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Title: Data Reduction and Feature Isolation for Computing Persistent Homology on High Dimensional Data
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 H0 and H1 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.  more » « less
Award ID(s):
1909096
PAR ID:
10350942
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Workshop on Applications of Topological Data Analysis to "Big Data"
Page Range / eLocation ID:
3860 to 3864
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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