Learning Algebraic Varieties from Samples

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.

References in corpus (4)

• Quartic Curves and Their Bitangents
• Moment Varieties of Gaussian Mixtures
• Sampling algebraic varieties for sum of squares programs
• An explicit expression of the Luroth invariant

Cited by in corpus (7)

• Learning Algebraic Models of Quantum Entanglement
• Kernel approximation on algebraic varieties
• Learning a performance metric of Buchberger's algorithm
• On the Error of Random Sampling: Uniformly Distributed Random Points on Parametric Curves
• Finding the Homology of Manifolds using Ellipsoids
• Computational complexity of learning algebraic varieties
• Flow-Aware Ellipsoidal Filtration for Persistent Homology of Recurrent Signals