Block-Term Tensor Decomposition Model Selection and Computation: The Bayesian Way

The so-called block-term decomposition (BTD) tensor model, especially in its rank-$(L_r,L_r,1)$ version, has been recently receiving increasing attention due to enhanced ability of representing systems and signals that are composed \emph{blocks} rank higher than one, a scenario encountered numerous diverse applications. Uniqueness conditions fitting methods have thus thoroughly studied. Nevertheless, the challenging problem estimating BTD model structure, namely number block terms, $R$, their individual ranks, $L_r$, only started attract significant attention, mainly through regularization-based approaches which entail need tune regularization parameter(s). In this work, we build on ideas sparse Bayesian learning (SBL) put forward fully automated approach. Through suitably crafted multi-level \emph{hierarchical} probabilistic gives rise heavy-tailed prior distributions for factors, structured sparsity is \emph{jointly} imposed. Ranks then estimated from numbers blocks ($R$) columns ($L_r$) non-negligible energy. Approximate posterior inference implemented, within variational framework. resulting iterative algorithm completely avoids hyperparameter tuning, defect methods. Alternative models also explored connections with counterparts brought light aid associated maximum a-posteriori (MAP) estimators. We report simulation results both synthetic real-word data, demonstrate merits proposed method terms estimation as compared state-of-the-art relevant