Continuation of point clouds via persistence diagrams

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Author(s):	Gameiro, Marcio ; Hiraoka, Yasuaki ; Obayashi, Ippei Total Authors: 3
Document type:	Journal article
Source:	PHYSICA D-NONLINEAR PHENOMENA; v. 334, p. 118-132, NOV 1 2016.
Web of Science Citations:	2
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 D', we gradually move from D to D', by successively computing intermediate point clouds until we finally find a point cloud P' having D' 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. (C) 2015 Elsevier B.V. All rights reserved. (AU)

FAPESP's process:	10/00875-9 - Topological methods and rigorous numerics for bifurcations of dynamical systems
Grantee:	Marcio Fuzeto Gameiro
Support Opportunities:	Regular Research Grants


FAPESP's process:	13/07460-7 - Rigorous computations for PDEs
Grantee:	Marcio Fuzeto Gameiro
Support Opportunities:	Regular Research Grants