Structuring data with block term decomposition: decomposition of joint tensors and variational block term decomposition as a parametrized mixture distribution model

The idea of using tensor decompositions as a parametric model for group data analysis is developed. Two models (deterministic and probabilistic) based on block term decomposition are presented using various formats of terms. The relationship between block term decomposition and mixtures of continuous latent probabilistic models is established; specifically, a mixture distribution model with a structured representation is constructed relying on block term decomposition. The models are tested as applied to the problem of clustering a set of color images and brain electrical activity data. The results show that the proposed approaches are capable of extracting a relevant individual component of the data.