Sounding Spider: An Efficient Way for Representing Uncertainties in High Dimensions

This article proposes a visualization method for multidimensional data based on: (i) Animated functional Hypothetical Outcome Plots (f-HOPs); (ii) 3-dimensional Kiviat plot; and (iii) data sonification. In an Uncertainty Quantification (UQ) framework, such analysis coupled with standard statistical analysis tools such as Probability Density Functions (PDF) can be used to augment the understanding of how the uncertainties in the numerical code inputs translate into uncertainties in the quantity of interest (QoI). In contrast with static representation of most advanced techniques such as functional Highest Density Region (HDR) boxplot or functional boxplot, f-HOPs is a dynamic visualization that enables the practitioners to infer the dynamics of the physics and enables to see functional correlations that may exist. While this technique only allows to represent the QoI, we propose a 3-dimensional version of the Kiviat plot to encode all input parameters. This new visualization takes advantage of information from f-HOPs through data sonification. All in all, this allows to analyse large datasets within a high-dimensional parameter space and a functional QoI in the same canvas. The proposed method is assessed and showed its benefits on two related environmental datasets.