Qualitative Analysis of Correspondence for Experimental Algorithmics

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.