Fiberwise dimensionality reduction of topologically complex data with vector bundles

@article{Scoccola2022FiberwiseDR,
  title={Fiberwise dimensionality reduction of topologically complex data with vector bundles},
  author={Luis Scoccola and Jose A. Perea},
  journal={ArXiv},
  year={2022},
  volume={abs/2206.06513}
}
Datasets with non-trivial large scale topology can be hard to embed in low-dimensional Euclidean space with existing dimensionality reduction algorithms. We propose to model topologically complex datasets using vector bundles, in such a way that the base space accounts for the large scale topology, while the fibers account for the local geometry. This allows one to reduce the dimensionality of the fibers, while preserving the large scale topology. We formalize this point of view, and, as an… 
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