Continuation of Point Clouds via Persistence Diagrams
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 , its persistence diagram , and a target persistence diagram , we gradually move from to , by successively computing intermediate point clouds until we finally find a point cloud having 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.
Keywords
Cite
@article{arxiv.1506.03147,
title = {Continuation of Point Clouds via Persistence Diagrams},
author = {Marcio Gameiro and Yasuaki Hiraoka and Ippei Obayashi},
journal= {arXiv preprint arXiv:1506.03147},
year = {2016}
}