Block term decomposition with rank estimation using group sparsity

In this paper, we propose a new rank-(L, L, 1) Block Term Decomposition (BTD) method. Contrarily to classical techniques, the proposed method estimates also the number of terms and the rank-(L, L, 1) of each term from an overestimated initialization of them. This is achieved by using Group Sparsity of the Loading (GSL) matrices. Numerical experiments with noisy tensors show the good behavior of GSL-BTD and its robustness with respect to the presence of noise in comparison with classical methods. Experiments on epileptic signals confirm its efficiency in practical contexts.