0-dimensional Homology Preserving Dimensionality Reduction with TopoMapDownload PDF

Oct 10, 2020 (edited Dec 02, 2020)NeurIPS 2020 Workshop TDA and Beyond Blind SubmissionReaders: Everyone
  • Keywords: Topological Data Analysis, Dimensionality Reduction, Computational Topology
  • Abstract: This note presents TopoMap, a novel dimensionality reduction technique which provides topological guarantees during the mapping process. In particular, TopoMap performs the mapping from a high-dimensional space to a visual space, while preserving the 0-dimensional persistence diagram of the Rips filtration of the high-dimensional data, ensuring that the filtrations generate the same connected components when applied to the original as well as projected data. The presented case studies show that the topological guarantee provided by TopoMap not only brings confidence to the visual analytic process but also can be used to assist in the assessment of other projection methods.
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