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Mathematical Programming

, Volume 169, Issue 1, pp 119–140 | Cite as

Visualizing data as objects by DC (difference of convex) optimization

  • Emilio Carrizosa
  • Vanesa Guerrero
  • Dolores Romero Morales
Full Length Paper Series B

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.

Keywords

Data visualization DC functions DC algorithm Multidimensional scaling analysis 

Mathematics Subject Classification

90C90 90C26 

Notes

Acknowledgements

We thank the reviewers for their helpful suggestions and comments, which have been very valuable to strengthen the paper and to improve its quality.

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Copyright information

© Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2017

Authors and Affiliations

  1. 1.IMUS - Instituto de Matemáticas de la Universidad de SevillaSevillaSpain
  2. 2.Copenhagen Business SchoolFrederiksbergDenmark

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