Optimal Low-Rank Tensor Singular Value Decompositions via Variable Projection
Katherine Keegan, Emory University
The inherent multidimensional nature of many real-world systems motivates the need to extend traditional matrix-based compression and dimensionality reduction techniques to tensors, or multidimensional arrays. One such method is the t-SVDM, a tensor singular value decomposition (SVD) which enables provably optimal low tensor-rank data representations. This representation depends on a choice of transformation matrix M, which gives rise to the tensor-tensor product used in the computation of the t-SVDM. In this poster, we introduce an optimization algorithm which uses variable projection and Riemannian optimization to simultaneously learn the optimal low tensor-rank representation and tensor-tensor product. We highlight the potential of this tensor-tensor product optimization in numerical examples for image compression and reduced-order modeling of dynamical systems.
Abstract Author(s): Katherine Keegan, Elizabeth Newman