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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
Version:
Accepted Manuscript

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Publisher copy:
10.1109/tpami.2018.2885516

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Institution:
University of Oxford
Role:
Author
ORCID:
0000-0002-5630-9694
More by this author
Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Role:
Author
More by this author
Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Oxford college:
St Hughs College
Role:
Author
ORCID:
0000-0003-2644-8906
Publisher:
IEEE Publisher's website
Journal:
IEEE Transactions on Pattern Analysis and Machine Intelligence Journal website
Publication date:
2018-12-07
Acceptance date:
2018-12-04
DOI:
EISSN:
1939-3539
ISSN:
0162-8828
Pubs id:
pubs:857812
URN:
uri:b5f8c42c-0354-4284-b19c-24af2b74b1a6
UUID:
uuid:b5f8c42c-0354-4284-b19c-24af2b74b1a6
Local pid:
pubs:857812

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