Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5500381 | Physica D: Nonlinear Phenomena | 2016 | 15 Pages |
Abstract
In this paper, we present a mathematical and algorithmic framework for the continuation of point clouds by persistence diagrams. A key property used in the method is that the persistence map, which assigns a persistence diagram to a point cloud, is differentiable. This allows us to apply the Newton-Raphson continuation method in this setting. Given an original point cloud P, its persistence diagram D, and a target persistence diagram Dâ², we gradually move from D to Dâ², by successively computing intermediate point clouds until we finally find a point cloud Pâ² having Dâ² as its persistence diagram. Our method can be applied to a wide variety of situations in topological data analysis where it is necessary to solve an inverse problem, from persistence diagrams to point cloud data.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Marcio Gameiro, Yasuaki Hiraoka, Ippei Obayashi,