This talk concerns the problem of reliably comparing cycle representatives from persistence modules drawn from separate data clouds given there exists a notion of cross-dissimilarity between the two sets. To do this, the talk features a primer on topological data analysis and the notion of distance between data clouds. It then will cover the tools required for a preliminary attempt at cycle comparison at the chain level using the Grassmannian distance. This method will then be outlined, and a minor result concerning its stability will be presented. Results from computer implementation will be presented along, and the talk will finish with potential refinements to the method that are being sought.