Learning algebraic varieties from samples. 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.
Keywords for this software
References in zbMATH (referenced in 9 articles )
Showing results 1 to 9 of 9.
- Brown, Adam; Wang, Bei: Sheaf-theoretic stratification learning from geometric and topological perspectives (2021)
- Pauwels, Edouard; Putinar, Mihai; Lasserre, Jean-Bernard: Data analysis from empirical moments and the Christoffel function (2021)
- Adams, Henry; Aminian, Manuchehr; Farnell, Elin; Kirby, Michael; Mirth, Joshua; Neville, Rachel; Peterson, Chris; Shonkwiler, Clayton: A fractal dimension for measures via persistent homology (2020)
- Di Rocco, Sandra; Eklund, David; Weinstein, Madeleine: The bottleneck degree of algebraic varieties (2020)
- Gäfvert, Oliver: Computational complexity of learning algebraic varieties (2020)
- Maxim, Laurentiu G.; Rodriguez, Jose Israel; Wang, Botong: Defect of Euclidean distance degree (2020)
- Díaz, Mateo; Quiroz, Adolfo J.; Velasco, Mauricio: Local angles and dimension estimation from data on manifolds (2019)
- Horobeţ, Emil; Weinstein, Madeleine: Offset hypersurfaces and persistent homology of algebraic varieties (2019)
- Breiding, Paul; Kališnik, Sara; Sturmfels, Bernd; Weinstein, Madeleine: Learning algebraic varieties from samples (2018)