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Making LargeScale Support Vector Machine Learning Practical
, 1998
"... Training a support vector machine (SVM) leads to a quadratic optimization problem with bound constraints and one linear equality constraint. Despite the fact that this type of problem is well understood, there are many issues to be considered in designing an SVM learner. In particular, for large lea ..."
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Cited by 465 (1 self)
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Training a support vector machine (SVM) leads to a quadratic optimization problem with bound constraints and one linear equality constraint. Despite the fact that this type of problem is well understood, there are many issues to be considered in designing an SVM learner. In particular, for large learning tasks with many training examples, offtheshelf optimization techniques for general quadratic programs quickly become intractable in their memory and time requirements. SV M light1 is an implementation of an SVM learner which addresses the problem of large tasks. This chapter presents algorithmic and computational results developed for SV M light V2.0, which make largescale SVM training more practical. The results give guidelines for the application of SVMs to large domains.
2005), ‘Linearly constrained reconstruction of functions by kernels with applications to machine learning’, Adv
"... at the occasion of his 60 th birthday This paper investigates the approximation of multivariate functions from data via linear combinations of translates of a positive definite kernel from a reproducing kernel Hilbert space. If standard interpolation conditions are relaxed by Chebyshev–type constrai ..."
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at the occasion of his 60 th birthday This paper investigates the approximation of multivariate functions from data via linear combinations of translates of a positive definite kernel from a reproducing kernel Hilbert space. If standard interpolation conditions are relaxed by Chebyshev–type constraints, one can minimize the norm of the approximant in the Hilbert space under these constraints. By standard arguments of optimization theory, the solutions will take a simple form, based on the data related to the active constraints, called support vectors in the context of machine learning, The corresponding quadratic programming problems are investigated to some extent. Using monotonicity results concerning the Hilbert space norm, iterative techniques based on small quadratic subproblems on active sets are shown to be finite, even if they drop part of their previous information and even if they are used for infinite data, e.g. in the context of online learning. Numerical experiments confirm the theoretical results.
/08/25 16:31
"... the fact that a collection of chapters can never be as homogeneous as a book conceived by a single person. We have tried to compensate for this by the selection and refereeing process of the submissions. In addition, we have written an introductory chapter describing the SV algorithm in some detail ..."
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the fact that a collection of chapters can never be as homogeneous as a book conceived by a single person. We have tried to compensate for this by the selection and refereeing process of the submissions. In addition, we have written an introductory chapter describing the SV algorithm in some detail (chapter 1), and added a roadmap (chapter 2) which describes the actual contributions which are to follow in chapters 3 through 20. Bernhard Scholkopf, Christopher J.C. Burges, Alexander J. Smola Berlin, Holmdel, July 1998/08/25 16:31 1 Introduction to Support Vector Learning The goal of this chapter, which describes the central ideas of SV learning, is twofold. First, we want to provide an introduction for readers unfamiliar with this field. Second, this introduction serves as a source of the basic equations for the chapters of this book. For more exhaustive treatments, we refer the interested reader to Vapnik (1995); Scholkopf (1997); Burges (1998). 1.1
Combining Support Vector and Mathematical . . .
 ADVANCES IN KERNEL METHODS  SUPPORT VECTOR LEARNING
, 1998
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