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:
We develop a topological analysis of robust traffic pace patterns using persistent homology. We develop Rips filtrations, parametrized by pace, for a symmetrization of traffic pace along the (naturally) directed edges in a road network. Our symmetrization is inspired by recent work of Turner (2019
- Award ID(s):
- 1727785
- NSF-PAR ID:
- 10304395
- Publisher / Repository:
- IOP Publishing
- Date Published:
- Journal Name:
- Journal of Physics: Complexity
- Volume:
- 2
- Issue:
- 2
- ISSN:
- 2632-072X
- Page Range / eLocation ID:
- Article No. 025007
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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