Publications [#378674] of Jianfeng Lu

Papers Published

1. Chen, Z; Lu, J; Zhang, A, ONE-DIMENSIONAL TENSOR NETWORK RECOVERY, SIAM Journal on Matrix Analysis and Applications, vol. 45 no. 3 (January, 2024), pp. 1217-1244 [doi]
   (last updated on 2024/11/18)

   Abstract:
   We study the recovery of the underlying graphs or permutations for tensors in the tensor ring or tensor train format. Our proposed algorithms compare the matricization ranks after down-sampling, whose complexity is O(dlogd) for dth-order tensors. We prove that our algorithms can almost surely recover the correct graph or permutation when tensor entries can be observed without noise. We further establish the robustness of our algorithms against observational noise. The theoretical results are validated by numerical experiments.