### Abstract

Language | English |
---|---|

Journal | Mathematical Programming |

Volume | 169 |

Issue number | 1 |

Pages | 119-140 |

Number of pages | 22 |

ISSN | 0025-5610 |

DOIs | |

State | Published - May 2018 |

### Bibliographical note

Epub ahead of print. Published online: 28. April 2017

### Keywords

- Data visualization
- DC functions
- DC algorithm
- Multidimensional scaling analysis

### Cite this

*Mathematical Programming*,

*169*(1), 119-140. DOI: 10.1007/s10107-017-1156-1

}

*Mathematical Programming*, vol. 169, no. 1, pp. 119-140. DOI: 10.1007/s10107-017-1156-1

**Visualizing Data as Objects by DC (Difference of Convex) Optimization.** / Carrizosa, Emilio; Guerrero, Vanesa; Romero Morales, Dolores .

Research output: Contribution to journal › Journal article › Research › peer-review

TY - JOUR

T1 - Visualizing Data as Objects by DC (Difference of Convex) Optimization

AU - Carrizosa,Emilio

AU - Guerrero,Vanesa

AU - Romero Morales,Dolores

N1 - Epub ahead of print. Published online: 28. April 2017

PY - 2018/5

Y1 - 2018/5

N2 - In this paper we address the problem of visualizing in a bounded region a set of individuals, which has attached a dissimilarity measure and a statistical value, as convex objects. This problem, which extends the standard Multidimensional Scaling Analysis, is written as a global optimization problem whose objective is the difference of two convex functions (DC). Suitable DC decompositions allow us to use the Difference of Convex Algorithm (DCA) in a very efficient way. Our algorithmic approach is used to visualize two real-world datasets.

AB - In this paper we address the problem of visualizing in a bounded region a set of individuals, which has attached a dissimilarity measure and a statistical value, as convex objects. This problem, which extends the standard Multidimensional Scaling Analysis, is written as a global optimization problem whose objective is the difference of two convex functions (DC). Suitable DC decompositions allow us to use the Difference of Convex Algorithm (DCA) in a very efficient way. Our algorithmic approach is used to visualize two real-world datasets.

KW - Data visualization

KW - DC functions

KW - DC algorithm

KW - Multidimensional scaling analysis

KW - Data visualization

KW - DC functions

KW - DC algorithm

KW - Multidimensional scaling analysis

UR - https://sfx-45cbs.hosted.exlibrisgroup.com/45cbs?url_ver=Z39.88-2004&url_ctx_fmt=info:ofi/fmt:kev:mtx:ctx&ctx_enc=info:ofi/enc:UTF-8&ctx_ver=Z39.88-2004&rfr_id=info:sid/sfxit.com:azlist&sfx.ignore_date_threshold=1&rft.object_id=954925422131

U2 - 10.1007/s10107-017-1156-1

DO - 10.1007/s10107-017-1156-1

M3 - Journal article

VL - 169

SP - 119

EP - 140

JO - Mathematical Programming

T2 - Mathematical Programming

JF - Mathematical Programming

SN - 0025-5610

IS - 1

ER -