J. F. Jardine
Published 2020-03-12Version 1
The hierarchy poset and branch point poset for a data set both admit a calculus of least upper bounds. A method involving upper bounds is used to show that the map of branch points associated to the inclusion of data sets is a controlled homotopy equivalence, where the control is expressed by an upper bound relation that is constrained by Hausdorff distance.
Comments: 8 pages. arXiv admin note: substantial text overlap with arXiv:1908.06323
Data and homotopy types
Triangular homotopy equivalences
Outlier-robust subsampling techniques for persistent homology
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