Learning Algebraic Varieties from Samples

Madeleine Weinstein, Paul Breiding, Bernd Sturmfels, and Sara Kališnik Verovšek

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Submission date: 27. Feb. 2018
published in: Revista matematica complutense, 31 (2018) 3, p. 545-593 
DOI number (of the published article): 10.1007/s13163-018-0273-6
Bibtex
Link to arXiv: See the arXiv entry of this preprint.

Abstract:
We seek to determine a real algebraic variety from a fixed finite subset of points. Existing methods are studied and new methods are developed. Our focus lies on aspects of topology and algebraic geometry, such as dimension and defining polynomials. All algorithms are tested on a range of datasets and made available in a Julia package.