Book Chapter10.1007/BFB0020166
The Support Vector Method
Vladimir Vapnik
- 08 Oct 1997
- pp 263-271
130
TL;DR: The general idea of the Support Vector method is described and theorems demonstrating that the generalization ability of the SV method is based on factors which classical statistics do not take into account are presented.
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Abstract: The Support Vector (SV) method is a new general method of function estimation which does not depend explicitly on the dimensionality of input space It was applied for pattern recognition, regression estimation, and density estimation problems as well as for problems of solving linear operator equations In this article we describe the general idea of the SV method and present theorems demonstrating that the generalization ability of the SV method is based on factors which classical statistics do not take into account We also describe the SV method for density estimation in a set of functions defined by a mixture of an infinite number of Gaussians
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Citations
A tutorial on support vector regression
TL;DR: This tutorial gives an overview of the basic ideas underlying Support Vector (SV) machines for function estimation, and includes a summary of currently used algorithms for training SV machines, covering both the quadratic programming part and advanced methods for dealing with large datasets.
Generalized Discriminant Analysis Using a Kernel Approach
G. Baudat,F. Anouar +1 more
TL;DR: A new method that is close to the support vector machines insofar as the GDA method provides a mapping of the input vectors into high-dimensional feature space to deal with nonlinear discriminant analysis using kernel function operator.
The connection between regularization operators and support vector kernels
TL;DR: It is proved that the Green's Functions associated with regularization operators are suitable support vector kernels with equivalent regularization properties and it is shown that a large number of radial basis functions, namely conditionally positive definite functions, may be used as support vector kernel.
715
An equivalence between sparse approximation and support vector machines
TL;DR: If the data are noiseless, the modified version of basis pursuit denoising proposed in this article 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.
Order of Nonlinearity as a Complexity Measure for Models Generated by Symbolic Regression via Pareto Genetic Programming
TL;DR: Results of the experiments suggest that alternating the order of nonlinearity of GP individuals with their structural complexity produces solutions that are both compact and have smoother response surfaces, and, hence, contributes to better interpretability and understanding.
380
References
•Book
The Nature of Statistical Learning Theory
Vladimir Vapnik
- 01 Jan 1995
TL;DR: Setting of the learning problem consistency of learning processes bounds on the rate of convergence ofLearning processes controlling the generalization ability of learning process constructing learning algorithms what is important in learning theory?
46K
Support-Vector Networks
Corinna Cortes,Vladimir Vapnik +1 more
TL;DR: High generalization ability of support-vector networks utilizing polynomial input transformations is demonstrated and the performance of the support- vector network is compared to various classical learning algorithms that all took part in a benchmark study of Optical Character Recognition.
A training algorithm for optimal margin classifiers
Bernhard E. Boser,Isabelle Guyon,Vladimir Vapnik +2 more
- 01 Jul 1992
TL;DR: A training algorithm that maximizes the margin between the training patterns and the decision boundary is presented, applicable to a wide variety of the classification functions, including Perceptrons, polynomials, and Radial Basis Functions.
•Proceedings Article
Support Vector Regression Machines
Harris Drucker,Christopher John Burges,Linda Kaufman,Alexander J. Smola,Vladimir Vapnik +4 more
- 03 Dec 1996
TL;DR: This work compares support vector regression (SVR) with a committee regression technique (bagging) based on regression trees and ridge regression done in feature space and expects that SVR will have advantages in high dimensionality space because SVR optimization does not depend on the dimensionality of the input space.
•Proceedings Article
Support Vector Method for Function Approximation, Regression Estimation and Signal Processing
Vladimir Vapnik,Steven E. Golowich,Alexander J. Smola +2 more
- 03 Dec 1996
TL;DR: This presentation reports results of applying the Support Vector method to problems of estimating regressions, constructing multidimensional splines, and solving linear operator equations.