Function Preserving Projection
With function preserving projection (FPP), we aim to address high-dimensional data exploration challenges common in many scientific applications. Instead of preserving the global or local geometric structure of a dataset like traditional dimensionality reduction methods (e.g., principal component analysis, t-stochastic neighborhood embedding), the proposed approach finds a linear projection that reveal interpretable (yet potentially nonlinear) pattern of the properties of interests defined on a highdimensional domain (e.g., simulation yield defined on the input parameter space). The key insight driving FPP is the fact that while non-linear embeddings are difficult to interpret, humans are highly skilled in understanding complex visual patterns. FPP lets users select the complexity of a pattern they consider interpretable, allows to find a joint projection that explains multiple functions, and provides a confidence statistic (akin to a p-value) indicating how salient the resulting pattern is. We demonstrate the efficacy of the proposed method on several synthetic and scientific datasets for both continuous (regression) and discrete (classification) problems of interests and illustrate the scalability of FPP by finding an optimal projection for close to 40 gigabytes in around 10 minutes.