Sampling real algebraic varieties for topological data analysis

Emilie Sonia Dufresne; Parker B. Edwards; Heather A Harrington; Jonathan D. Hauenstein

doi:10.1109/ICMLA.2019.00253

Sampling real algebraic varieties for topological data analysis

Emilie Sonia Dufresne, Parker B. Edwards, Heather A Harrington, Jonathan D. Hauenstein

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

Topological data analysis (TDA) provides tools for computing geometric and topological information about spaces from a finite sample of points. We present an adaptive algorithm for finding provably dense samples of points on real algebraic varieties given a set of defining polynomials for use as input to TDA. The algorithm utilizes methods from numerical algebraic geometry to give formal guarantees about the density of the sampling, and also employs geometric heuristics to reduce the size of the sample. As TDA methods consume significant computational resources that scale poorly in the number of sample points, our sampling minimization makes applying TDA methods more feasible. We provide a software package that implements the algorithm, and showcase it through several examples.

Original language	English
Title of host publication	18th IEEE International Conference on Machine Learning and Applications
Subtitle of host publication	ICMLA 2019
Publisher	IEEE
Number of pages	6
ISBN (Print)	978-1-7281-4549-5
DOIs	https://doi.org/10.1109/ICMLA.2019.00253
Publication status	Published - 17 Feb 2020
Event	IEEE International Conference On Machine Learning And Applications - Boca Raton, United States Duration: 16 Dec 2019 → 19 Dec 2019 Conference number: 18th

Conference

Conference	IEEE International Conference On Machine Learning And Applications
Abbreviated title	ICMLA
Country/Territory	United States
City	Boca Raton
Period	16/12/19 → 19/12/19

Access to Document

10.1109/ICMLA.2019.00253

TDANAG-Edwards-Dufresne-Harrington-HauensteinAccepted author manuscript, 641 KBLicence: Unspecified

Cite this

@inproceedings{1b878cd67ca54d97abd2c22d420e3bdb,

title = "Sampling real algebraic varieties for topological data analysis",

abstract = "Topological data analysis (TDA) provides tools for computing geometric and topological information about spaces from a finite sample of points. We present an adaptive algorithm for finding provably dense samples of points on real algebraic varieties given a set of defining polynomials for use as input to TDA. The algorithm utilizes methods from numerical algebraic geometry to give formal guarantees about the density of the sampling, and also employs geometric heuristics to reduce the size of the sample. As TDA methods consume significant computational resources that scale poorly in the number of sample points, our sampling minimization makes applying TDA methods more feasible. We provide a software package that implements the algorithm, and showcase it through several examples. ",

author = "Dufresne, {Emilie Sonia} and Edwards, {Parker B.} and Harrington, {Heather A} and Hauenstein, {Jonathan D.}",

year = "2020",

month = feb,

day = "17",

doi = "10.1109/ICMLA.2019.00253",

language = "English",

isbn = "978-1-7281-4549-5",

booktitle = "18th IEEE International Conference on Machine Learning and Applications",

publisher = "IEEE",

address = "United States",

note = "IEEE International Conference On Machine Learning And Applications, ICMLA ; Conference date: 16-12-2019 Through 19-12-2019",

}

Dufresne, ES, Edwards, PB, Harrington, HA & Hauenstein, JD 2020, Sampling real algebraic varieties for topological data analysis. in 18th IEEE International Conference on Machine Learning and Applications : ICMLA 2019. IEEE, IEEE International Conference On Machine Learning And Applications, Boca Raton, United States, 16/12/19. https://doi.org/10.1109/ICMLA.2019.00253

TY - GEN

T1 - Sampling real algebraic varieties for topological data analysis

AU - Dufresne, Emilie Sonia

AU - Edwards, Parker B.

AU - Harrington, Heather A

AU - Hauenstein, Jonathan D.

N1 - Conference code: 18th

PY - 2020/2/17

Y1 - 2020/2/17

N2 - Topological data analysis (TDA) provides tools for computing geometric and topological information about spaces from a finite sample of points. We present an adaptive algorithm for finding provably dense samples of points on real algebraic varieties given a set of defining polynomials for use as input to TDA. The algorithm utilizes methods from numerical algebraic geometry to give formal guarantees about the density of the sampling, and also employs geometric heuristics to reduce the size of the sample. As TDA methods consume significant computational resources that scale poorly in the number of sample points, our sampling minimization makes applying TDA methods more feasible. We provide a software package that implements the algorithm, and showcase it through several examples.

AB - Topological data analysis (TDA) provides tools for computing geometric and topological information about spaces from a finite sample of points. We present an adaptive algorithm for finding provably dense samples of points on real algebraic varieties given a set of defining polynomials for use as input to TDA. The algorithm utilizes methods from numerical algebraic geometry to give formal guarantees about the density of the sampling, and also employs geometric heuristics to reduce the size of the sample. As TDA methods consume significant computational resources that scale poorly in the number of sample points, our sampling minimization makes applying TDA methods more feasible. We provide a software package that implements the algorithm, and showcase it through several examples.

U2 - 10.1109/ICMLA.2019.00253

DO - 10.1109/ICMLA.2019.00253

M3 - Conference contribution

SN - 978-1-7281-4549-5

BT - 18th IEEE International Conference on Machine Learning and Applications

PB - IEEE

T2 - IEEE International Conference On Machine Learning And Applications

Y2 - 16 December 2019 through 19 December 2019

ER -