Improving homology estimates with random walks

Journal Article (Journal Article)

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.

Full Text

Duke Authors

Cited Authors

  • Bendich, P; Galkovskyi, T; Harer, J

Published Date

  • December 1, 2011

Published In

Volume / Issue

  • 27 / 12

Electronic International Standard Serial Number (EISSN)

  • 1361-6420

International Standard Serial Number (ISSN)

  • 0266-5611

Digital Object Identifier (DOI)

  • 10.1088/0266-5611/27/12/124002

Citation Source

  • Scopus