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...

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Bibliographic Details
Published in:IEEE transactions on pattern analysis and machine intelligence Vol. 42; no. 1; pp. 192 - 202
Main Authors: Chevyrev, Ilya, Nanda, Vidit, Oberhauser, Harald
Format: Journal Article
Language:English
Published: United States IEEE 01.01.2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algebra
Bar codes
barcodes
Bars
Data analysis
Extraterrestrial measurements
Feature maps
Homology
Kernel
kernel learning
Mathematical analysis
signature features
Tensors
Topological data analysis
Vector space
ISSN:0162-8828, 1939-3539, 2160-9292, 1939-3539
Online Access:Get full text
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Summary: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.
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ISSN:0162-8828
1939-3539
2160-9292
1939-3539
DOI:10.1109/TPAMI.2018.2885516