### Abstract

Relation between a family of generalized Support Vector Machine (SVM) problems and the novel ε-sparse representation is provided. In defining ε-sparse representations, we use a natural generalization of the classical εinsensitive cost function for vectors. The insensitive parameter of the SVM problem is transformed into component-wise insensitivity and thus overall sparsification is replaced by component-wise sparsification. The connection between these two problems is built through the generalized Moore-Penrose inverse of the Gram matrix associated to the kernel.

Original language | English |
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Pages (from-to) | 605-614 |

Number of pages | 10 |

Journal | Acta Cybernetica |

Volume | 17 |

Issue number | 3 |

Publication status | Published - 2006 |

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### ASJC Scopus subject areas

- Hardware and Architecture
- Software
- Computational Theory and Mathematics
- Theoretical Computer Science

### Cite this

*Acta Cybernetica*,

*17*(3), 605-614.

**ε-Sparse representations : Generalized sparse approximation and the equivalent family of SVM tasks.** / Szabó, Zoltán; Lőrincz, A.

Research output: Contribution to journal › Article

*Acta Cybernetica*, vol. 17, no. 3, pp. 605-614.

}

TY - JOUR

T1 - ε-Sparse representations

T2 - Generalized sparse approximation and the equivalent family of SVM tasks

AU - Szabó, Zoltán

AU - Lőrincz, A.

PY - 2006

Y1 - 2006

N2 - Relation between a family of generalized Support Vector Machine (SVM) problems and the novel ε-sparse representation is provided. In defining ε-sparse representations, we use a natural generalization of the classical εinsensitive cost function for vectors. The insensitive parameter of the SVM problem is transformed into component-wise insensitivity and thus overall sparsification is replaced by component-wise sparsification. The connection between these two problems is built through the generalized Moore-Penrose inverse of the Gram matrix associated to the kernel.

AB - Relation between a family of generalized Support Vector Machine (SVM) problems and the novel ε-sparse representation is provided. In defining ε-sparse representations, we use a natural generalization of the classical εinsensitive cost function for vectors. The insensitive parameter of the SVM problem is transformed into component-wise insensitivity and thus overall sparsification is replaced by component-wise sparsification. The connection between these two problems is built through the generalized Moore-Penrose inverse of the Gram matrix associated to the kernel.

UR - http://www.scopus.com/inward/record.url?scp=33746041491&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33746041491&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:33746041491

VL - 17

SP - 605

EP - 614

JO - Acta Cybernetica

JF - Acta Cybernetica

SN - 0324-721X

IS - 3

ER -