5 papers · 1 filter
Euclidean Distance Optimization Within the Grassmannian
Hannah Friedman, Serkan Hoşten, Andrea Rosana
Given a subvariety of the Grassmannian and a data point, we seek to find a point on the subvariety minimizing the Euclidean distance to the data point. The number of complex critic…
Degree of tensor train varieties via integral geometry
Andrea Rosana, Otto T. P. Schmidt
In this work we consider tensor train varieties. These are varieties of tensors arising in a range of fields, including quantum many-body physics and machine learning. Using method…
Distance Optimization in the Grassmannian of Lines
Hannah Friedman, Andrea Rosana, Bernd Sturmfels
The square of a skew-symmetric matrix is a symmetric matrix whose eigenvalues have even multiplicities. When the matrices have rank two, they represent the Grassmannian of lines, a…
Typical ranks of random order-three tensors
Paul Breiding, Sarah Eggleston, Andrea Rosana
In this paper we study typical ranks of real tensors. In the case the typical ranks are contained in ,…
What is the probability that a random symmetric tensor is close to rank-one?
Alberto Cazzaniga, Antonio Lerario, Andrea Rosana
We address the general problem of estimating the probability that a real symmetric tensor is close to rank-one tensors. Using Weyl's tube formula, we turn this question into a diff…