M. Premalatha, C. Vijaya Lakshmi
Department of Mathematics
Sathyabama University, Chennai, INDIA
Department of Mathematics
VIT University
Chennai, INDIA

Abstract. Machine Learning is considered as a subfield of Artificial Intelligence and it is concerned with the development of techniques and methods which enable the computer to learn. In classification problems generalization control is obtained by maximizing the margin, which corresponds to minimization of the weight vector. The minimization of the weight vector can be used in regression problems, with a loss function. The problem of classification for linearly separable data and introduces the concept of margin and the essence of SVM - margin maximization. In this paper gives the soft margin SVM introduces the idea of slack variables and the trade-off between maximizing the margin and minimizing the number of misclassified variables. A presentation of linear SVM followed by its extension to nonlinear SVM and SVM regression is then provided to give the basic mathematical details. SRM minimizes an upper bound on the expected risk, where as ERM minimizes the error on the training data. It also develops the concept of SVM technique can be used for regression. SVR attempts to minimize the generalization error bound so as to achieve generalized performance instead of minimizing the observed training error.

Received: September 6, 2013

AMS Subject Classification: 62H30, 26A24, 90C51, 90C20

Key Words and Phrases: linear and non-linear classification, machine learning, SVM mathematical, SVM trade-off, SVM regression

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