Using persistent homology to understand dimensionality reduction in resting-state fMRI

Ty O Easley, Kevin Freese, Elizabeth Munch, Janine Diane Bijsterbosch

Keywords: persistent homology, neuroimaging, neuroscience, manifold learning, dimensionality reduction, topological data analysis

TL;DR: We use persistent homology to measure differences between low-dimensional embeddings of neuroimaging data, and we find that different embeddings give drastically different accounts of subject variability.

Abstract: Evaluating the success of a manifold learning method remains a challenging problem, especially for methods adapted to a specific application domain. The present work investigates shared geometric structure across different dimensionality reduction (DR) algorithms within the scope of neuroimaging applications. We examine reduced-dimension embeddings produced by a representative assay of dimension reductions for brain data (“brain representations”) through the lens of persistent homology, making statistical claims about topological differences using a recent topological boostrap method. We cluster these methods based on their induced topologies, finding feature type and number --- rather than reduction algorithm --- as the main drivers of observed topological differences.

Submission Number: 2959