  Insightful visualization of multidimensional scalar fields, in particular
parameter spaces, is key to many fields in computational science and
engineering. We propose a principal component-based approach to visualize such
fields that accurately reflects their sensitivity to input parameters. The
method performs dimensionality reduction on the vast $L^2$ Hilbert 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. Our
mapping provides a direct geometrical and visual interpretation in terms of
Sobol's celebrated method for variance-based sensitivity analysis. We
furthermore contribute a practical realization of the proposed method by means
of tensor decomposition, which enables accurate yet interactive integration and
multilinear principal component analysis of high-dimensional models.
