A fast alternating least squares method for third-order tensors based on a compression procedure

抄録

The alternating least squares (ALS) method is frequently used for the computation of the canonical polyadic decomposition (CPD) of tensors. It generally gives accurate solutions, but demands much time. An alternative is the alternating slice-wise diagonalization (ASD) method, which provides an efficient way for third-order tensors, utilizing compression based on matrix singular value decomposition. In this paper, we propose a new simple algorithm, Reduced ALS, which employs the same compression procedure as ASD, but applies it more directly to ALS. Numerical experiments show that Reduced ALS runs as fast as ASD, avoiding instability ASD sometimes exhibits.