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Date
2024-06Type
- Journal Article
ETH Bibliography
yes
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Abstract
Persistent homology is a central methodology in topological data analysis that has been successfully implemented in many fields and is becoming increasingly popular and relevant. The output of persistent homology is a persistence diagram ---a multiset of points supported on the upper halfplane ---that is often used as a statistical summary of the topological features of data. In this paper, we study the random nature of persistent homology and estimate the density of expected persistence diagrams from observations using wavelets; we show that our wavelet -based estimator is optimal. Furthermore, we propose an estimator that offers a sparse representation of the expected persistence diagram that achieves near -optimality. We demonstrate the utility of our contributions in a machine learning task in the context of dynamical systems. Show more
Publication status
publishedExternal links
Journal / series
SIAM/ASA Journal on Uncertainty QuantificationVolume
Pages / Article No.
Publisher
SIAMSubject
nonparametric density estimation; persistent homology; persistence measures; waveletsMore
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ETH Bibliography
yes
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