Mapper is a very important tool in the implementation of topological data analysis and has been used with great success in many contexts. Despite this the Mapper method is rather ad hoc, varying a lot with respect changes in the input parameters. We develop a numerical measure for the stability of Mapper based on the exiting theory of clustering instability. This allows us to obtain concrete reasons for high values of Mapper instability and experimentally demonstrate how it can be applied to determine good Mapper outputs over variations of the Mapper parameters.
Our approach tackles directly the inherent instability of the choice of clustering procedure and requires very few assumption on the specifics of the data or chosen Mapper construction, making it applicable to any Mapper-type algorithm.
This is Joint work with Francisco Belchì, Jacek Brodzki, and Mahesan Niranjan.