Nesterov-based Alternating Optimization for Nonnegative Tensor Factorization: Algorithm and Parallel Implementations

We consider the problem of nonnegative tensor factorization. Our aim is to derive an efficient algorithm that is also suitable for parallel implementation. We adopt the alternating optimization (AO) framework and solve each matrix nonnegative least-squares problem via a Nesterov-type algorithm for strongly convex problems. We describe two parallel implementations of the algorithm, with and without data replication. We test the efficiency of the algorithm in extensive numerical experiments and measure the attained speedup in a parallel computing environment. It turns out that the derived algorithm is a competitive candidate for the solution of very large-scale dense nonnegative tensor factorization problems.