Homology-Preserving Dimensionality Reduction Via Manifold Landmarking And Tearing

Dimensionality reduction is an integral part of data visualization. It is a process that obtains a structure preserving low-dimensional representation of the high-dimensional data. Two common criteria can be used to achieve a dimensionality reduction: distance preservation and topology preservation. Inspired by recent work in topological data analysis, we are on the quest for a dimensionality reduction technique that achieves the criterion of homology preservation, a generalized version of topology preservation. Specifically, we are interested in using topology-inspired manifold landmarking and manifold tearing to aid such a process and evaluate their effectiveness.

Lin Yan, Yaodong Zhao, Paul Rosen, Carlos Scheidegger, and Bei Wang. Homology-Preserving Dimensionality Reduction Via Manifold Landmarking And Tearing. Visualization in Data Science (VDS), 2018.

@inproceedings{yan2018homology,
  title = {Homology-Preserving Dimensionality Reduction via Manifold Landmarking and
    Tearing},
  author = {Yan, Lin and Zhao, Yaodong and Rosen, Paul and Scheidegger, Carlos and Wang,
    Bei},
  booktitle = {Visualization in Data Science (VDS)},
  year = {2018},
  abstract = {Dimensionality reduction is an integral part of data visualization. It is a
    process that obtains a structure preserving low-dimensional representation of the
    high-dimensional data. Two common criteria can be used to achieve a dimensionality
    reduction: distance preservation and topology preservation. Inspired by recent work in
    topological data analysis, we are on the quest for a dimensionality reduction technique
    that achieves the criterion of homology preservation, a generalized version of topology
    preservation. Specifically, we are interested in using topology-inspired manifold
    landmarking and manifold tearing to aid such a process and evaluate their effectiveness.}
}