19 citations · 24 across the 8 of their papers we have counts for
11 papers
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…
The critical curvature degree of an algebraic variety
Emil Horobet
In this article, we study the complexity involved in the computation of the reach in arbitrary dimension and in particular the computation of the critical spherical curvature point…
Data loci in algebraic optimization
Emil Horobet, Jose Israel Rodriguez
In this article we provide examples, methods and algorithms to determine conditions on the parameters of certain type of parametric optimization problems, such that among the resul…
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…
Orthogonal and unitary tensor decomposition from an algebraic perspective
Ada Boralevi, Jan Draisma, Emil Horobet +1
While every matrix admits a singular value decomposition, in which the terms are pairwise orthogonal in a strong sense, higher-order tensors typically do not admit such an orthogon…
The Maximum Likelihood Data Singular Locus
Emil Horobet, Jose Israel Rodriguez
For general data, the number of complex solutions to the likelihood equations is constant and this number is called the (maximum likelihood) ML-degree of the model. In this article…
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…
Algebraic boundary of matrices of nonnegative rank at most three
Rob H. Eggermont, Emil Horobet, Kaie Kubjas
The Zariski closure of the boundary of the set of matrices of nonnegative rank at most 3 is reducible. We give a minimal generating set for the ideal of each irreducible component.…
The average number of critical rank-one approximations to a tensor
Jan Draisma, Emil Horobet
Motivated by the many potential applications of low-rank multi-way tensor approximations, we set out to count the rank-one tensors that are critical points of the distance function…
The Euclidean distance degree of an algebraic variety
Jan Draisma, Emil Horobet, Giorgio Ottaviani +2
The nearest point map of a real algebraic variety with respect to Euclidean distance is an algebraic function. For instance, for varieties of low rank matrices, the Eckart-Young Th…