ParCube: Sparse Parallelizable CANDECOMP-PARAFAC Tensor Decomposition

摘要

How can we efficiently decompose a tensor into sparse factors, when the data do not fit in memory? Tensor decompositions have gained a steadily increasing popularity in data-mining applications; however, the current state-of-art decomposition algorithms operate on main memory and do not scale to truly large datasets. In this work, we propose PaRCube, a new and highly parallelizable method for speeding up tensor decompositions that is well suited to produce sparse approximations. Experiments with even moderately large data indicate over 90% sparser outputs and 14 times faster execution, with approximation error close to the current state of the art irrespective of computation and memory requirements. We provide theoretical guarantees for the algorithm's correctness and we experimentally validate our claims through extensive experiments, including four different real world datasets (Enron, Lbnl, Facebook and Nell), demonstrating its effectiveness for data-mining practitioners. In particular, we are the first to analyze the very large Nell dataset using a sparse tensor decomposition, demonstrating that ParCube enables us to handle effectively and efficiently very large datasets. Finally, we make our highly scalable parallel implementation publicly available, enabling reproducibility of our work.