Blockwise acceleration of alternating least squares for canonical tensor decomposition

The canonical polyadic (CP) decomposition of tensors is one the most important tensor decompositions. While well-known alternating least squares (ALS) algorithm often considered workhorse for computing CP decomposition, it known to suffer from slow convergence in many cases and various algorithms have been proposed accelerate it. In this article, we propose a new accelerated ALS that accelerates blockwise manner using simple momentum-based extrapolation technique random perturbation technique. Specifically, our updates factor matrix (i.e., block) at time, as ALS, with each update consisting minimization step directly reduces reconstruction error, an moves along previous direction, breaking bottlenecks. Our strategy takes simpler form than state-of-the-art strategies easier implement. has negligible computational overheads relative apply. Empirically, shows strong performance compared acceleration techniques on both simulated real tensors.