Feature Fusion via Tensor Network Summation

Tensor networks (TNs) have been earning considerable attention as multiway data analysis tools owing to their ability to tackle the curse of dimensionality through the representation of large-scale tensors via smaller-scale interconnections of their intrinsic features. However, despite the obvious benefits, the current treatment of TNs as stand-alone entities does not take full advantage of their underlying structure and the associated feature localization. To this end, we exploit the analogy with feature fusion to propose a rigorous framework for the combination of TNs, with a particular focus on their summation as a natural way of their combination. The proposed framework is shown to allow for feature combination of any number of tensors, as long as their TN representation topologies are isomorphic. Simulations involving multi-class classification of an image dataset show the benefits of the proposed framework.