Sampling real algebraic varieties for topological data analysis

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

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


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 languageEnglish
Title of host publication18th IEEE International Conference on Machine Learning and Applications
Subtitle of host publicationICMLA 2019
Number of pages6
ISBN (Print)978-1-7281-4549-5
Publication statusPublished - 17 Feb 2020
EventIEEE International Conference On Machine Learning And Applications - Boca Raton, United States
Duration: 16 Dec 201919 Dec 2019
Conference number: 18th


ConferenceIEEE International Conference On Machine Learning And Applications
Abbreviated titleICMLA
Country/TerritoryUnited States
CityBoca Raton

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