Block-Term Tensor Decomposition: Model Selection and Computation

Abstract

The so-called block-term decomposition (BTD) tensor model has been recently receiving increasing attention due to its enhanced ability of representing systems and signals that are composed of blocks of rank higher than one, a scenario encountered in numerous diverse applications. Its uniqueness and approximation have thus been thoroughly studied. Nevertheless, the problem of estimating the BTD model structure, namely the number of block terms and their individual ranks, has only recently started to attract significant attention, as it is more challenging compared to more classical tensor models such as canonical polyadic decomposition (CPD) and Tucker decomposition (TD). This paper reports our recent results on this topic, which are based on an appropriate extension to the BTD model of our earlier rank-revealing work on low-rank matrix approximation. The idea is to impose column sparsity jointly on the factors and successively estimate the ranks as the numbers of factor columns of non-negligible magnitude, with the aid of alternating iteratively reweighted least squares (IRLS). Simulation results are reported that demonstrate the effectiveness of our method in accurately estimating both the ranks and the factors of the least squares BTD approximation.