Low rank tensor deconvolution

In this paper, we propose a low-rank tensor deconvolution problem which seeks multiway replicative patterns and corresponding activating tensors of rank-1. An alternating least squares (ALS) algorithm has been derived for the model to sequentially update loading components and the patterns. In addition, together with a good initialisation method using tensor diagonalization, the update rules have been implemented with a low cost using fast inversion of block Toeplitz matrices as well as an efficient update strategy. Experiments show that the proposed model and the algorithm are promising in feature extraction and clustering.