Variable projection applied to block term decomposition of higher-order tensors

Abstract

Higher-order tensors have become popular in many areas of applied mathematics such as statistics, scientific computing, signal processing or machine learning, notably thanks to the many possible ways of decomposing a tensor. In this paper, we focus on the best approximation in the least-squares sense of a higher-order tensor by a block term decomposition. Using variable projection, we express the tensor approximation problem as a minimization of a cost function on a Cartesian product of Stiefel manifolds. The effect of variable projection on the Riemannian gradient algorithm is studied through numerical experiments.