Algorithm 1026: Concurrent Alternating Least Squares for Multiple Simultaneous Canonical Polyadic Decompositions

Tensor decompositions, such as CANDECOMP/PARAFAC (CP), are widely used in a variety of applications, chemometrics, signal processing, and machine learning. A broadly method for computing decompositions relies on the Alternating Least Squares (ALS) algorithm. When number components is small, regardless its implementation, ALS exhibits low arithmetic intensity, which severely hinders performance makes GPU offloading ineffective. We observe that, practice, experts often have to compute multiple same tensor, each with small (typically fewer than 20), ultimately find best ones use application at hand. In this paper, we illustrate how tensor can be fused together algorithmic level increase intensity. Therefore, it becomes possible make efficient GPUs further speedups; time technique compatible many enhancements typically ALS, line search, extrapolation, non-negativity constraints. introduce Concurrent algorithm library, offers an interface Matlab, mechanism effectively deal issue that complete different times. Experimental results artificial real datasets demonstrate shorter completion due increased