Stochastic convergence of persistence landscapes and silhouettes
<p>Persistent homology is a widely used tool in Topological Data Analysis that encodes multi-scale topological information as a multiset of points in the plane called a persistence diagram. It is difficult to apply statistical theory directly to a random sample of diagrams. Instead, we summari...
Main Authors: | , , , , |
---|---|
Format: | Article |
Language: | English |
Published: |
Carleton University
2015-03-01
|
Series: | Journal of Computational Geometry |
Online Access: | http://jocg.org/index.php/jocg/article/view/203 |
id |
doaj-bb41563c58104972aa5edb5a64b70f27 |
---|---|
record_format |
Article |
spelling |
doaj-bb41563c58104972aa5edb5a64b70f272020-11-24T23:05:08ZengCarleton UniversityJournal of Computational Geometry1920-180X2015-03-016210.20382/jocg.v6i2a866Stochastic convergence of persistence landscapes and silhouettesFrédéric ChazalBrittany Terese FasyFabrizio LecciAlessandro RinaldoLarry Wasserman<p>Persistent homology is a widely used tool in Topological Data Analysis that encodes multi-scale topological information as a multiset of points in the plane called a persistence diagram. It is difficult to apply statistical theory directly to a random sample of diagrams. Instead, we summarize persistent homology with a persistence landscape, introduced by Bubenik, which converts a diagram into a well-behaved real-valued function. We investigate the statistical properties of landscapes, such as weak convergence of the average landscapes and convergence of the bootstrap. In addition, we introduce an alternate functional summary of persistent homology, which we call the silhouette, and derive an analogous statistical theory.</p>http://jocg.org/index.php/jocg/article/view/203 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Frédéric Chazal Brittany Terese Fasy Fabrizio Lecci Alessandro Rinaldo Larry Wasserman |
spellingShingle |
Frédéric Chazal Brittany Terese Fasy Fabrizio Lecci Alessandro Rinaldo Larry Wasserman Stochastic convergence of persistence landscapes and silhouettes Journal of Computational Geometry |
author_facet |
Frédéric Chazal Brittany Terese Fasy Fabrizio Lecci Alessandro Rinaldo Larry Wasserman |
author_sort |
Frédéric Chazal |
title |
Stochastic convergence of persistence landscapes and silhouettes |
title_short |
Stochastic convergence of persistence landscapes and silhouettes |
title_full |
Stochastic convergence of persistence landscapes and silhouettes |
title_fullStr |
Stochastic convergence of persistence landscapes and silhouettes |
title_full_unstemmed |
Stochastic convergence of persistence landscapes and silhouettes |
title_sort |
stochastic convergence of persistence landscapes and silhouettes |
publisher |
Carleton University |
series |
Journal of Computational Geometry |
issn |
1920-180X |
publishDate |
2015-03-01 |
description |
<p>Persistent homology is a widely used tool in Topological Data Analysis that encodes multi-scale topological information as a multiset of points in the plane called a persistence diagram. It is difficult to apply statistical theory directly to a random sample of diagrams. Instead, we summarize persistent homology with a persistence landscape, introduced by Bubenik, which converts a diagram into a well-behaved real-valued function. We investigate the statistical properties of landscapes, such as weak convergence of the average landscapes and convergence of the bootstrap. In addition, we introduce an alternate functional summary of persistent homology, which we call the silhouette, and derive an analogous statistical theory.</p> |
url |
http://jocg.org/index.php/jocg/article/view/203 |
work_keys_str_mv |
AT fredericchazal stochasticconvergenceofpersistencelandscapesandsilhouettes AT brittanyteresefasy stochasticconvergenceofpersistencelandscapesandsilhouettes AT fabriziolecci stochasticconvergenceofpersistencelandscapesandsilhouettes AT alessandrorinaldo stochasticconvergenceofpersistencelandscapesandsilhouettes AT larrywasserman stochasticconvergenceofpersistencelandscapesandsilhouettes |
_version_ |
1725627292240052224 |