Supervised Learning Using Homology Stable Rank Kernels

Supervised Learning Using Homology Stable Rank Kernels

Exciting recent developments in Topological Data Analysis have aimed at combining homology-based invariants with Machine Learning. In this article, we use hierarchical stabilization to bridge between persistence and kernel-based methods by introducing the so-called stable rank kernels. A fundamental...

Full description

Bibliographic Details
Main Authors: Jens Agerberg, Ryan Ramanujam, Martina Scolamiero, Wojciech Chachólski
Format: Article
Language:English
Published: Frontiers Media S.A. 2021-07-01
Series:Frontiers in Applied Mathematics and Statistics
Subjects:
topological data analysis
kernel methods
metrics
hierarchical stabilisation
persistent homology
Online Access:https://www.frontiersin.org/articles/10.3389/fams.2021.668046/full
id doaj-84a516fddb8b498c89b25eaf7de664dd
record_format Article
spelling doaj-84a516fddb8b498c89b25eaf7de664dd2021-07-09T12:25:45ZengFrontiers Media S.A.Frontiers in Applied Mathematics and Statistics2297-46872021-07-01710.3389/fams.2021.668046668046Supervised Learning Using Homology Stable Rank KernelsJens Agerberg0Ryan Ramanujam1Ryan Ramanujam2Martina Scolamiero3Wojciech Chachólski4KTH Royal Institute of Technology, Mathematics Department, Stockholm, SwedenKTH Royal Institute of Technology, Mathematics Department, Stockholm, SwedenDepartment of Clinical Neuroscience, Karolinska Institutet, Stockholm, SwedenKTH Royal Institute of Technology, Mathematics Department, Stockholm, SwedenKTH Royal Institute of Technology, Mathematics Department, Stockholm, SwedenExciting recent developments in Topological Data Analysis have aimed at combining homology-based invariants with Machine Learning. In this article, we use hierarchical stabilization to bridge between persistence and kernel-based methods by introducing the so-called stable rank kernels. A fundamental property of the stable rank kernels is that they depend on metrics to compare persistence modules. We illustrate their use on artificial and real-world datasets and show that by varying the metric we can improve accuracy in classification tasks.https://www.frontiersin.org/articles/10.3389/fams.2021.668046/fulltopological data analysiskernel methodsmetricshierarchical stabilisationpersistent homology
collection DOAJ
language English
format Article
sources DOAJ
author Jens Agerberg
Ryan Ramanujam
Ryan Ramanujam
Martina Scolamiero
Wojciech Chachólski
spellingShingle Jens Agerberg
Ryan Ramanujam
Ryan Ramanujam
Martina Scolamiero
Wojciech Chachólski
Supervised Learning Using Homology Stable Rank Kernels
Frontiers in Applied Mathematics and Statistics
topological data analysis
kernel methods
metrics
hierarchical stabilisation
persistent homology
author_facet Jens Agerberg
Ryan Ramanujam
Ryan Ramanujam
Martina Scolamiero
Wojciech Chachólski
author_sort Jens Agerberg
title Supervised Learning Using Homology Stable Rank Kernels
title_short Supervised Learning Using Homology Stable Rank Kernels
title_full Supervised Learning Using Homology Stable Rank Kernels
title_fullStr Supervised Learning Using Homology Stable Rank Kernels
title_full_unstemmed Supervised Learning Using Homology Stable Rank Kernels
title_sort supervised learning using homology stable rank kernels
publisher Frontiers Media S.A.
series Frontiers in Applied Mathematics and Statistics
issn 2297-4687
publishDate 2021-07-01
description Exciting recent developments in Topological Data Analysis have aimed at combining homology-based invariants with Machine Learning. In this article, we use hierarchical stabilization to bridge between persistence and kernel-based methods by introducing the so-called stable rank kernels. A fundamental property of the stable rank kernels is that they depend on metrics to compare persistence modules. We illustrate their use on artificial and real-world datasets and show that by varying the metric we can improve accuracy in classification tasks.
topic topological data analysis
kernel methods
metrics
hierarchical stabilisation
persistent homology
url https://www.frontiersin.org/articles/10.3389/fams.2021.668046/full
work_keys_str_mv AT jensagerberg supervisedlearningusinghomologystablerankkernels
AT ryanramanujam supervisedlearningusinghomologystablerankkernels
AT ryanramanujam supervisedlearningusinghomologystablerankkernels
AT martinascolamiero supervisedlearningusinghomologystablerankkernels
AT wojciechchacholski supervisedlearningusinghomologystablerankkernels
_version_ 1721311312779149312

Similar Items