## Multiclass Classification with Multi-Prototype Support Vector Machines (2005)

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Venue: | Journal of Machine Learning Research |

Citations: | 11 - 0 self |

### BibTeX

@ARTICLE{Aiolli05multiclassclassification,

author = {Fabio Aiolli and Alessandro Sperduti and Yoram Singer},

title = {Multiclass Classification with Multi-Prototype Support Vector Machines},

journal = {Journal of Machine Learning Research},

year = {2005},

volume = {6},

pages = {2005}

}

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### Abstract

Winner-take-all multiclass classifiers are built on the top of a set of prototypes each representing one of the available classes. A pattern is then classified with the label associated to the most `similar' prototype. Recent proposal of SVM extensions to multiclass can be considered instances of the same strategy with one prototype per class.

### Citations

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Citation Context ... exp(−λ||x − y|| 2 ),λ ≥ 0. Kernel machines, and the SVM in particular, has been initially devised for the binary setting. However, extensions to the multiclass case have been promptly proposed (e.g. =-=Vapnik, 1998-=-; Weston and Watkins, 1999; Guermeur et al., 2000; Crammer and Singer, 2000). The discriminant functions generated by general kernel-based methods are implicitly defined in terms of a subset of the tr... |

1441 |
Making large-Scale SVM Learning Practical
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Citation Context ...on accuracy. 5.5 Brief Discussion The type of strategies we have analyzed in earlier sections are very similar to the ones used by SMO (Platt, 1998), modified SMO (Keerthi et al., 1999) and svmlight (=-=Joachims, 1999-=-) algorithms for binary SVM. In these cases, linear constraints involving dual variables which are related to different patterns (derived by KKT conditions over the bias term) are present. However, in... |

1011 |
Fast training of support vector machines using sequential minimal optimization
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- 1998
(Show Context)
Citation Context ... all the variables apart for the two variables under consideration. In this section, we analyze different algorithms that are based on the step given above. The basic idea is the same as SMO for SVM (=-=Platt, 1998-=-), that is to repeat a process in which 826 (13) (14)sMULTICLASS CLASSIFICATION WITH MULTI-PROTOTYPE SUPPORT VECTOR MACHINES BasicStep(p, ra, rb) ν = 1 2 (yra p −y r b p )− fra (xp)+ fr b (xp) 2Kpp if... |

597 |
An Introduction to Computational Learning Theory
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(Show Context)
Citation Context ...y three-layer perceptrons defined as above. This class of functions is completely characterized by the set of collective states that the σ perceptrons at the first layer can assume. It is well known (=-=Kearns and Vazirani, 1994-=-) that, by Sauer Lemma, the growth function of a single perceptron (with 0 threshold) is bounded from above by the quantity (en/d) d , and so the growth function of our class of networks is bounded fr... |

569 | Solving Multiclass Learning Problems via Error-Correcting Output Codes - Dietterich, Bakiri - 1995 |

553 | Sparse bayesian learning and the relevance vector machine. Journal of machine learning research - Tipping - 2001 |

419 | Reducing Multiclass to Binary: A Unifying Approach for Margin Classifiers - Allwein, Schapire, et al. - 2000 |

367 | On the algorithmic implementation of multiclass kernel-based vector machines
- Crammer, Singer
- 2001
(Show Context)
Citation Context ...ated string is most ’similar’ to the output of the binary classifiers on that instance is returned as output. Extensions to codes with values in {−1,0,+1} (Allwein et al., 2000) and continuous codes (=-=Crammer and Singer, 2000-=-) have been recently proposed. Recently, large margin kernel-based methods have shown state-of-the-art performance in a wide range of applications. They search for a large margin linear discriminant m... |

