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

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.

Analysis and Consequences on Some Aggregation Functions of PRISM (Partial Risk Map) Risk Assessment Method

“…If the ideal rank is not known or cannot be explicitly determined, the average rank of the objects can be used since the errors of the different methods cancel each other and the maximum likelihood principle ensures that the most probable ranking is provided by the average [40]. This method is non-parametric and robust, and it is used in several fields of science, see, e.g., [41,42]. In contrast to other statistical methods, such as Spearman's rho, Kendall's tau, and Mann-Whitney U test, the SRD not only provides pairwise comparison but also puts all the assessed rankings (aggregation methods) into an order according to their similarity (or dissimilarity) to the golden standard [40].…”