A Practical Randomized CP Tensor Decomposition
Abstract
The CANDECOMP/PARAFAC (CP) decomposition is a leading method for the analysis of multiway data. The standard alternating least squares algorithm for the CP decomposition (CP-ALS) involves a series of highly overdetermined linear least squares problems. We extend randomized least squares methods to tensors and show the workload of CP-ALS can be drastically reduced without a sacrifice in quality. We introduce techniques for efficiently preprocessing, sampling, and computing randomized least squares on a dense tensor of arbitrary order, as well as an efficient sampling-based technique for checking the stopping condition. We also show more generally that the Khatri-Rao product (used within the CP-ALS iteration) produces conditions favorable for direct sampling. In numerical results, we see improvements in speed, reductions in memory requirements, and robustness with respect to initialization.
Keywords
Cite
@article{arxiv.1701.06600,
title = {A Practical Randomized CP Tensor Decomposition},
author = {Casey Battaglino and Grey Ballard and Tamara G. Kolda},
journal= {arXiv preprint arXiv:1701.06600},
year = {2018}
}