An Introduction to Hierarchical (H-) Rank and TT-Rank of Tensors with Examples
An Introduction to Hierarchical (H-) Rank and TT-Rank of Tensors with Examples
Abstract We review two similar concepts of hierarchical rank of tensors (which extend the matrix rank to higher order tensors): the TT-rank and the H-rank (hierarchical or H-Tucker rank). Based on this notion of rank, one can define a data-sparse representation of tensors involving O(dnk + dk^3) data for order …