Using persistent homology to understand dimensionality reduction in resting-state fMRI
- Resource Type
- Authors
- Easley, Ty; Freese, Kevin; Munch, Elizabeth; Bijsterbosch, Janine
- Source
- Subject
- Computational Geometry (cs.CG)
FOS: Computer and information sciences
Quantitative Biology - Neurons and Cognition
FOS: Biological sciences
Image and Video Processing (eess.IV)
FOS: Electrical engineering, electronic engineering, information engineering
FOS: Mathematics
Computer Science - Computational Geometry
Algebraic Topology (math.AT)
Neurons and Cognition (q-bio.NC)
Mathematics - Algebraic Topology
Electrical Engineering and Systems Science - Image and Video Processing
- Language
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.
Comment: Preprint of submission for NeurIPS 2023 conference