A system and method for using inverse mathematical principles in the analysis of compatible datasets so that correlations and trends within and between said datasets can be uncovered. The present invention is tailored to the analysis of datasets that are extremely large; result from passive, privacy-secure, or anonymous, data collections; and are relatively unbiased. Correlations and trends uncovered by such analysis can be further examined by data mining and prediction portions of the present invention, which uncover and make use of interrelated rules that determine data structures.