Nonlinear least squares updating of the canonical polyadic decomposition

Current batch tensor methods often struggle to keep up with fast-arriving data. Even storing the full tensors that have to be decomposed can be problematic. To alleviate these limitations, tensor updating methods modify a tensor decomposition using efficient updates instead of recomputing the entire decomposition when new data becomes available. In this paper, the structure of the decomposition is exploited to achieve fast updates for the canonical polyadic decomposition whenever new slices are added to the tensor in a certain mode. A batch NLS-algorithm is adapted so that it can be used in an updating context. By only storing the old decomposition and the new slice of the tensor, the algorithm is both time- and memory efficient. Experimental results show that the proposed method is faster than batch ALS and NLS methods, while maintaining a good accuracy for the decomposition.