  Tensors are ubiquitous in science and engineering and tensor factorization
approaches have become important tools for the characterization of higher order
structure. Factorizations includes the outer-product rank Canonical Polyadic
Decomposition (CPD) as well as the multi-linear rank Tucker decomposition in
which the Block-Term Decomposition (BTD) is a structured intermediate
interpolating between these two representations. Whereas CPD, Tucker, and BTD
have traditionally relied on maximum-likelihood estimation, Bayesian inference
has been use to form probabilistic CPD and Tucker. We propose, an efficient
variational Bayesian probabilistic BTD, which uses the von-Mises Fisher matrix
distribution to impose orthogonality in the multi-linear Tucker parts forming
the BTD. On synthetic and two real datasets, we highlight the Bayesian
inference procedure and demonstrate using the proposed pBTD on noisy data and
for model order quantification. We find that the probabilistic BTD can quantify
suitable multi-linear structures providing a means for robust inference of
patterns in multi-linear data.

Machine Learning;Machine Learning;Applications