Haiyan Yang’s research while affiliated with University of Zurich and other places

Sobol's method is one of the most powerful and widely used frameworks for global sensitivity analysis, and it maps every possible combination of input variables to an associated Sobol index. However, these indices are often challenging to analyze in depth, due in part to the lack of suitable, flexible enough, and fast‐to‐query data access structures as well as visualization techniques. We propose a visualization tool that leverages tensor decomposition, a compressed data format that can quickly and approximately answer sophisticated queries over exponential‐sized sets of Sobol indices. This way, we are able to capture the complete global sensitivity information of high‐dimensional scalar models. Our application is based on a three‐stage visualization, to which variables to be analyzed can be added or removed interactively. It includes a novel hourglass‐like diagram presenting the relative importance for any single variable or combination of input variables with respect to any composition of the rest of the input variables. We showcase our visualization with a range of example models, whereby we demonstrate the high expressive power and analytical capability made possible with the proposed method.

Tensor decomposition methods and multilinear algebra are powerful tools to cope with challenges around multidimensional and multivariate data in computer graphics, image processing and data visualization, in particular with respect to compact representation and processing of increasingly large-scale data sets. Initially proposed as an extension of the concept of matrix rank for 3 and more dimensions, tensor decomposition methods have found applications in a remarkably wide range of disciplines. We briefly review the main concepts of tensor decompositions and their application to multidimensional visual data. Furthermore, we will include a first outlook on porting these techniques to multivariate data such as vector and tensor fields.