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## Support-Vector Networks (1995)

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Venue: | Machine Learning |

Citations: | 3703 - 35 self |

### Citations

3698 | Learning internal representations by error propagation - Rumelhart, Hinton, et al. - 1986 |

1865 | A training algorithm for optimal margin classifiers
- Boser, Guyon, et al.
- 1992
(Show Context)
Citation Context ...ribed as a two layer network (Fig. 3). However, even if the optimal hyperplane generalizes well the technical problem of how to treat the high dimensional feature space remains. In 1992 it was shown (=-=Boser, Guyon, & Vapnik, 1992-=-), that the order of operations for constructing a decision function can be interchanged: instead of making a non-linear transformation of the input vectors followed by dot-products with support vecto... |

1571 |
The use of multiple measurements in taxonomic problems.
- Fisher
- 1936
(Show Context)
Citation Context ...ognition. Keywords: pattern recognition, efficient learning algorithms, neural networks, radial basis function classifiers, polynomial classifiers. 1. Introduction More than 60 years ago R.A. Fisher (=-=Fisher, 1936-=-) suggested the first algorithm for pattern recognition. He considered a model of two normal distributed populations, N(mt, ~1) and N(m2, ~2) ofn dimensional vectors x with mean vectors ml and m2 and ... |

398 | Theoretical foundations of the potential function method in pattern recognition, - Aizerman, Braverman, et al. - 1964 |

285 | Handwritten digit recognition with a back-propagation network. In
- Cun, Boser, et al.
- 1990
(Show Context)
Citation Context ...t depend on the degree of the polynomial---only the number of support vectors. Even in the worst case it is fastet than the best performing neural network, constructed specially for the task, LeNetl (=-=LeCun, et al., 1990-=-). The performance of this neural network is 5.1% raw error. Polynomials with degree 2 or higher outperform LeNetl. 6.2.2. Experiments with the NIST Database. TheNISTdatabasewasusedforbenchmark studie... |

147 | Learning internal representations by back-propagating errors,” - Rumelhart, Hinton, et al. - 1986 |

101 |
Comparison of classifier methods: a case study in handwriting digit recognition. ’’
- Bottou, Cortes, et al.
- 1994
(Show Context)
Citation Context ...recognition (LeNetl and LeNet4). The authors only contributed with results for support-vector networks. The results of the benchmark are given in Fig. 9. We conclude this section by citing the paper (=-=Bottou, et al., 1994-=-) describing results of the benchmark: For quite a long time LeNetl was considered state of the art... Through a series of experiments in architecture, combined with an analysis of the characteristics... |

93 |
Learning Logic,”
- Parker
- 1985
(Show Context)
Citation Context ...ights of the neural network to adapt in order locally to minimize the error on a set of vectors belonging to a pattern recognition problem was found in 1986 (Rumelhart, Hinton & Williams, 1986, 1987; =-=Parker, 1985-=-; LeCun, 1985) when the back-propagation algorithm was discovered. The solution involves a slight modification of the mathematical model of neurons. Therefore, neural networks implement "piece-wise li... |

68 |
Une procédure d’apprentissage pour réseau à seuil asymétrique
- LeCun
- 1985
(Show Context)
Citation Context ...eural network to adapt in order locally to minimize the error on a set of vectors belonging to a pattern recognition problem was found in 1986 (Rumelhart, Hinton & Williams, 1986, 1987; Parker, 1985; =-=LeCun, 1985-=-) when the back-propagation algorithm was discovered. The solution involves a slight modification of the mathematical model of neurons. Therefore, neural networks implement "piece-wise linear-type" de... |

29 |
Classification into two multivariate normal distributions with different covariance matrices
- Anderson, Bahadur
- 1962
(Show Context)
Citation Context ... the dot-products: f(x) = q~(x)- w + b = S Yi°ti~(x)" ~b(xi) + b. i=1 (33) The idea of constructing support-vector networks comes from considering general forms of the dot-product in a Hilbert space (=-=Anderson & Bahadur, 1966-=-): ~b (u)- <p (v) - K (u, v). (34) According to the Hilbert-Schmidt Theory (Courant & Hilbert, 1953) any symmetric function K(u, v), with K(u, v) ~ Le, can be expanded in the form oo K(u, v) = Z i=l ~... |

14 | Learning intemal representations by error propagation. - Hinton, Williams - 1986 |

13 |
Neural-network and k-nearest-neighbor classifiers
- Bromley, Sackinger
- 1991
(Show Context)
Citation Context ... x 106 4 4.3 165 ~I x 109 5 4.3 175 ~1 x 1012 6 4.2 185 ~1 x 1014 7 4.3 190 ~1 x 1016 from publications and own experiments. The result of human performance was reported by J. Bromley & E. Sackinger (=-=Bromley & Sackinger, 1991-=-). The result with CART was carried out by Daryl Pregibon and Michael D. Riley at Bell Labs., Murray Hill, NJ. The results of C4.5 and the best 2-layer neural network (with optimal number of hidden un... |

5 | Estimation of Dependences Based on Empirical Data, Addendum 1 - Vapnik - 1982 |

3 |
Principles ofNeurodynamics, Spartan
- Rosenblatt
- 1962
(Show Context)
Citation Context ...put unit. The gray-shading of the vector entries reflects their numeric value. were therefore from the very beginning associated with the construction of linear decision surfaces. In 1962 Rosenblatt (=-=Rosenblatt, 1962-=-) explored a different kind of learning machines: perceptrons or neural networks. The perceptron consists of connected neurons, where each neuron implements a separating hyperplane, so the perceptron ... |

2 |
Principles ofNeurodynamics, Spartan Books, New York. 297 Rumelhart
- Rosenblatt
- 1962
(Show Context)
Citation Context ...put unit. The gray-shading of the vector entries reflects their numeric value. were therefore from the very beginning associated with the construction of linear decision surfaces. In 1962 Rosenblatt (=-=Rosenblatt, 1962-=-) explored a different kind of learning machines: perceptrons or neural networks. The perceptron consists of connected neurons, where each neuron implements a separating hyperplane, so the perceptron ... |

1 | Principles of Neurodynamics. Spartam - Rosenblatt - 1962 |

1 |
Estimation ofDependences Based on Empirical Data, Addendum 1
- Vapnik
- 1982
(Show Context)
Citation Context ...uct polynomial of degree 4 or 5 in a 200 dimensionai space it may be necessary to construct hyperplanes in a billion dimensional feature space. The conceptual part of this problem was solved in 1965 (=-=Vapnik, 1982-=-) for the case of optimal hyperplanes for separable classes. An optimal hyperplane is here defined as the linear decision function with maximal margin between the vectors of the two classes, see Fig. ... |

1 |
Neural-network and it-nearest-neighbor classifiers
- Bromley, Sackinger
- 1991
(Show Context)
Citation Context ...sionality of feature space 256 -33000 -1 x 106 ~1 x 109 ~1 x 1012 ~1 x 1014 ~1 x 1016 from publications and own experiments. The result of human performance was reported by J. Bromley & E. Sackinger (=-=Bromley & Sackinger, 1991-=-). The result with CART was carried out by Daryl Pregibon and Michael D. Riley at Bell Labs., Murray Hill, NJ. The results of C4.5 and the best 2-layer neural network (with optimal number of hidden un... |