259 | Large margin DAG’s for multiclass classification
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(Show Context)
Citation Context ...case r = yp, where yp is the positive prototype associated to the pattern xp, i.e. such that π yp p > 0. To give the margin-based bound on the generalization error, we use the same technique as in an(=-=Platt et al., 2000-=-) for general Perceptron DDAG1 (and thus SVM-DAG also), i.e. we show how the original multiclass problem can be reduced into one made of multiple binary decisions. The structure of our proof resembles... |

191 | K.: “Improvements to Platt’s SMO algorithm for SVM classifier design”, Neural Computation 13
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(Show Context)
Citation Context ...ment can be applied to the recognition accuracy. 5.5 Brief Discussion The type of strategies we have analyzed in earlier sections are very similar to the ones used by SMO (Platt, 1998), modified SMO (=-=Keerthi et al., 1999-=-) and svmlight (Joachims, 1999) algorithms for binary SVM. In these cases, linear constraints involving dual variables which are related to different patterns (derived by KKT conditions over the bias ... |

185 | Extracting support data for a given task - Schölkopf, Burges, et al. - 1995 |

88 | Input space versus feature space in kernel-based methods - Schölkopf, Mika, et al. - 1999 |

86 | LVQ_PAK: the learning vector quantization program package
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(Show Context)
Citation Context ... WTA strategy. Another class of methods for multiclass classification are the so called prototype based methods, one of the most relevant of which is the learning vector quantization (LVQ) algorithm (=-=Kohonen et al., 1996-=-). Although different versions of the LVQ algorithm exist, in the more general case these algorithms quantize input patterns into codeword vectors ci and use these vectors for 1-NN classification. Sev... |

59 | Exact simplification of support vector solutions - Downs, Gates, et al. - 2001 |

32 |
C4.5: Programs for empirical learning
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Citation Context ...based and loss-based decoding respectively). 1.1 Motivations and Related Work Several well-known methods for binary classification, including neural networks (Rumelhart et al., 1986), decision trees (=-=Quinlan, 1993-=-), k-NN (see for example (Mitchell, 1997)), can be naturally extended to the multiclass domain and can be viewed as instances of the WTA strategy. Another class of methods for multiclass classificatio... |

24 |
A new multi-class svm based on a uniform convergence result
- Guermeur, Elisseeff, et al.
- 2000
(Show Context)
Citation Context ...nes, and the SVM in particular, has been initially devised for the binary setting. However, extensions to the multiclass case have been promptly proposed (e.g. Vapnik, 1998; Weston and Watkins, 1999; =-=Guermeur et al., 2000-=-; Crammer and Singer, 2000). The discriminant functions generated by general kernel-based methods are implicitly defined in terms of a subset of the training patterns, the so called support vectors, o... |

21 | Minimal kernel classifiers - Fung, Mangasarian, et al. |

17 |
Iterated local search. Handbook of metaheuristics
- Lourenco, Martin, et al.
- 2003
(Show Context)
Citation Context ... approach we suggest can be considered an instance of Iterated Local Search (ILS). ILS is a family of general purpose metaheuristics for finding good solutions of combinatorial optimization problems (=-=Lourenco et al., 2002-=-). These algorithms are based on 837sAIOLLI AND SPERDUTI building a sequence of solutions by first perturbing the current solution and then applying local search to that modified solution. In the prev... |

8 | Discriminant pattern recognition using transformation-invariant neurons - Sona, Sperduti |

3 | A re-weighting strategy for improving margins - Aiolli, Sperduti - 2002 |

2 | Multi-prototype support vector machine
- Aiolli, Sperduti
- 2003
(Show Context)
Citation Context ...with respect to the complexity of the generated solution and with respect to the generalization error. This paper substantially extends the material contained in other two conference papers. Namely, (=-=Aiolli and Sperduti, 2003-=-) which contains the basic idea and the theory of the multi-prototype SVM together with preliminary experimental work and (Aiolli and Sperduti, 2002a) which proposes and analyzes selection heuristics ... |

1 | An efficient SMO-like algortihm for multiclass SVM - Aiolli, Sperduti - 2002 |