Memory-efficient parallel computation of tensor and matrix products for big tensor decomposition

Abstract—Low-rank tensor decomposition has many applica-tions in signal processing and machine learning, and is becoming increasingly important for analyzing big data. A significant challenge is the computation of intermediate products which can be much larger than the final result of the computation, or even the original tensor. We propose a scheme that allows memory-efficient in-place updates of intermediate matrices. Motivated by recent advances in big tensor decomposition from multiple compressed replicas, we also consider the related problem of memory-efficient tensor compression. The resulting algorithms can be parallelized, and can exploit but do not require sparsity. I