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Polynomial representation for persistence diagram
© 2019 IEEE. Persistence diagram (PD) has been considered as a compact descriptor for topological data analysis (TDA). Unfortunately, PD cannot be directly used in machine learning methods since it is a multiset of points. Recent efforts have been devoted to transforming PDs into vectors to accommodate machine learning methods. However, they share one common shortcoming: the mapping of PDs to a feature representation depends on a pre-defined polynomial. To address this limitation, this paper proposes an algebraic representation for PDs, i.e., polynomial representation. In this work, we discover a set of general polynomials that vanish on vectorized PDs and extract the task-adapted feature representation from these polynomials. We also prove two attractive properties of the proposed polynomial representation, i.e., stability and linear separability. Experiments also show that our method compares favorably with state-of-the-art TDA methods.
History
Event
Computer Vision and Pattern Recognition. Conference (2019 : Long Beach, California)Pagination
6116 - 6125Publisher
IEEELocation
Long Beach, CaliforniaPlace of publication
Piscataway, N.J.Publisher DOI
Start date
2019-06-15End date
2019-06-20ISSN
1063-6919ISBN-13
9781728132938Language
engPublication classification
E1 Full written paper - refereedTitle of proceedings
CVPR 2019 : Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern RecognitionUsage metrics
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