Corpus ID: 235421846

Improving Metric Dimensionality Reduction with Distributed Topology

@article{Wagner2021ImprovingMD,
  title={Improving Metric Dimensionality Reduction with Distributed Topology},
  author={Alexander Wagner and Elchanan Solomon and Paul Bendich},
  journal={ArXiv},
  year={2021},
  volume={abs/2106.07613}
}
We propose a novel approach to dimensionality reduction combining techniques of metric geometry and distributed persistent homology, in the form of a gradient-descent based method called DIPOLE. DIPOLE is a dimensionalityreduction post-processing step that corrects an initial embedding by minimizing a loss functional with both a local, metric term and a global, topological term. By fixing an initial embedding method (we use Isomap), DIPOLE can also be viewed as a full dimensionality-reduction… Expand

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