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Improving homology estimates with random walks

Publication ,  Journal Article
Bendich, P; Galkovskyi, T; Harer, J
Published in: Inverse Problems
December 1, 2011

This experimental paper makes the case for a new approach to the use of persistent homology in the study of shape and feature in datasets. By introducing ideas from diffusion geometry and random walks, we discover that homological features can be enhanced and more effectively extracted from spaces that are sampled densely and evenly, and with a small amount of noise. This study paves the way for a more theoretical analysis of how random walk metrics affect persistence diagrams, and provides evidence that combining topological data analysis with techniques inspired by diffusion geometry holds great promise for new analyses of a wide variety of datasets. © 2011 IOP Publishing Ltd.

Duke Scholars

Published In

Inverse Problems

DOI

EISSN

1361-6420

ISSN

0266-5611

Publication Date

December 1, 2011

Volume

27

Issue

12

Related Subject Headings

  • Applied Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0105 Mathematical Physics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics
 

Citation

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MLA
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Bendich, P., Galkovskyi, T., & Harer, J. (2011). Improving homology estimates with random walks. Inverse Problems, 27(12). https://doi.org/10.1088/0266-5611/27/12/124002
Bendich, P., T. Galkovskyi, and J. Harer. “Improving homology estimates with random walks.” Inverse Problems 27, no. 12 (December 1, 2011). https://doi.org/10.1088/0266-5611/27/12/124002.
Bendich P, Galkovskyi T, Harer J. Improving homology estimates with random walks. Inverse Problems. 2011 Dec 1;27(12).
Bendich, P., et al. “Improving homology estimates with random walks.” Inverse Problems, vol. 27, no. 12, Dec. 2011. Scopus, doi:10.1088/0266-5611/27/12/124002.
Bendich P, Galkovskyi T, Harer J. Improving homology estimates with random walks. Inverse Problems. 2011 Dec 1;27(12).
Journal cover image

Published In

Inverse Problems

DOI

EISSN

1361-6420

ISSN

0266-5611

Publication Date

December 1, 2011

Volume

27

Issue

12

Related Subject Headings

  • Applied Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0105 Mathematical Physics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics