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Sampling real algebraic varieties for topological data analysis

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Title of host publication18th IEEE International Conference on Machine Learning and Applications
DateAccepted/In press - 7 Oct 2019
DatePublished (current) - 17 Feb 2020
Number of pages6
PublisherIEEE
Original languageEnglish
ISBN (Print)978-1-7281-4549-5

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.

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