Speaker
Description
Canonical polyadic tensor decomposition and approximation are fundamental problems in multilinear algebra with broad applications in signal processing, machine learning, and scientific computing. The difficulty of those problems depends on both the rank and order of the tensors. We introduce a new method for middle-rank tensor approximation and prove a new criterion for reshaping higher-order tensors. Our method leverages generating polynomials and utilizes linear algebra to generate a good starting point for the middle rank tensor approximation problem. When the given tensor is sufficiently close to a tensor whose rank is below a certain bound, we prove that our algorithm gives a quasi-optimal tensor approximation. Numerical experiments demonstrate that our algorithm can produce accurate tensor approximations for order 3 and higher-order tensors.