In this paper, we prove several results on interleavings for persistent relative homology of sub-level sets, (Formula presented.) complexes and Rips complexes. To prove the relative interleavings for (Formula presented.) complexes and Rips complexes, we define a relative correspondence which is related to the Gromov-Hausdorff distance. We also apply the relative Rips interleaving to a coverage problem in sensor networks, and show that the interleaving captures some features about the sensors after perturbation from the information of the unperturbed system.
|Number of pages||22|
|Journal||Japan Journal of Industrial and Applied Mathematics|
|Publication status||Published - 2016 Feb 1|
- Persistent homology
- Sensor networks
ASJC Scopus subject areas
- Applied Mathematics