The article “High-dimensional scalar function visualization using principal parameterizations” written by Rafael Ballester et al. has been published by the Visual Computer journal, a venue focused on data visualization.

The article proposes a principal component-based approach to visualize high-dimensional functions and accurately reflects their sensitivity to their input parameters. The method first performs dimensionality reduction on the space formed by all possible partial functions (i.e., those defined by fixing one or more input parameters to specific values), which are projected to low-dimensional parameterized manifolds such as 3D curves, surfaces, and ensembles thereof. The mapping provides a direct geometrical and visual interpretation in terms of Sobol’s celebrated method for variance-based sensitivity analysis. In addition, it uses tensor decomposition as a numerical technique to enable accurate yet interactive integration and multilinear principal component analysis of high-dimensional models. The method is demonstrated in a case study modeling the Ebola virus spread, a model of the cell division cycle, and several dynamical systems arising from robotics and engineering.

The article is available at https://link.springer.com/article/10.1007/s00371-023-02937-4.