Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
11024726 | Advances in Applied Mathematics | 2019 | 30 Pages |
Abstract
Methods from topological data analysis in general metric spaces detect more complicated patterns such as holes and voids that persist for a large interval in a 1-parameter family of shapes associated to a cloud. These features can be visualized in the form of a 1-dimensional homologically persistent skeleton, which optimally extends a minimum spanning tree of a point cloud to a graph with cycles. We generalize this skeleton to higher dimensions and prove its optimality among all complexes that preserve topological features of data at any scale.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Sara Kališnik, Vitaliy Kurlin, Davorin Lešnik,