By the same authors

Sampling real algebraic varieties for topological data analysis

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Standard

Sampling real algebraic varieties for topological data analysis. / Dufresne, Emilie Sonia; Edwards, Parker B.; Harrington, Heather A; Hauenstein, Jonathan D.

18th IEEE International Conference on Machine Learning and Applications : ICMLA 2019. IEEE, 2020.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Harvard

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

APA

Dufresne, E. S., Edwards, P. B., Harrington, H. A., & Hauenstein, J. D. (2020). Sampling real algebraic varieties for topological data analysis. In 18th IEEE International Conference on Machine Learning and Applications : ICMLA 2019 IEEE. https://doi.org/10.1109/ICMLA.2019.00253

Vancouver

Dufresne ES, Edwards PB, Harrington HA, Hauenstein JD. Sampling real algebraic varieties for topological data analysis. In 18th IEEE International Conference on Machine Learning and Applications : ICMLA 2019. IEEE. 2020 https://doi.org/10.1109/ICMLA.2019.00253

Author

Dufresne, Emilie Sonia ; Edwards, Parker B. ; Harrington, Heather A ; Hauenstein, Jonathan D. / Sampling real algebraic varieties for topological data analysis. 18th IEEE International Conference on Machine Learning and Applications : ICMLA 2019. IEEE, 2020.

Bibtex - Download

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

}

RIS (suitable for import to EndNote) - Download

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 -