Tensorlab 3.0 — Numerical optimization strategies for large-scale constrained and coupled matrix/tensor factorization

Abstract

We give an overview of recent developments in numerical optimization-based computation of tensor decompositions that have led to the release of Tensorlab 3.0 in March 2016 (www.tensorlab.net). By careful exploitation of tensor product structure in methods such as quasi-Newton and nonlinear least squares, good convergence is combined with fast computation. A modular approach extends the computation to coupled factorizations and structured factors. Given large datasets, different compact representations (polyadic, Tucker,…) may be obtained by stochastic optimization, randomization, compressed sensing, etc. Exploiting the representation structure allows us to scale the algorithms for constrained/coupled factorizations to large problem sizes.