A Pipeline Computing Method of SpTV for Three-Order Tensors on CPU and GPU

Tensors have drawn a growing attention in many applications, such as physics, engineering science, social networks, recommended systems. Tensor decomposition is the key to explore the inherent intrinsic data relationship of tensor. There are many sparse tensor and vector multiplications (SpTV) in tensor decomposition. We analyze a variety of storage formats of sparse tensors and develop a piecewise compression strategy to improve the storage efficiency of large sparse tensors. This compression strategy can avoid storing a large number of empty slices and empty fibers in sparse tensors, and thus the storage space is significantly reduced. A parallel algorithm for the SpTV based on the high-order compressed format based on slices is designed to greatly improve its computing performance on graphics processing unit. Each tensor is cut into multiple slices to form a series of sparse matrix and vector multiplications, which form the pipelined parallelism. The transmission time of the slices can be hidden through pipelined parallel to further optimize the performance of the SpTV.