- 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...
Expand abstract - Publication status:
- Published
- Peer review status:
- Peer reviewed
- Version:
- Accepted Manuscript
- Files:
-
-
(pdf, 5.1MB)
-
- Publisher copy:
- 10.1109/tpami.2018.2885516
-
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- 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
- Language:
- English
- Keywords:
- Copyright holder:
- IEEE
- Copyright date:
- 2018
- Notes:
- Copyright © 2018 IEEE. This is the accepted manuscript version of the article. The final version is available online from the Institute of Electrical and Electronics Engineers at: 10.1109/tpami.2018.2885516
Journal article
Persistence paths and signature features in topological data analysis
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