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An equivalence between sparse approximation and Support Vector Machines
 A.I. Memo 1606, MIT Arti cial Intelligence Laboratory
, 1997
"... This publication can be retrieved by anonymous ftp to publications.ai.mit.edu. The pathname for this publication is: aipublications/15001999/AIM1606.ps.Z This paper shows a relationship between two di erent approximation techniques: the Support Vector Machines (SVM), proposed by V.Vapnik (1995), ..."
Abstract

Cited by 232 (7 self)
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This publication can be retrieved by anonymous ftp to publications.ai.mit.edu. The pathname for this publication is: aipublications/15001999/AIM1606.ps.Z This paper shows a relationship between two di erent approximation techniques: the Support Vector Machines (SVM), proposed by V.Vapnik (1995), and a sparse approximation scheme that resembles the Basis Pursuit DeNoising algorithm (Chen, 1995 � Chen, Donoho and Saunders, 1995). SVM is a technique which can be derived from the Structural Risk Minimization Principle (Vapnik, 1982) and can be used to estimate the parameters of several di erent approximation schemes, including Radial Basis Functions, algebraic/trigonometric polynomials, Bsplines, and some forms of Multilayer Perceptrons. Basis Pursuit DeNoising is a sparse approximation technique, in which a function is reconstructed by using a small number of basis functions chosen from a large set (the dictionary). We show that, if the data are noiseless, the modi ed version of Basis Pursuit DeNoising proposed in this paper is equivalent to SVM in the following sense: if applied to the same data set the two techniques give the same solution, which is obtained by solving the same quadratic programming problem. In the appendix we also present a derivation of the SVM technique in the framework of regularization theory, rather than statistical learning theory, establishing a connection between SVM, sparse approximation and regularization theory.
On the relationship between the support vector machine for classification and sparsified Fisher's linear discriminant
 Neural Processing Letters
, 1999
"... We show that the orientation and location of the separating hyperplane for 2class supervised pattern classification obtained by the Support Vector Machine (SVM) proposed by Vapnik and his colleagues, is equivalent to the solution obtained by Fisher's Linear Discriminant on the set of Support ..."
Abstract

Cited by 14 (0 self)
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We show that the orientation and location of the separating hyperplane for 2class supervised pattern classification obtained by the Support Vector Machine (SVM) proposed by Vapnik and his colleagues, is equivalent to the solution obtained by Fisher's Linear Discriminant on the set of Support Vectors. In other words, SVM can be seen as a way to "sparsify" Fisher's Linear Discriminant in order to obtain the most generalizing classification from the training set.