4 papers · 1 filter
Decomposing tensors via rank-one approximations
Alvaro Ribot, Emil Horobet, Anna Seigal +1
Matrices can be decomposed via rank-one approximations: the best rank-one approximation is a singular vector pair, and the singular value decomposition writes a matrix as a sum of…
When does subtracting a rank-one approximation decrease tensor rank?
Emil Horobet, Ettore Teixeira Turatti
Subtracting a critical rank-one approximation from a matrix always results in a matrix with a lower rank. This is not true for tensors in general. Motivated by this, we ask the que…
Offset Hypersurfaces and Persistent Homology of Algebraic Varieties
Emil Horobet, Madeleine Weinstein
In this paper, we study the persistent homology of the offset filtration of algebraic varieties. We prove the algebraicity of two quantities central to the computation of persisten…
The Data Singular and the Data Isotropic Loci for Affine Cones
Emil Horobet
The generic number of critical points of the Euclidean distance function from a data point to a variety is called the Euclidean distance degree. The two special loci of the data po…