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2017.30: Persistent homology for low-complexity models

2017.30: Martin Lotz (2017) Persistent homology for low-complexity models.

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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 2000 > 52 Convex and discrete geometry
MSC 2000 > 60 Probability theory and stochastic processes
MSC 2000 > 65 Numerical analysis
MSC 2000 > 68 Computer science
MIMS number:2017.30
Deposited By:Dr. Martin Lotz
Deposited On:11 September 2017

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