IDEAS home Printed from https://ideas.repec.org/a/eee/jomega/v86y2019icp125-136.html
   My bibliography  Save this article

Visualization of complex dynamic datasets by means of mathematical optimization

Author

Listed:
  • Carrizosa, Emilio
  • Guerrero, Vanesa
  • Romero Morales, Dolores

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.

Suggested Citation

  • Carrizosa, Emilio & Guerrero, Vanesa & Romero Morales, Dolores, 2019. "Visualization of complex dynamic datasets by means of mathematical optimization," Omega, Elsevier, vol. 86(C), pages 125-136.
    • Handle: RePEc:eee:jomega:v:86:y:2019:i:c:p:125-136
    DOI: 10.1016/j.omega.2018.07.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0305048317304024
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.omega.2018.07.008?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Kimon Fountoulakis & Jacek Gondzio, 2016. "Performance of first- and second-order methods for $$\ell _1$$ ℓ 1 -regularized least squares problems," Computational Optimization and Applications, Springer, vol. 65(3), pages 605-635, December.
    2. Olafsson, Sigurdur & Li, Xiaonan & Wu, Shuning, 2008. "Operations research and data mining," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1429-1448, June.
    3. Carrizosa, Emilio & Guerrero, Vanesa & Romero Morales, Dolores, 2018. "On Mathematical Optimization for the visualization of frequencies and adjacencies as rectangular maps," European Journal of Operational Research, Elsevier, vol. 265(1), pages 290-302.
    4. Sahand Negahban & Sewoong Oh & Devavrat Shah, 2017. "Rank Centrality: Ranking from Pairwise Comparisons," Operations Research, INFORMS, vol. 65(1), pages 266-287, February.
    5. J. G. Dai & Pengyi Shi, 2017. "A Two-Time-Scale Approach to Time-Varying Queues in Hospital Inpatient Flow Management," Operations Research, INFORMS, vol. 65(2), pages 514-536, April.
    6. Véronique Van Vlasselaer & Tina Eliassi-Rad & Leman Akoglu & Monique Snoeck & Bart Baesens, 2017. "GOTCHA! Network-Based Fraud Detection for Social Security Fraud," Management Science, INFORMS, vol. 63(9), pages 3090-3110, September.
    7. Izak Benbasat & Albert S. Dexter, 1985. "An Experimental Evaluation of Graphical and Color-Enhanced Information Presentation," Management Science, INFORMS, vol. 31(11), pages 1348-1364, November.
    8. Bart Baesens & Rudy Setiono & Christophe Mues & Jan Vanthienen, 2003. "Using Neural Network Rule Extraction and Decision Tables for Credit-Risk Evaluation," Management Science, INFORMS, vol. 49(3), pages 312-329, March.
    9. Yang Bao & Anindya Datta, 2014. "Simultaneously Discovering and Quantifying Risk Types from Textual Risk Disclosures," Management Science, INFORMS, vol. 60(6), pages 1371-1391, June.
    10. Groenen, Patrick J. F. & Franses, Philip Hans, 2000. "Visualizing time-varying correlations across stock markets," Journal of Empirical Finance, Elsevier, vol. 7(2), pages 155-172, August.
    11. Sahand Negahban & Sewoong Oh & Devavrat Shah, 2017. "Rank Centrality: Ranking from Pairwise Comparisons," Operations Research, INFORMS, vol. 65(1), pages 266-287, February.
    12. Dimitris Bertsimas & Allison O’Hair & Stephen Relyea & John Silberholz, 2016. "An Analytics Approach to Designing Combination Chemotherapy Regimens for Cancer," Management Science, INFORMS, vol. 62(5), pages 1511-1531, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Alexandros Nikas & Angelos Fountoulakis & Aikaterini Forouli & Haris Doukas, 2022. "A robust augmented ε-constraint method (AUGMECON-R) for finding exact solutions of multi-objective linear programming problems," Operational Research, Springer, vol. 22(2), pages 1291-1332, April.
    2. Emilio Carrizosa, 2020. "Comments on: Distance geometry and data science," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 346-347, July.
    3. Emilio Carrizosa & Vanesa Guerrero & Dolores Romero Morales, 2023. "On mathematical optimization for clustering categories in contingency tables," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(2), pages 407-429, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Emilio Carrizosa & Cristina Molero-Río & Dolores Romero Morales, 2021. "Mathematical optimization in classification and regression trees," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 5-33, April.
