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Comprehensible Visualization of Multidimensional Data: Sum of Ranking Differences-Based Parallel Coordinates

Author

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  • Ádám Ipkovich

    (MTA-PE “Lendület” Complex Systems Monitoring Research Group, University of Pannonia, Egyetem u. 10, H-8200 Veszprem, Hungary)

  • Károly Héberger

    (ELKH Research Centre for Natural Sciences, Institute of Excellence of the Hungarian Academy of Sciences, Magyar Tudósok Krt. 2, H-1117 Budapest, Hungary)

  • János Abonyi

    (MTA-PE “Lendület” Complex Systems Monitoring Research Group, University of Pannonia, Egyetem u. 10, H-8200 Veszprem, Hungary)

Abstract

A novel visualization technique is proposed for the sum of ranking differences method (SRD) based on parallel coordinates. An axis is defined for each variable, on which the data are depicted row-wise. By connecting data, the lines may intersect. The fewer intersections between the variables, the more similar they are and the clearer the figure becomes. Therefore, the visualization depends on what techniques are used to order the variables. The key idea is to employ the SRD method to measure the degree of similarity of the variables, establishing a distance-based order. The distances between the axes are not uniformly distributed in the proposed visualization; their closeness reflects similarity, according to their SRD value. The proposed algorithm identifies false similarities through an iterative approach, where the angles between the SRD values determine which side a variable is plotted. Visualization of the algorithm is provided by MATLAB/Octave source codes. The proposed tool is applied to study how the sources of greenhouse gas emissions can be grouped based on the statistical data of the countries. A comparison to multidimensional scaling (MDS)-based ordering is also given. The use case demonstrates the applicability of the method and the synergies of the incorporation of the SRD method into parallel coordinates.

Suggested Citation

  • Ádám Ipkovich & Károly Héberger & János Abonyi, 2021. "Comprehensible Visualization of Multidimensional Data: Sum of Ranking Differences-Based Parallel Coordinates," Mathematics, MDPI, vol. 9(24), pages 1-17, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:24:p:3203-:d:700164
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    Cited by:

    1. Ferenc Bognár & Csaba Hegedűs, 2022. "Analysis and Consequences on Some Aggregation Functions of PRISM (Partial Risk Map) Risk Assessment Method," Mathematics, MDPI, vol. 10(5), pages 1-19, February.

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