Generating a subway map that can capture the essential features of a system while potentially reducing the effect of noisy data. Mapper-generated representation is analogous to For example, in case of studying anatomical heterogeneity across participants, the data points could be individual participants themselves and the Mapper-generated graph would link participants with similar anatomical features closer as compared with participants with dissimilar anatomy. Intuitively, Mapper helps construct a skeletonized graph of a high-dimensional dataset to encapsulate the original shape of the data by representing similar points as more closely linked than dissimilar points in the generated shape graph. Lum et al., 2013 Singh, Mémoli & Carlsson, 2007) has been used to graphically represent the brain’s overall dynamical organization (i.e., the shape graph) without arbitrarily collapsing data in space or time (Saggar et al., 2018). More recently, an approach based on topological data analysis (TDA) called Mapper (Carlsson, 2009
These approaches provide valuable insights however, they cannot uncover the threshold-free optimal spatiotemporal scale that best captures behaviorally relevant dynamics (Preti et al., 2016).
Several innovative methods have been proposed to examine and quantify fluctuations in both functional activity (Karahanoğlu & Van De Ville, 2015 Liu & Duyn, 2013 Liu, Zhang, Chang, & Duyn, 2018) and connectivity (Preti et al., 2016 Shine et al., 2015 Xu & Lindquist, 2015).
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. 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. 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 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. 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. 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).
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