-great- grandfather and his brother who came to the United States to make a better life for themselves helping to build the transcontinental railroad.
Author | : Ionut B. Brandusoiu |
Publisher | : GAER Publishing House |
Total Pages | : 78 |
Release | : 2020-08-19 |
Genre | : Computers |
ISBN | : 9737208064 |
Download HOW TO FINE-TUNE SUPPORT VECTOR MACHINES FOR CLASSIFICATION Book in PDF, ePub and Kindle
This book covers in the first part the theoretical aspects of support vector machines and their functionality, and then based on the discussed concepts it explains how to find-tune a support vector machine to yield highly accurate prediction results which are adaptable to any classification tasks. The introductory part is extremely beneficial to someone new to learning support vector machines, while the more advanced notions are useful for everyone who wants to understand the mathematics behind support vector machines and how to find-tune them in order to generate the best predictive performance of a certain classification model.
Author | : Zhuang Wang |
Publisher | : |
Total Pages | : 124 |
Release | : 2010 |
Genre | : |
ISBN | : |
Download Budgeted Online Kernel Classifiers for Large Scale Learning Book in PDF, ePub and Kindle
In the environment where new large scale problems are emerging in various disciplines and pervasive computing applications are becoming more common, there is an urgent need for machine learning algorithms that could process increasing amounts of data using comparatively smaller computing resources in a computational efficient way. Previous research has resulted in many successful learning algorithms that scale linearly or even sub-linearly with sample size and dimension, both in runtime and in space. However, linear or even sub-linear space scaling is often not sufficient, because it implies an unbounded growth in memory with sample size. This clearly opens another challenge: how to learn from large, or practically infinite, data sets or data streams using memory limited resources. Online learning is an important learning scenario in which a potentially unlimited sequence of training examples is presented one example at a time and can only be seen in a single pass. This is opposed to offline learning where the whole collection of training examples is at hand. The objective is to learn an accurate prediction model from the training stream. Upon on repetitively receiving fresh example from stream, typically, online learning algorithms attempt to update the existing model without retraining. The invention of the Support Vector Machines (SVM) attracted a lot of interest in adapting the kernel methods for both offline and online learning. Typical online learning for kernel classifiers consists of observing a stream of training examples and their inclusion as prototypes when specified conditions are met. However, such procedure could result in an unbounded growth in the number of prototypes. In addition to the danger of the exceeding the physical memory, this also implies an unlimited growth in both update and prediction time. To address this issue, in my dissertation I propose a series of kernel-based budgeted online algorithms, which have constant space and constant update and prediction time. This is achieved by maintaining a fixed number of prototypes under the memory budget. Most of the previous works on budgeted online algorithms focus on kernel perceptron. In the first part of the thesis, I review and discuss these existing algorithms and then propose a kernel perceptron algorithm which removes the prototype with the minimal impact on classification accuracy to maintain the budget. This is achieved by dual use of cached prototypes for both model presentation and validation. In the second part, I propose a family of budgeted online algorithms based on the Passive-Aggressive (PA) style. The budget maintenance is achieved by introducing an additional constraint into the original PA optimization problem. A closed-form solution was derived for the budget maintenance and model update. In the third part, I propose a budgeted online SVM algorithm. The proposed algorithm guarantees that the optimal SVM solution is maintained on all the prototype examples at any time. To maximize the accuracy, prototypes are constructed to approximate the data distribution near the decision boundary. In the fourth part, I propose a family of budgeted online algorithms for multi-class classification. The proposed algorithms are the recently proposed SVM training algorithm Pegasos. I prove that the gap between the budgeted Pegasos and the optimal SVM solution directly depends on the average model degradation due to budget maintenance. Following the analysis, I studied greedy multi-class budget maintenance methods based on removal, projection and merging of SVs. In each of these four parts, the proposed algorithms were experimentally evaluated against the state-of-art competitors. The results show that the proposed budgeted online algorithms outperform the competitive algorithm and achieve accuracy comparable to non-budget counterparts while being extremely computationally efficient.
Author | : Nello Cristianini |
Publisher | : |
Total Pages | : 189 |
Release | : 2000 |
Genre | : Electronic book |
ISBN | : 9781316085417 |
Download An Introduction to Support Vector Machines Book in PDF, ePub and Kindle
A comprehensive introduction to this recent method for machine learning and data mining.