  Tensor networks (TNs) have been gaining interest as multiway data analysis
tools owing to their ability to tackle the curse of dimensionality and to
represent tensors as smaller-scale interconnections of their intrinsic
features. However, despite the obvious advantages, the current treatment of TNs
as stand-alone entities does not take full benefit of their underlying
structure and the associated feature localization. To this end, embarking upon
the analogy with a feature fusion, we propose a rigorous framework for the
combination of TNs, focusing on their summation as the natural way for their
combination. This allows for feature combination for any number of tensors, as
long as their TN representation topologies are isomorphic. The benefits of the
proposed framework are demonstrated on the classification of several groups of
partially related images, where it outperforms standard machine learning
algorithms.
