Co-PARAFAC: A Novel Cost-Efficient Scalable Tensor Decomposition Algorithm

This paper proposes a novel tensor decomposition method, cooperative parallel factor (Co-PARAFAC), that is devised to achieve higher accuracy with lower computational complexity and memory requirements than the conventional PARAFAC. The rationale relies on dividing a given tensor, even with a large size, into smaller disjoint sub-tensors, which are independently and parallelly decomposed using the conventional PARAFAC. The intermediate results are then properly merged to obtain the decomposition of the original tensor. As case study, we apply Co-PARAFAC to estimate the uplink channels of RIS-assisted wireless communications. Simulation results corroborate the efficiency of the Co-PARAFAC in achieving significantly lower computational complexity and higher channel estimation accuracy than the conventional PARAFAC. Broadly, the proposed algorithm is advantageous in various fields requiring efficient and high accurate tensor decomposition.