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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.
We introduce a new family of positive-definite kernels that mimic the computation in large neural networks. We derive the different members of this family by considering neural networks with different activation functions. Using these kernels as building blocks, we also show how to construct other positive-definite kernels by operations such as composition, multiplication, and averaging. We explore the use of these kernels in standard models of supervised learning, such as support vector machines for large margin classification, as well as in new models of unsupervised learning based on deep architectures. On several problems, we obtain better results than previous, leading benchmarks from both support vector machines with Gaussian kernels as well as deep belief nets. Finally, we examine the properties of these kernels by analyzing the geometry of surfaces that they induce in Hilbert space.
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.
Offering a fundamental basis in kernel-based learning theory, this book covers both statistical and algebraic principles. It provides over 30 major theorems for kernel-based supervised and unsupervised learning models. The first of the theorems establishes a condition, arguably necessary and sufficient, for the kernelization of learning models. In addition, several other theorems are devoted to proving mathematical equivalence between seemingly unrelated models. With over 25 closed-form and iterative algorithms, the book provides a step-by-step guide to algorithmic procedures and analysing which factors to consider in tackling a given problem, enabling readers to improve specifically designed learning algorithms, build models for new applications and develop efficient techniques suitable for green machine learning technologies. Numerous real-world examples and over 200 problems, several of which are Matlab-based simulation exercises, make this an essential resource for graduate students and professionals in computer science, electrical and biomedical engineering. Solutions to problems are provided online for instructors.
What Is Kernel Methods In the field of machine learning, kernel machines are a class of methods for pattern analysis. The support-vector machine (also known as SVM) is the most well-known member of this group. Pattern analysis frequently makes use of specific kinds of algorithms known as kernel approaches. Utilizing linear classifiers in order to solve nonlinear issues is what these strategies entail. Finding and studying different sorts of general relations present in datasets is the overarching goal of pattern analysis. Kernel methods, on the other hand, require only a user-specified kernel, which can be thought of as a similarity function over all pairs of data points computed using inner products. This is in contrast to many algorithms that solve these tasks, which require the data in their raw representation to be explicitly transformed into feature vector representations via a user-specified feature map. According to the Representer theorem, although the feature map in kernel machines has an unlimited number of dimensions, all that is required as user input is a matrix with a finite number of dimensions. Without parallel processing, computation on kernel machines is painfully slow for data sets with more than a few thousand individual cases. How You Will Benefit (I) Insights, and validations about the following topics: Chapter 1: Kernel method Chapter 2: Support vector machine Chapter 3: Radial basis function Chapter 4: Positive-definite kernel Chapter 5: Sequential minimal optimization Chapter 6: Regularization perspectives on support vector machines Chapter 7: Representer theorem Chapter 8: Radial basis function kernel Chapter 9: Kernel perceptron Chapter 10: Regularized least squares (II) Answering the public top questions about kernel methods. (III) Real world examples for the usage of kernel methods in many fields. (IV) 17 appendices to explain, briefly, 266 emerging technologies in each industry to have 360-degree full understanding of kernel methods' 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 kernel methods.
Few developments have influenced the field of computer vision in the last decade more than the introduction of statistical machine learning techniques. Particularly kernel-based classifiers, such as the support vector machine, have become indispensable tools, providing a unified framework for solving a wide range of image-related prediction tasks, including face recognition, object detection and action classification. By emphasizing the geometric intuition that all kernel methods rely on, Kernel Methods in Computer Vision provides an introduction to kernel-based machine learning techniques accessible to a wide audience including students, researchers and practitioners alike, without sacrificing mathematical correctness. It covers not only support vector machines but also less known techniques for kernel-based regression, outlier detection, clustering and dimensionality reduction. Additionally, it offers an outlook on recent developments in kernel methods that have not yet made it into the regular textbooks: structured prediction, dependency estimation and learning of the kernel function. Each topic is illustrated with examples of successful application in the computer vision literature, making Kernel Methods in Computer Vision a useful guide not only for those wanting to understand the working principles of kernel methods, but also for anyone wanting to apply them to real-life problems.
"This book presents an extensive introduction to the field of kernel methods and real world applications. The book is organized in four parts: the first is an introductory chapter providing a framework of kernel methods; the others address Bioegineering, Signal Processing and Communications and Image Processing"--Provided by publisher.
The kernel functions methodology described here provides a powerful and unified framework for disciplines ranging from neural networks and pattern recognition to machine learning and data mining. This book provides practitioners with a large toolkit of algorithms, kernels and solutions ready to be implemented, suitable for standard pattern discovery problems.
This volume develops an effective theory approach to understanding deep neural networks of practical relevance.
This book shows machine learning enthusiasts and practitioners how to get the best of both worlds by deriving Fisher kernels from deep learning models. In addition, the book shares insight on how to store and retrieve large-dimensional Fisher vectors using feature selection and compression techniques. Feature selection and feature compression are two of the most popular off-the-shelf methods for reducing data’s high-dimensional memory footprint and thus making it suitable for large-scale visual retrieval and classification. Kernel methods long remained the de facto standard for solving large-scale object classification tasks using low-level features, until the revival of deep models in 2006. Later, they made a comeback with improved Fisher vectors in 2010. However, their supremacy was always challenged by various versions of deep models, now considered to be the state of the art for solving various machine learning and computer vision tasks. Although the two research paradigms differ significantly, the excellent performance of Fisher kernels on the Image Net large-scale object classification dataset has caught the attention of numerous kernel practitioners, and many have drawn parallels between the two frameworks for improving the empirical performance on benchmark classification tasks. Exploring concrete examples on different data sets, the book compares the computational and statistical aspects of different dimensionality reduction approaches and identifies metrics to show which approach is superior to the other for Fisher vector encodings. It also provides references to some of the most useful resources that could provide practitioners and machine learning enthusiasts a quick start for learning and implementing a variety of deep learning models and kernel functions.