Visual Representation of Region Transitions in Multi-dimensional Parameter Spaces

Abstract

We propose a novel visual representation of transitions between homogeneous regions in multi-dimensional parameter space. While our approach is generally applicable for the analysis of arbitrary continuous parameter spaces, we particularly focus on scientific applications, like physical variables in simulation ensembles. To generate our representation, we use unsupervised learning to cluster the ensemble members according to their mutual similarity. In doing this, clusters are sorted such that similar clusters are located next to each other. We then further partition the clusters into connected regions with respect to their location in parameter space. In the visualization, the resulting regions are represented as glyphs in a matrix, indicating parameter changes which induce a transition to another region. To unambiguously associate a change of data characteristics to a single parameter, we specifically isolate changes by dimension. With this, our representation provides an intuitive visualization of the parameter transitions that influence the outcome of the underlying simulation or measurement. We demonstrate the generality and utility of our approach on diverse types of data, namely simulations from the field of computational fluid dynamics and thermodynamics, as well as an ensemble of raycasting performance data.