Learning Algebraic Varieties from Samples

TL;DR

This paper develops new algorithms to identify real algebraic varieties from finite samples, focusing on topology and algebraic geometry, and provides a Julia package for practical implementation.

Contribution

It introduces novel methods for learning algebraic varieties from samples, emphasizing topology and algebraic properties, with comprehensive testing and software release.

Findings

Algorithms successfully recover variety properties from samples

Methods effectively determine dimension and defining polynomials

Software implementation available in Julia package

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.