  Correspondence identifies relationships among objects via similarities among
their components; it is ubiquitous in the analysis of spatial datasets,
including images, weather maps, and computational simulations. This paper
develops a novel multi-level mechanism for qualitative analysis of
correspondence. Operators leverage domain knowledge to establish
correspondence, evaluate implications for model selection, and leverage
identified weaknesses to focus additional data collection. The utility of the
mechanism is demonstrated in two applications from experimental algorithmics --
matrix spectral portrait analysis and graphical assessment of Jordan forms of
matrices. Results show that the mechanism efficiently samples computational
experiments and successfully uncovers high-level problem properties. It
overcomes noise and data sparsity by leveraging domain knowledge to detect
mutually reinforcing interpretations of spatial data.
