6 papers
Minimality of Tree Tensor Network Ranks
Jana Jovcheva, Tim Seynnaeve, Nick Vannieuwenhoven
For a given tree tensor network , we call a tuple of bond dimensions minimal if there exists a tensor that can be represented by this network but not on the same tree topolo…
Manifold-valued function approximation from multiple tangent spaces
Hang Wang, Raf Vandebril, Joeri Van der Veken +1
Approximating a manifold-valued function from samples of input-output pairs consists of modeling the relationship between an input from a vector space and an output on a Riemannian…
A chiseling algorithm for low-rank Grassmann decomposition of skew-symmetric tensors
Nick Vannieuwenhoven
A numerical algorithm to decompose an exact low-rank skew-symmetric tensor into a sum of elementary (rank-) skew-symmetric tensors is introduced. The algorithm uncovers this Gra…
Warped geometries of Segre-Veronese manifolds
Simon Jacobsson, Lars Swijsen, Joeri Van der Veken +1
Segre-Veronese manifolds are smooth submanifolds of tensors comprising the partially symmetric rank-1 tensors. We investigate a one-parameter family of warped geometries of Segre-V…
Approximating maps into manifolds with lower curvature bounds
Simon Jacobsson, Raf Vandebril, Joeri van der Veken +1
Many interesting functions arising in applications map into Riemannian manifolds. We present an algorithm, using the manifold exponential and logarithm, for approximating such func…
Hadamard-Hitchcock decompositions: identifiability and computation
Alessandro Oneto, Nick Vannieuwenhoven
A Hadamard-Hitchcock decomposition of a multidimensional array is a decomposition that expresses the latter as a Hadamard product of several tensor rank decompositions. Such decomp…