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

Emilio Carrizosa, Vanesa Guerrero, Dolores Romero Morales

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

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.
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.
LanguageEnglish
JournalMathematical Programming
Volume169
Issue number1
Pages119-140
Number of pages22
ISSN0025-5610
DOIs
StatePublished - 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

Carrizosa, Emilio ; Guerrero, Vanesa ; Morales, Dolores Romero. / Visualizing Data as Objects by DC (Difference of Convex) Optimization. In: Mathematical Programming. 2018 ; Vol. 169, No. 1. pp. 119-140
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Visualizing Data as Objects by DC (Difference of Convex) Optimization. / Carrizosa, Emilio; Guerrero, Vanesa; Morales, Dolores Romero.

In: Mathematical Programming, Vol. 169, No. 1, 05.2018, p. 119-140.

Research output: Contribution to journalJournal articleResearchpeer-review

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