Statistical linkage across high dimensional observational domains

Many experimental sciences collect different kinds of high-dimensional data on the same experimental units. When comparing relationships among homogeneous regions in one high dimensional domain with regions in another high dimensional domain, the number of possible comparisons may be extremely large and their set complexity unknown. We outline procedures for identifying possible relationships among regions in two different high-dimensional domains. If the data are dense enough, then statistical measures of association can be estimated. These procedures can identify and measure the probability of inter-domain associations of mixed complexity.