Polynomial representation for persistence diagram

Zhichao WANG, Qian LI, Gang LI, Guandong XU

Research output: Chapter in Book/Report/Conference proceedingChapters

8 Citations (Scopus)

Abstract

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. Copyright © 2019 IEEE.

Original languageEnglish
Title of host publicationProceedings of 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2019
Place of PublicationUSA
PublisherIEEE
Pages6116-6125
ISBN (Electronic)9781728132938
DOIs
Publication statusPublished - Jun 2019

Citation

Wang, Z., Li, Q., Li, G., & Xu, G. (2019). Polynomial representation for persistence diagram. In Proceedings of 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2019 (pp. 6116-6125). IEEE. https://doi.org/10.1109/CVPR.2019.00628

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