Faster tensor train decomposition for sparse data

In recent years, the application of tensors has become more widespread in fields that involve data analytics and numerical computation. Due to explosive growth data, low-rank tensor decompositions have a powerful tool harness notorious curse dimensionality . The main forms decomposition include CP decomposition, Tucker train (TT) etc. Each existing TT algorithms, including TT-SVD randomized TT-SVD, is successful field, but neither can both accurately efficiently decompose large-scale sparse tensors. Based on previous research, this paper proposes new quasi-optimal fast algorithm for with proven correctness upper bound computational complexity derived. It also produce no error slightly larger TT-ranks demand. experiments, we verify proposed much faster speed than advantages speed, precision versatility over TT-cross. And, it realize matrix was previously unachievable, enabling based algorithms be applied scenarios.