Baby Morse Theory in Data Analysis
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2011-05-16 v1
Abstract
A methodology is proposed for inferring the topology underlying point cloud data. The approach employs basic elements of Morse Theory, and is capable of producing not only a point estimate of various topological quantities (e.g., genus), but it can also assess their sampling uncertainty in a probabilistic fashion. Several examples of point cloud data in three dimensions are utilized to demonstrate how the method yields interval estimates for the topology of the data as a 2-dimensional surface embedded in R^3.
Cite
@article{arxiv.1105.2582,
title = {Baby Morse Theory in Data Analysis},
author = {Caren Marzban and Ulvi Yurtsever},
journal= {arXiv preprint arXiv:1105.2582},
year = {2011}
}