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...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Frontiers Media S.A.
2021-07-01
|
| Series: | Frontiers in Applied Mathematics and Statistics |
| Subjects: | |
| Online Access: | https://www.frontiersin.org/articles/10.3389/fams.2021.668046/full |
| _version_ | 1830510925579288576 |
|---|---|
| author | Jens Agerberg Ryan Ramanujam Ryan Ramanujam Martina Scolamiero Wojciech Chachólski |
| author_facet | Jens Agerberg Ryan Ramanujam Ryan Ramanujam Martina Scolamiero Wojciech Chachólski |
| author_sort | Jens Agerberg |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-12-22T02:02:20Z |
| format | Article |
| id | doaj.art-84a516fddb8b498c89b25eaf7de664dd |
| institution | Directory Open Access Journal |
| issn | 2297-4687 |
| language | English |
| last_indexed | 2024-12-22T02:02:20Z |
| publishDate | 2021-07-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Applied Mathematics and Statistics |
| spelling | doaj.art-84a516fddb8b498c89b25eaf7de664dd2022-12-21T18:42:38ZengFrontiers 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 |
| 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 |
| title | 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_short | Supervised Learning Using Homology Stable Rank Kernels |
| title_sort | supervised learning using homology stable rank kernels |
| 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 |