Principal component analysis of persistent homology rank functions with case studies of spatial point patterns, sphere packing and colloids

Persistent homology, while ostensibly measuring changes in topology, captures multiscale geometrical information. It is a natural tool for the analysis of point patterns. In this paper we explore the statistical power of the persistent homology rank functions. For a point pattern X we construct a fi...

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Bibliographic Details

Published in:	Physica. D Vol. 334; pp. 99 - 117
Main Authors:	Robins, Vanessa, Turner, Katharine
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 01.11.2016
Subjects:	Betti numbers Stochastic geometry Topological data analysis Stochastic geometry Topological data analysis Betti numbers
ISSN:	0167-2789, 1872-8022
Online Access:	Get full text
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