Visualizing Proportions and Dissimilarities by Space-filling Maps: A Large Neighborhood Search Approach

Emilio Carrizosa, Vanesa Guerrero, Dolores Romero Morales

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

In this paper we address the problem of visualizing a set of individuals, which have attached a statistical value given as a proportion, and a dissimilarity measure. Each individual is represented as a region within the unit square, in such a way that the area of the regions represent the proportions and the distances between them represent the dissimilarities. To enhance the interpretability of the representation, the regions are required to satisfy two properties. First, they must form a partition of the unit square, namely, the portions in which it is divided must cover its area without overlapping. Second, the portions must be made of a connected union of rectangles which verify the so-called box-connectivity constraints, yielding a visualization map called Space-filling Box-connected Map (SBM). The construction of an SBM is formally stated as a mathematical optimization problem, which is solved heuristically by using the Large Neighborhood Search technique. The methodology proposed in this paper is applied to three real-world datasets: the first one concerning financial markets in Europe and Asia, the second one about the letters in the English alphabet, and finally the provinces of The Netherlands as a geographical application.
In this paper we address the problem of visualizing a set of individuals, which have attached a statistical value given as a proportion, and a dissimilarity measure. Each individual is represented as a region within the unit square, in such a way that the area of the regions represent the proportions and the distances between them represent the dissimilarities. To enhance the interpretability of the representation, the regions are required to satisfy two properties. First, they must form a partition of the unit square, namely, the portions in which it is divided must cover its area without overlapping. Second, the portions must be made of a connected union of rectangles which verify the so-called box-connectivity constraints, yielding a visualization map called Space-filling Box-connected Map (SBM). The construction of an SBM is formally stated as a mathematical optimization problem, which is solved heuristically by using the Large Neighborhood Search technique. The methodology proposed in this paper is applied to three real-world datasets: the first one concerning financial markets in Europe and Asia, the second one about the letters in the English alphabet, and finally the provinces of The Netherlands as a geographical application.
LanguageEnglish
JournalComputers & Operations Research
Volume78
Pages369-380
Number of pages27
ISSN0305-0548
DOIs
StatePublished - Feb 2017

Keywords

  • Data Visualization
  • Box-connectivity
  • Proportions
  • Dissimilarities
  • Large Neighborhood Search

Cite this

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title = "Visualizing Proportions and Dissimilarities by Space-filling Maps: A Large Neighborhood Search Approach",
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Visualizing Proportions and Dissimilarities by Space-filling Maps : A Large Neighborhood Search Approach. / Carrizosa, Emilio; Guerrero, Vanesa; Morales, Dolores Romero.

In: Computers & Operations Research, Vol. 78, 02.2017, p. 369-380 .

Research output: Contribution to journalJournal articleResearchpeer-review

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