RTSMS: Randomized Tucker with single-mode sketching

<p dir="ltr">We propose RTSMS (Randomized Tucker with Single-Mode-Sketching), a randomized algorithm for approximately computing a low-rank Tucker decomposition of a given tensor. It uses sketching and the least-squares method to compute the Tucker decomposition in a sequentially truncated manner. RTSMS essentially only sketches one mode at a time, so the sketch matrices are significantly smaller than for alternative approaches. It uses a rank estimator to adaptively find an appropriate rank for the Tucker decomposition, without requiring it as input. RTSMS is demonstrated to be competitive with existing methods, sometimes outperforming them by a large margin.</p><p><br></p>