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The Support Vector Machine

  • Walker H. LandJr.
  • J. David Schaffer
Chapter

Abstract

Three separate sections comprise this chapter. The first presents an overview of statistical learning theory (SLT) as applied to machine learning. The topics covered are empirical or true risk minimization, the risk minimization principle (RMP), theoretical concept of risk minimization, function f0(X) that minimizes the expected (or true) risk, asymptotic consistency or uniform convergence, an example of the generalized bound for binary classification and finally, how are learning machines formed.

The second part of the chapter covers the theory of support vector machine (SVM) learning theory and develops solutions for the following three classes of problems:
  • Linear separable systems

  • Linear non-separable systems

  • And non-linear, non-separable systems

It then introduces the topic of kernels, what they are, and how they might be chosen. A brief pointer is provided to the SVM literature available on the web.

These sections are followed by a sketch of how the SVM may be hybridized with the GA for feature subset selection and points the way to the value of further hybridization with an ensemble approach, the topic of the next chapter.

Keywords

Support vector machine Statistical learning theory Empirical risk minimization VC dimension 

Abbreviations

ERM

Empirical risk minimization

GA

Genetic algorithm

QP

Quadratic programming

RBF

Radial basis function

RMP

Risk minimization principle

SLT

Statistical learning theory

SMO

Sequential minimization optimization

SRM

Structured risk minimization

SVM

Support vector machine

VC

Vapnik Chervonenkis

References

  1. Azerman A, Bowerna EM (1964) Theoretical formulation of the potential function method in pattern recognition. Autom Remote Control, (Automat I Telemekh) 25:917–932Google Scholar
  2. Mercer J (1909) Functions of positive and negative type, and their connection with the theory of integral equations. Philos Trans R Soc Lond A 209:415–446CrossRefGoogle Scholar
  3. Rozložník M (2018) Saddle point problems and their iterative solution. Springer, New YorkCrossRefGoogle Scholar
  4. Vapnik VN, Chervonenkis AY (1974) Teoriya raspoznavaniya obrazov: Statisticheskie problemy obucheniya. (Russian) [Theory of pattern recognition: Statistical problems of learning]. Moscow: Nauka.Google Scholar
  5. Vapnik VN (1995) The nature of statistical learning theory. Springer, New YorkCrossRefGoogle Scholar
  6. Vapnik VN (1998) Statistical learning theory. Wiley, New YorkzbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Walker H. LandJr.
    • 1
  • J. David Schaffer
    • 2
  1. 1.Binghamton UniversityBowieUSA
  2. 2.Binghamton UniversityBinghamtonUSA

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