    2. Tino Werner, 2022. "Elicitability of Instance and Object Ranking," Decision Analysis, INFORMS, vol. 19(2), pages 123-140, June.
    3. Blanquero, Rafael & Carrizosa, Emilio & Molero-Río, Cristina & Romero Morales, Dolores, 2020. "Sparsity in optimal randomized classification trees," European Journal of Operational Research, Elsevier, vol. 284(1), pages 255-272.
    4. Dipankar Das, 2023. "A Model of Competitive Assortment Planning Algorithm," Papers 2307.09479, arXiv.org.
    5. Christis Katsouris, 2023. "Statistical Estimation for Covariance Structures with Tail Estimates using Nodewise Quantile Predictive Regression Models," Papers 2305.11282, arXiv.org, revised Jul 2023.
    6. Höppner, Sebastiaan & Baesens, Bart & Verbeke, Wouter & Verdonck, Tim, 2022. "Instance-dependent cost-sensitive learning for detecting transfer fraud," European Journal of Operational Research, Elsevier, vol. 297(1), pages 291-300.
    7. Emilio Carrizosa & Vanesa Guerrero & Dolores Romero Morales, 2023. "On mathematical optimization for clustering categories in contingency tables," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(2), pages 407-429, June.
    8. Tinglong Dai & Sridhar Tayur, 2020. "OM Forum—Healthcare Operations Management: A Snapshot of Emerging Research," Manufacturing & Service Operations Management, INFORMS, vol. 22(5), pages 869-887, September.
    9. Koen W. de Bock & Kristof Coussement & Arno De Caigny & Roman Slowiński & Bart Baesens & Robert N Boute & Tsan-Ming Choi & Dursun Delen & Mathias Kraus & Stefan Lessmann & Sebastián Maldonado & David , 2023. "Explainable AI for Operational Research: A Defining Framework, Methods, Applications, and a Research Agenda," Post-Print hal-04219546, HAL.
    10. Weijie J. Su, 2022. "A Truthful Owner-Assisted Scoring Mechanism," Papers 2206.08149, arXiv.org.
    11. Lessmann, Stefan & Voß, Stefan, 2009. "A reference model for customer-centric data mining with support vector machines," European Journal of Operational Research, Elsevier, vol. 199(2), pages 520-530, December.
    12. Alwyn Lim & Shawn Pope, 2022. "What drives companies to do good? A “universal” ordering of corporate social responsibility motivations," Corporate Social Responsibility and Environmental Management, John Wiley & Sons, vol. 29(1), pages 233-255, January.
    13. Perera, H. Niles & Hurley, Jason & Fahimnia, Behnam & Reisi, Mohsen, 2019. "The human factor in supply chain forecasting: A systematic review," European Journal of Operational Research, Elsevier, vol. 274(2), pages 574-600.
    14. Hoffmann, F. & Baesens, B. & Mues, C. & Van Gestel, T. & Vanthienen, J., 2007. "Inferring descriptive and approximate fuzzy rules for credit scoring using evolutionary algorithms," European Journal of Operational Research, Elsevier, vol. 177(1), pages 540-555, February.
    15. Chen, Cathy Yi-Hsuan & Fengler, Matthias R. & Härdle, Wolfgang Karl & Liu, Yanchu, 2022. "Media-expressed tone, option characteristics, and stock return predictability," Journal of Economic Dynamics and Control, Elsevier, vol. 134(C).
    16. Kwon, He-Boong & Lee, Jooh, 2019. "Exploring the differential impact of environmental sustainability, operational efficiency, and corporate reputation on market valuation in high-tech-oriented firms," International Journal of Production Economics, Elsevier, vol. 211(C), pages 1-14.
    17. Wang, Deshen & Chen, Bintong & Chen, Jing, 2019. "Credit card fraud detection strategies with consumer incentives," Omega, Elsevier, vol. 88(C), pages 179-195.
    18. Martens, David & Baesens, Bart & Van Gestel, Tony & Vanthienen, Jan, 2007. "Comprehensible credit scoring models using rule extraction from support vector machines," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1466-1476, December.
    19. Carolina Camassa, 2023. "Legal NLP Meets MiCAR: Advancing the Analysis of Crypto White Papers," Papers 2310.10333, arXiv.org, revised Oct 2023.
    20. Mark Gilchrist & Deana Lehmann Mooers & Glenn Skrubbeltrang & Francine Vachon, 2012. "Knowledge Discovery in Databases for Competitive Advantage," Journal of Management and Strategy, Journal of Management and Strategy, Sciedu Press, vol. 3(2), pages 2-15, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jomega:v:86:y:2019:i:c:p:125-136. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/375/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.