  In this paper, we propose a novel tensor graph convolutional neural network
(TGCNN) to conduct convolution on factorizable graphs, for which here two types
of problems are focused, one is sequential dynamic graphs and the other is
cross-attribute graphs. Especially, we propose a graph preserving layer to
memorize salient nodes of those factorized subgraphs, i.e. cross graph
convolution and graph pooling. For cross graph convolution, a parameterized
Kronecker sum operation is proposed to generate a conjunctive adjacency matrix
characterizing the relationship between every pair of nodes across two
subgraphs. Taking this operation, then general graph convolution may be
efficiently performed followed by the composition of small matrices, which thus
reduces high memory and computational burden. Encapsuling sequence graphs into
a recursive learning, the dynamics of graphs can be efficiently encoded as well
as the spatial layout of graphs. To validate the proposed TGCNN, experiments
are conducted on skeleton action datasets as well as matrix completion dataset.
The experiment results demonstrate that our method can achieve more competitive
performance with the state-of-the-art methods.
