Comparing representations of high-dimensional data with persistent homology: a case study in neuroimaging

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Publication date: 23 June 2023

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.

Has companion code repository: https://github.com/tyo8/brain_representations

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