The Support Vector Machine
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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 f_{0}(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.

Linear separable systems

Linear nonseparable systems

And nonlinear, nonseparable 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 dimensionAbbreviations
 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
 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
 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
 Rozložník M (2018) Saddle point problems and their iterative solution. Springer, New YorkCrossRefGoogle Scholar
 Vapnik VN, Chervonenkis AY (1974) Teoriya raspoznavaniya obrazov: Statisticheskie problemy obucheniya. (Russian) [Theory of pattern recognition: Statistical problems of learning]. Moscow: Nauka.Google Scholar
 Vapnik VN (1995) The nature of statistical learning theory. Springer, New YorkCrossRefGoogle Scholar
 Vapnik VN (1998) Statistical learning theory. Wiley, New YorkzbMATHGoogle Scholar