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Approximating local homology from samples.
| Content Provider | CiteSeerX |
|---|---|
| Author | Skraba, Primoz Wang, Bei |
| Abstract | Abstract. Recently, multi-scale notions of local homology (a variant of persistent homology) have been used to study the local structure of spaces around a given point from a point cloud sample. Current reconstruction guarantees rely on constructing embedded complexes which become difficult in high dimensions. We show that the persistence diagrams used for estimating local homology, can be approximated using families of Vietoris-Rips complexes, whose simple constructions are robust in any dimension. To the best of our knowledge, our results, for the first time, make applications based on local homology, such as stratification learning, feasible in high dimensions. 1 |
| File Format | |
| Access Restriction | Open |
| Subject Keyword | Local Homology High Dimension Point Cloud Sample Multi-scale Notion Simple Construction Current Reconstruction Guarantee Persistent Homology First Time Vietoris-rips Complex Local Structure Persistence Diagram Stratification Learning |
| Content Type | Text |
| Resource Type | Article |
