Multi-Ensemble Visual Analytics via Fuzzy Sets

Analysis of ensemble datasets, i.e., collections of complex elements such as geochemical maps, is widespread in science and industry. The elements' complexity arises from the data they capture, which are often multivariate or spatio-temporal. We speak of multi-ensemble datasets when the analysis pertains to multiple ensembles. While many visualization approaches were suggested for ensemble datasets, multi-ensemble datasets remain comparatively underexplored. Our years-long collaboration with statisticians and geochemists taught us that they frame many questions about multi-ensemble data as set operations. E.g., what are the most common members (intersection of ensembles), or what features exist in one member but not another (difference of members)? As classical crisp set relations cannot account for the elements' complexity, we propose to model multi-ensembles as fuzzy relations. We provide examples of fuzzy set-based queries on a multi-ensemble of geochemical maps and integrate this approach into an existing ensemble visualization pipeline. We evaluated two visualizations obtained by applying this pipeline with experts in geochemistry and statistics. The experts confirmed known information and got directions for further research, which is one Visual Analytics (VA) goal. Hence, our proposal is highly promising for an interactive VA approach.