CP decomposition for tensors via alternating least squares with QR decomposition

The CP tensor decomposition is used in applications such as machine learning and signal processing to discover latent low-rank structure multidimensional data. Computing a via an alternating least squares (ALS) method reduces the problem several linear problems. standard way solve these subproblems use normal equations, which inherit special that can be exploited for computational efficiency. However, equations are sensitive numerical ill-conditioning, compromise results of decomposition. In this paper, we develop versions CP-ALS algorithm using QR singular value decomposition, more numerically stable than Our algorithms utilize efficiently, have same complexity when input dense rank small, shown examples produce ill-conditioning present. MATLAB implementation achieves running time small ranks, show new methods obtain lower approximation error.