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 noninvasive 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 to any dataset.

Author Summary Modern neuroimaging promises to transform how we understand human brain function, as well as how we diagnose and treat mental disorders. However, this promise hinges on the development of computational tools for distilling complex, high-dimensional neuroimaging data into simple representations that can be explored in research or clinical settings. The Mapper approach from topological data analysis (TDA) can be used to generate such representations. Here, we introduce several improvements to the underlying algorithm to aid scalability and parameter selection for high-dimensional neuroimaging data. We also provide new analytical tools for annotating and extracting neurobiological and behavioral insights from the generated representations. We hope this new framework will help facilitate translational applications of precision neuroimaging in clinical settings. Abstract For better translational outcomes, researchers and clinicians alike demand novel tools to distill complex neuroimaging data into simple yet behaviorally relevant representations at the single-participant level. Recently, the Mapper approach from topological data analysis (TDA) has been successfully applied on noninvasive human neuroimaging data to characterize the entire dynamical landscape of whole-brain configurations at the individual level without requiring any spatiotemporal averaging at the outset. Despite promising results, initial applications of Mapper to neuroimaging data were constrained by (1) the need for dimensionality reduction and (2) lack of a biologically grounded heuristic for efficiently exploring the vast parameter space. Here, we present a novel computational framework for Mapper—designed specifically for neuroimaging data—that removes limitations and reduces computational costs associated with dimensionality reduction and parameter exploration. We also introduce new meta-analytic approaches to better anchor Mapper-generated representations to neuroanatomy and behavior. Our new NeuMapper framework was developed and validated using multiple fMRI datasets where participants engaged in continuous multitask experiments that mimic “ongoing” cognition. Looking forward, we hope our framework will help researchers push the boundaries of psychiatric neuroimaging toward generating insights at the single-participant level across consortium-size datasets.

In this article, we present an open source neuroinformatics platform for exploring, analyzing, and validating distilled graphical representations of high-dimensional neuroimaging data extracted using topological data analysis (TDA). TDA techniques like Mapper have been recently applied to examine the brain’s dynamical organization during ongoing cognition without averaging data in space, in time, or across participants at the outset. Such TDA-based approaches mark an important deviation from standard neuroimaging analyses by distilling complex high-dimensional neuroimaging data into simple—yet neurophysiologically valid and behaviorally relevant—representations that can be interactively explored at the single-participant level. To facilitate wider use of such techniques within neuroimaging and general neuroscience communities, our work provides several tools for visualizing, interacting with, and grounding TDA-generated graphical representations in neurophysiology. Through Python-based Jupyter notebooks and open datasets, we provide a platform to assess and visualize different intermittent stages of Mapper and examine the influence of Mapper parameters on the generated representations. We hope this platform could enable researchers and clinicians alike to explore topological representations of neuroimaging data and generate biological insights underlying complex mental disorders. Author Summary To develop biologically grounded psychiatric diagnosis, researchers and clinicians need tools for distilling complex high-dimensional neuroimaging data into simple yet interactive and clinically relevant representations. Further, for translational outcomes, these representations should be conceivable at the single-participant level. Topological data analysis techniques such as Mapper allow generation of these representations. Here, we introduce a set of tools that can facilitate wider acceptance of Mapper within the neuroscience community and provide a series of easy-to-follow steps for visualizing Mapper-generated graphical representations. We provide detailed examples to reveal the “under-the-hood” workings of Mapper.