Performance Analysis and Optimization for MTTKRP of Sparse Tensor on CPU and GPU

Abstract

CANDECOMP/PARAFAC Decomposition (CPD), as a significant method for processing high-dimensional data, can perform dimension reduction and feature extraction while preserving the potential structural relationships effectively. However, the performance of CPD is limited by Matricized-tensor times Khatri-Rao product (MTTKRP). In this paper, we improve the computational efficiency of MTTKRP based on the GPU parallel technology. First, we use a tensor compressed format that eliminates redundant computational steps and enhances parallelism for the computing characteristics in MTTKRP. Second, we implement an algorithm of MTTKRP on sparse tensors. Third, we propose threads division strategies to maximize the computational efficiency of GPU. The inter-warp load imbalance is avoided by combining the warp execution method and shared memory. Compared to the state-of-the-art library ParTI, our optimized approach achieves up to $3. 58 \times $ speedup on artist tensor in mode-1 and $1. 59 \times $ average speedup on five tensors.