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

TL;DR

The paper introduces CP-TT, a greedy algorithm leveraging TT-SVD for efficient and stable CP tensor approximation, especially effective for high-order tensors, with promising numerical results.

Contribution

It presents a novel greedy method based on TT-SVD for computing CP tensor approximations, extending to rank-k updates with stability.

Findings

Performs well on high-order tensors

Outperforms ALS and ASVD in experiments

Stable computation of rank-k updates

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.