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Local homology transfer and stratification learning

Publication ,  Conference
Bendich, P; Wang, B; Mukherjee, S
Published in: Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
January 1, 2012

The objective of this paper is to show that point cloud data can under certain circumstances be clustered by strata in a plausible way. For our purposes, we consider a stratified space to be a collection of manifolds of different dimensions which are glued together in a locally trivial manner inside some Euclidean space. To adapt this abstract definition to the world of noise, we first define a multi-scale notion of stratified spaces, providing a stratification at different scales which are indexed by a radius parameter. We then use methods derived from kernel and cokernel persistent homology to cluster the data points into different strata. We prove a correctness guarantee for this clustering method under certain topological conditions. We then provide a probabilistic guarantee for the clustering for the point sample setting - we provide bounds on the minimum number of sample points required to state with high probability which points belong to the same strata. Finally, we give an explicit algorithm for the clustering. Copyright © SIAM.

Duke Scholars

Published In

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

DOI

ISBN

9781611972108

Publication Date

January 1, 2012

Start / End Page

1355 / 1370
 

Citation

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Bendich, P., Wang, B., & Mukherjee, S. (2012). Local homology transfer and stratification learning. In Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms (pp. 1355–1370). https://doi.org/10.1137/1.9781611973099.107
Bendich, P., B. Wang, and S. Mukherjee. “Local homology transfer and stratification learning.” In Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, 1355–70, 2012. https://doi.org/10.1137/1.9781611973099.107.
Bendich P, Wang B, Mukherjee S. Local homology transfer and stratification learning. In: Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms. 2012. p. 1355–70.
Bendich, P., et al. “Local homology transfer and stratification learning.” Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, 2012, pp. 1355–70. Scopus, doi:10.1137/1.9781611973099.107.
Bendich P, Wang B, Mukherjee S. Local homology transfer and stratification learning. Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms. 2012. p. 1355–1370.

Published In

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

DOI

ISBN

9781611972108

Publication Date

January 1, 2012

Start / End Page

1355 / 1370