Computation of low-rank tensor approximation under existence constraint via a forward-backward algorithm

Abstract

The Canonical Polyadic (CP) tensor decomposition has become an attractive mathematical tool in several fields during the last ten years. This decomposition is very powerful for representing and analyzing multidimensional data. The most attractive feature of the CP decomposition is its uniqueness, contrary to rank-revealing matrix decompositions, where the problem of rotational invariance remains. This paper presents the performance analysis of iterative descent algorithms for calculating the CP decomposition of tensors when columns of factor matrices are almost collinear – i.e. swamp problems arise. We propose in this paper a new and efficient proximal algorithm based on the Forward Backward splitting method. More precisely, the existence of the best low-rank tensor approximation is ensured thanks to a coherence constraint implemented via a logarithmic regularized barrier. Computer experiments demonstrate the efficiency and stability of the proposed algorithm in comparison to other iterative algorithms in the literature for the normal case, and also producing significant results even in difficult situations.