Deconstructing the Mapper algorithm to extract richer topological and temporal features from functional neuroimaging data.

Capturing and tracking large-scale brain activity dynamics holds the potential to deepen our understanding of cognition. Previously, tools from Topological Data Analysis, especially Mapper, have been successfully used to mine brain activity dynamics at the highest spatiotemporal resolutions. Even though it is a relatively established tool within the field of Topological Data Analysis, Mapper results are highly impacted by parameter selection. Given that non-invasive human neuroimaging data (e.g., from fMRI) is typically fraught with artifacts and no gold standards exist regarding "true" state transitions, we argue for a thorough examination of Mapper parameter choices to better reveal their impact. Using synthetic data (with known transition structure) and real fMRI data, we explore a variety of parameter choices for each Mapper step, thereby providing guidance and heuristics for the field. We also release our parameter-exploration toolbox as a software package to make it easier for scientists to investigate and apply Mapper on any dataset.