Persistence paths and signature features in topological data analysis
We introduce a new feature map for barcodes as they arise in persistent homology computation. The main idea is to first realize each barcode as a path in a convenient vector space, and to then compute its path signature which takes values in the tensor algebra of that vector space. The composition o...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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IEEE
2018
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| _version_ | 1797108846287650816 |
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| author | Chevyrev, I Nanda, V Oberhauser, H |
| author_facet | Chevyrev, I Nanda, V Oberhauser, H |
| author_sort | Chevyrev, I |
| collection | OXFORD |
| description | We introduce a new feature map for barcodes as they arise in persistent homology computation. The main idea is to first realize each barcode as a path in a convenient vector space, and to then compute its path signature which takes values in the tensor algebra of that vector space. The composition of these two operations - barcode to path, path to tensor series - results in a feature map that has several desirable properties for statistical learning, such as universality and characteristicness, and achieves state-of-the-art results on common classification benchmarks. |
| first_indexed | 2024-03-07T07:33:48Z |
| format | Journal article |
| id | oxford-uuid:b5f8c42c-0354-4284-b19c-24af2b74b1a6 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:33:48Z |
| publishDate | 2018 |
| publisher | IEEE |
| record_format | dspace |
| spelling | oxford-uuid:b5f8c42c-0354-4284-b19c-24af2b74b1a62023-02-09T12:56:12ZPersistence paths and signature features in topological data analysisJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:b5f8c42c-0354-4284-b19c-24af2b74b1a6EnglishSymplectic Elements at OxfordIEEE2018Chevyrev, INanda, VOberhauser, HWe introduce a new feature map for barcodes as they arise in persistent homology computation. The main idea is to first realize each barcode as a path in a convenient vector space, and to then compute its path signature which takes values in the tensor algebra of that vector space. The composition of these two operations - barcode to path, path to tensor series - results in a feature map that has several desirable properties for statistical learning, such as universality and characteristicness, and achieves state-of-the-art results on common classification benchmarks. |
| spellingShingle | Chevyrev, I Nanda, V Oberhauser, H Persistence paths and signature features in topological data analysis |
| title | Persistence paths and signature features in topological data analysis |
| title_full | Persistence paths and signature features in topological data analysis |
| title_fullStr | Persistence paths and signature features in topological data analysis |
| title_full_unstemmed | Persistence paths and signature features in topological data analysis |
| title_short | Persistence paths and signature features in topological data analysis |
| title_sort | persistence paths and signature features in topological data analysis |
| work_keys_str_mv | AT chevyrevi persistencepathsandsignaturefeaturesintopologicaldataanalysis AT nandav persistencepathsandsignaturefeaturesintopologicaldataanalysis AT oberhauserh persistencepathsandsignaturefeaturesintopologicaldataanalysis |