Mapper-Based Rough Sets

This paper presents a new approach to analyzing numerical data sets using covering-based rough sets based on the Mapper algorithm, a fundamental tool of topological data analysis (TDA). Specifically, by varying the parameters of Mapper, our approach generates different coverings from a numerical dataset that can be used to define lower approximations, and the associated quality of classification, for covering-based rough sets. We discuss the fundamental ideas of how to integrate both theories, and explore possible lines of further work.