---
res:
bibo_abstract:
- We investigate a sheaf-theoretic interpretation of stratification learning from
geometric and topological perspectives. Our main result is the construction of
stratification learning algorithms framed in terms of a sheaf on a partially ordered
set with the Alexandroff topology. We prove that the resulting decomposition is
the unique minimal stratification for which the strata are homogeneous and the
given sheaf is constructible. In particular, when we choose to work with the local
homology sheaf, our algorithm gives an alternative to the local homology transfer
algorithm given in Bendich et al. (Proceedings of the 23rd Annual ACM-SIAM Symposium
on Discrete Algorithms, pp. 1355–1370, ACM, New York, 2012), and the cohomology
stratification algorithm given in Nanda (Found. Comput. Math. 20(2), 195–222,
2020). Additionally, we give examples of stratifications based on the geometric
techniques of Breiding et al. (Rev. Mat. Complut. 31(3), 545–593, 2018), illustrating
how the sheaf-theoretic approach can be used to study stratifications from both
topological and geometric perspectives. This approach also points toward future
applications of sheaf theory in the study of topological data analysis by illustrating
the utility of the language of sheaf theory in generalizing existing algorithms.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Adam
foaf_name: Brown, Adam
foaf_surname: Brown
foaf_workInfoHomepage: http://www.librecat.org/personId=70B7FDF6-608D-11E9-9333-8535E6697425
- foaf_Person:
foaf_givenName: Bei
foaf_name: Wang, Bei
foaf_surname: Wang
bibo_doi: 10.1007/s00454-020-00206-y
dct_date: 2020^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/0179-5376
- http://id.crossref.org/issn/1432-0444
dct_language: eng
dct_publisher: Springer Nature@
dct_title: Sheaf-theoretic stratification learning from geometric and topological
perspectives@
...