Visualization of Complex Dynamic Datasets by Means of Mathematical Optimization

Emilio Carrizosa, Vanesa Guerrero, Dolores Romero Morales

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

In this paper we propose an optimization model and a solution approach to visualize datasets which are made up of individuals observed along different time periods. These individuals have attached a time-dependent magnitude and a dissimilarity measure, which may vary over time. Difference of convex optimization techniques, namely, the so-called Difference of Convex Algorithm, and nonconvex quadratic binary optimization techniques are used to heuristically solve the optimization model and develop this visualization framework. This way, the so-called Dynamic Visualization Map is obtained, in which the individuals are represented by geometric objects chosen from a catalogue. A Dynamic Visualization Map faithfully represents the dynamic magnitude by means of the areas of the objects, while it trades off three different goodness of fit criteria, namely the correct match of the dissimilarities between the individuals and the distances between the objects representing them, the spreading of such objects in the visual region, and the preservation of the mental map by ensuring smooth transitions along snapshots. Our procedure is successfully tested on dynamic geographic and linguistic datasets.
In this paper we propose an optimization model and a solution approach to visualize datasets which are made up of individuals observed along different time periods. These individuals have attached a time-dependent magnitude and a dissimilarity measure, which may vary over time. Difference of convex optimization techniques, namely, the so-called Difference of Convex Algorithm, and nonconvex quadratic binary optimization techniques are used to heuristically solve the optimization model and develop this visualization framework. This way, the so-called Dynamic Visualization Map is obtained, in which the individuals are represented by geometric objects chosen from a catalogue. A Dynamic Visualization Map faithfully represents the dynamic magnitude by means of the areas of the objects, while it trades off three different goodness of fit criteria, namely the correct match of the dissimilarities between the individuals and the distances between the objects representing them, the spreading of such objects in the visual region, and the preservation of the mental map by ensuring smooth transitions along snapshots. Our procedure is successfully tested on dynamic geographic and linguistic datasets.
LanguageEnglish
JournalOmega: The International Journal of Management Science
Number of pages12
ISSN0305-0483
DOIs
StatePublished - 26 Jul 2018

Bibliographical note

Epub ahead of print. Published online: 26. July 2018

Keywords

  • Visualization
  • Dynamic magnitude
  • Multidimensional scaling
  • Difference of convex optimization

Cite this

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title = "Visualization of Complex Dynamic Datasets by Means of Mathematical Optimization",
abstract = "In this paper we propose an optimization model and a solution approach to visualize datasets which are made up of individuals observed along different time periods. These individuals have attached a time-dependent magnitude and a dissimilarity measure, which may vary over time. Difference of convex optimization techniques, namely, the so-called Difference of Convex Algorithm, and nonconvex quadratic binary optimization techniques are used to heuristically solve the optimization model and develop this visualization framework. This way, the so-called Dynamic Visualization Map is obtained, in which the individuals are represented by geometric objects chosen from a catalogue. A Dynamic Visualization Map faithfully represents the dynamic magnitude by means of the areas of the objects, while it trades off three different goodness of fit criteria, namely the correct match of the dissimilarities between the individuals and the distances between the objects representing them, the spreading of such objects in the visual region, and the preservation of the mental map by ensuring smooth transitions along snapshots. Our procedure is successfully tested on dynamic geographic and linguistic datasets.",
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year = "2018",
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language = "English",
journal = "Omega: The International Journal of Management Science",
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Visualization of Complex Dynamic Datasets by Means of Mathematical Optimization. / Carrizosa, Emilio; Guerrero, Vanesa; Morales, Dolores Romero.

In: Omega: The International Journal of Management Science, 26.07.2018.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Visualization of Complex Dynamic Datasets by Means of Mathematical Optimization

AU - Carrizosa,Emilio

AU - Guerrero,Vanesa

AU - Morales,Dolores Romero

N1 - Epub ahead of print. Published online: 26. July 2018

PY - 2018/7/26

Y1 - 2018/7/26

N2 - In this paper we propose an optimization model and a solution approach to visualize datasets which are made up of individuals observed along different time periods. These individuals have attached a time-dependent magnitude and a dissimilarity measure, which may vary over time. Difference of convex optimization techniques, namely, the so-called Difference of Convex Algorithm, and nonconvex quadratic binary optimization techniques are used to heuristically solve the optimization model and develop this visualization framework. This way, the so-called Dynamic Visualization Map is obtained, in which the individuals are represented by geometric objects chosen from a catalogue. A Dynamic Visualization Map faithfully represents the dynamic magnitude by means of the areas of the objects, while it trades off three different goodness of fit criteria, namely the correct match of the dissimilarities between the individuals and the distances between the objects representing them, the spreading of such objects in the visual region, and the preservation of the mental map by ensuring smooth transitions along snapshots. Our procedure is successfully tested on dynamic geographic and linguistic datasets.

AB - In this paper we propose an optimization model and a solution approach to visualize datasets which are made up of individuals observed along different time periods. These individuals have attached a time-dependent magnitude and a dissimilarity measure, which may vary over time. Difference of convex optimization techniques, namely, the so-called Difference of Convex Algorithm, and nonconvex quadratic binary optimization techniques are used to heuristically solve the optimization model and develop this visualization framework. This way, the so-called Dynamic Visualization Map is obtained, in which the individuals are represented by geometric objects chosen from a catalogue. A Dynamic Visualization Map faithfully represents the dynamic magnitude by means of the areas of the objects, while it trades off three different goodness of fit criteria, namely the correct match of the dissimilarities between the individuals and the distances between the objects representing them, the spreading of such objects in the visual region, and the preservation of the mental map by ensuring smooth transitions along snapshots. Our procedure is successfully tested on dynamic geographic and linguistic datasets.

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KW - Difference of convex optimization

KW - Visualization

KW - Dynamic magnitude

KW - Multidimensional scaling

KW - Difference of convex optimization

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