Low rank canonical polyadic decomposition of tensors based on group sparsity

Abstract

A new and robust method for low rank Canonical Polyadic (CP) decomposition of tensors is introduced in this paper. The proposed method imposes the Group Sparsity of the coefficients of each Loading (GSL) matrix under orthonormal subspace. By this way, the low rank CP decomposition problem is solved without any knowledge of the true rank and without using any nuclear norm regularization term, which generally leads to computationally prohibitive iterative optimization for large-scale data. Our GSL-CP technique can be then implemented using only an upper bound of the rank. It is compared in terms of performance with classical methods, which require to know exactly the rank of the tensor. Numerical simulated experiments with noisy tensors and results on fluorescence data show the advantages of the proposed GSL-CP method in comparison with classical algorithms.