Accelerating Block Coordinate Descent for Nonnegative Tensor Factorization

A N -way array or N -th order tensor T is a multidimensional array in the product R I 1 ... I N of the vector spaces R I i for i 1, 2,...,N . A vector x R I 1 is a first-order tensor, and a matrix M R I 1 I 2 is a second-order tensor. The goal of NTF is to approximate a tensor T by a structured tensor X . Using the squared Frobenius norm as a distance metric, defined as nullXnull 2 F null j 1,j 2,...j NX 2 j 1j 2...j N, NTF is the following optimization problem: min a (i) p 0, 1 i N, 1 p r null null null null null nullT r null p 1 N null i 1a (i) p null null null null null null 2 F, (1) This work was supported by the Fonds de la Recherche Scientifique - FNRS and the Fonds Wetenschappelijk Onderzoek - Vlanderen (FWO) under EOS Project no O005318F-RG47, and by the European Research Council (ERC starting grant no 679515).