A central challenge in topological data analysis is the interpretation of barcodes. The classical algebraic-topological approach to interpreting homology classes is to build maps to spaces whose homology carries semantics we understand and then to appeal to functoriality. However, we often lack such maps in real data; instead, we must rely on a cross-dissimilarity measure between our observations of a system and a reference. In this paper, we develop a pair of computational homological algebra approaches for relating persistent homology classes and barcodes:
- Award ID(s):
- 2017980
- NSF-PAR ID:
- 10422657
- Editor(s):
- Bahoo, Yeganeh; Georgiou, Konstantinos
- Date Published:
- Journal Name:
- Canadian Conference in Computational Geometry
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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