Persistent homology for low-complexity models

Lotz, Martin (2017) Persistent homology for low-complexity models. [MIMS Preprint]

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Abstract

We show that recent results on randomized dimension reduction schemes that exploit structural properties of data can be applied in the context of persistent homology. In the spirit of compressed sensing, the dimension reduction is determined by the Gaussian width of a structure associated to the data set, rather than its size. The Gaussian width also turns out to be useful for studying the complexity of other methods for approximating persistent homology.

Item Type:	MIMS Preprint
Uncontrolled Keywords:	Persistent homology; Topological data analysis; randomized dimension reduction; Johnson-Lindenstrauss
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 52 Convex and discrete geometry MSC 2010, the AMS's Mathematics Subject Classification > 60 Probability theory and stochastic processes MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis MSC 2010, the AMS's Mathematics Subject Classification > 68 Computer science
Depositing User:	Dr. Martin Lotz
Date Deposited:	03 Oct 2017
Last Modified:	08 Nov 2017 18:18
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/2580

Available Versions of this Item

• Persistent homology for low-complexity models. (deposited 11 Sep 2017)
  • Persistent homology for low-complexity models. (deposited 03 Oct 2017) [Currently Displayed]

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