Title: Data Reduction and Feature Isolation for Computing Persistent Homology on High Dimensional Data
Abstract:Persistent Homology (PH) is computationally expensive and is thus generally employed with strict limits on the (i) maximum connectivity distance and (ii) dimensions of homology groups to compute (unle...Persistent Homology (PH) is computationally expensive and is thus generally employed with strict limits on the (i) maximum connectivity distance and (ii) dimensions of homology groups to compute (unless working with trivially small data sets). As a result, most studies with PH only work with H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> and H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> homology groups. This paper examines the identification and isolation of regions of data sets where high dimensional topological features are suspected to be located. These regions are analyzed with PH to characterize the high dimensional homology groups contained in that region. Since only the region around a suspected topological feature is analyzed, it is possible to identify high dimension homologies piecewise and then assemble the results into a scalable characterization of the original data set.Read More
Publication Year: 2021
Publication Date: 2021-12-15
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 4
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