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Persistence paths and signature features in topological data analysis

Abstract:

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 characteristicnes...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1109/TPAMI.2018.2885516

Authors


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Institution:
University of Oxford
Division:
College Only
Department:
St Johns College
Oxford college:
St John's College
Role:
Author
ORCID:
0000-0002-5630-9694
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Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Oxford college:
Pembroke College
Role:
Author
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Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Oxford college:
St Hugh's College
Role:
Author
More from this funder
Funding agency for:
Nanda, V
Grant:
EP/N510129/1
More from this funder
Funding agency for:
Nanda, V
Grant:
EP/N510129/1
Publisher:
Institute of Electrical and Electronics Engineers Publisher's website
Journal:
IEEE Transactions on Pattern Analysis and Machine Intelligence Journal website
Volume:
42
Issue:
1
Publication date:
2018-12-07
Acceptance date:
2018-12-04
DOI:
EISSN:
1939-3539
ISSN:
0162-8828
Source identifiers:
950312
Keywords:
Pubs id:
pubs:950312
UUID:
uuid:3086b7fc-4ce4-486a-9623-2f57b4a232b2
Local pid:
pubs:950312
Deposit date:
2018-12-04

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