CPD Updating Using Low-Rank Weights

Tensor updating methods enable tensor decompositions to adapt quickly when new data is added to the tensor. At present, updating methods for the canonical polyadic decomposition (CPD) give every tensor entry the same weight. In practice, however, data quality or relative importance might differ between tensor entries, which warrants the use of more general weighting schemes. In this paper, an NLS updating method is developed for the CPD that uses a weighted least squares (WLS) approach with a low-rank weight tensor. This weight tensor itself can also be updated to allow dynamic weighting schemes. By exploiting the CPD structure of both the data and weight tensors, the algorithm obtains better accuracy than the unweighted updating methods, while being more time- and memory efficient than batch WLS methods.