Parallel tensor decomposition with distributed memory based on hierarchical singular value decomposition

As an important tool of multiway/tensor data analysis tool, Tucker decomposition has been applied widely in various fields. But traditional sequential Tucker algorithms have been outdated because tensor data is growing rapidly in term of size. To address this problem, in this article, we focus on parallel Tucker decomposition of dense tensors on distributed-memory systems. The proposed method uses hierarchical SVD to accelerate the SVD step in traditional sequential algorithms, which usually takes up most computation time. The data distribution strategy is designed to follow the implementation of hierarchical SVD. We also find that compared with the state-of-the-art method, the proposed method has lower communication cost in large-scale parallel cases under the assumption of the alpha-beta model.