CP-TT: using TT-SVD to greedily construct a Canonical Polyadic tensor approximation

Abstract: In the present work, a method is proposed in order to compute a Canonical Polyadic (CP) approximation of a given tensor. It is based on a greedy method and an adaptation of the TT-SVD method. The proposed approach can be straightforwardly extended to compute rank-$k$ updates in a stable way. Some numerical experiments are proposed, in which the proposed method is compared to ALS and ASVD methods and performs particularly well for high-order tensors.