Abstract

This paper introduces a new approach for the scalable Tucker decomposition problem. Given a tensor X , the algorithm proposed, named Singleshot, allows to perform the inference task by processing one subtensor drawn from X at a time. The key principle of our approach is based on the recursive computations of the gradient and on cyclic update of the latent factors involving only one single step of gradient descent. We further improve the computational efficiency of Singleshot by proposing an inexact gradient version named Singleshotinexact. The two algorithms are backed with theoretical guarantees of convergence and convergence rates under mild conditions. The scalabilty of the proposed approaches, which can be easily extended to handle some common constraints encountered in tensor decomposition (e.g non-negativity), is proven via numerical experiments on both synthetic and real data sets.