  The era of "data deluge" has sparked renewed interest in graph-based learning
methods and their widespread applications ranging from sociology and biology to
transportation and communications. In this context of graph-aware methods, the
present paper introduces a tensor-graph convolutional network (TGCN) for
scalable semi-supervised learning (SSL) from data associated with a collection
of graphs, that are represented by a tensor. Key aspects of the novel TGCN
architecture are the dynamic adaptation to different relations in the tensor
graph via learnable weights, and the consideration of graph-based regularizers
to promote smoothness and alleviate over-parameterization. The ultimate goal is
to design a powerful learning architecture able to: discover complex and highly
nonlinear data associations, combine (and select) multiple types of relations,
scale gracefully with the graph size, and remain robust to perturbations on the
graph edges. The proposed architecture is relevant not only in applications
where the nodes are naturally involved in different relations (e.g., a
multi-relational graph capturing family, friendship and work relations in a
social network), but also in robust learning setups where the graph entails a
certain level of uncertainty, and the different tensor slabs correspond to
different versions (realizations) of the nominal graph. Numerical tests
showcase that the proposed architecture achieves markedly improved performance
relative to standard GCNs, copes with state-of-the-art adversarial attacks, and
leads to remarkable SSL performance over protein-to-protein interaction
networks.
